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AN OUTLINE
OF
STELLAR ASTRONOMY
BY
PETER DOIG, F.RAS,
HUTCHINSON'S SCIENTIFIC AND TECHNICAL PUBLICATIONS
LONDON, NEW YORK. MELBOURNE. SYDNEY, CAPE TOWN
CON TEN IS
Page
INTRODUCTORY 1
Part I The Individual Star Observational Data
Chap.
I DIMENSIONS, LUMINOSITIES AND MASSES OF THE
STARS 5
II THE MOVEMENTS, NUMBERS AND DISTRIBUTION OF THE
STARS 15
III BINARY STARS, VARIABLE STARS AND NOVAE ... 38
Part II The Nature of a Star
I A STAR'S SURFACE AND SURROUNDINGS 61
II A STAR'S INTERIOR 73
III THE EVOLUTION OF THE STARS 83
IV THE CAUSES OF STELLAR VARIABILITY 93
Part III The Stellar Universe
I THE GALACTIC SYSTEM 101
II EXTERNAL SYSTEMS : THE UNIVERSE 127
TABLES
Page
1. Measured diameters of certain Giant Stars, and of Sirius
and the Sun 8
2. Average Absolute Magnitudes for Stars of Different
Types 10
3. Absolute Magnitudes, Masses, Diameters and Densities
of Stars of Different Types 13
4. Stars of large Proper Motions 15
5. Average Proper Motions and Radial Velocities of Stars
of Different Types 17
6. Mean Parallaxes for Stars of given Magnitudes ... 19
7. Total numbers of Stars brighter than a given Visual
Magnitude 26
8. Approximate numbers of Stars per square degree of
different Galactic Latitudes 30
9. Numbers of Stars per million cubic Light Years near
the Sun 33
10. Spectral Types of Stars brighter than 8 m .25 (photographic) 34
11. Spectral Types and Limiting Distances and numbers
per million cubic Light Years 35
12. Percentage Distribution in Galactic Longitude ... 37
13. Spectra of Double Stars Percentage Numbers ... 40
14. Eccentricities and Periods of Double Star Orbits ... 45
15. Eclipsing Pairs (Classification) 49
16. The Period-Luminosity Relation 51
17. Campbell's Classification of Long Period Variables ... 53
18. Order of Abundance of commonest elements shown in
Solar Spectrum 66
19. Luminosity and Variability of Red Giant Stars ... 93
20. Distances, Dimensions and Temperatures of certain
Planetary Nebulae 104
21. Planetary and Diffuse Nebulae and Associated Types
of Stars 106
22. A Classification of Galactic Clusters 112
23. Distances and Dimensions of certain Galactic Clusters 114
24. Distances and Dimensions of certain Globular Clusters 118
25. Distances of Clusters of Galaxies 135
26. Types, Distances, Luminosities and Dimensions of
"Members of the Local Group of Galaxies 136
APPENDICES
Page
A Explanation and derivation of astrophysical terms ... 148
B Spectral characteristics 150
C Stellar temperature and distribution of energy in spectra 151
D Modern indirect methods of parallax estimation ... 151
E Apparent angular diameters of the stars 154
F Average distance of a star to its nearest neighbours ... 155
G Density of matter in galaxy ... 155
H Approaches and collisions between stars 156
J Relation between apparent magnitudes and distances of
galaxies 156
K The Cepheid Period Luminosity Relation 157
L The mean distance of a galaxy to its nearest neighbour 158
M Hypothesis of Cosmic Evolution 158
GLOSSARY 160
INDEX 163
INTRODUCTORY
THIS book gives an outline of the state of knowledge of the
constitution, dimensions, motions and distribution in space
of the stars and nebulae.
The advance to an unexpected degree in ascertainment of the
distances and disposition throughout the Universe of the stars,
during the past two or three generations, can perhaps not be better
illustrated than by a quotation from a book by the well-known
astronomical writer, R. A. Proctor, published seventy years ago.
By no means a pessimist as regards the progress of scientific discovery
he nevertheless wrote as follows : "Even the mighty instruments
of our own day, wielded with all the skill and acumen which a long
experience has generated, have not sufficed to enable us to measure
the distance of more than about a dozen stars. Nor probably will
it ever be possible for man. to count by the hundred the number
of stars whose distances are known. The real architecture of the
stellar system must remain for ever unknown to us, except as
respects a relatively minute portion, lying within certain limits of
distances from the Earth." ("Our Place among Infinities/'
p. 188, 1875).*
In this book the extent to which the above views have become
far from correct, owing to great improvement in old methods and
development of new means for estimating celestial distances, will
be made evident, f
The new ideas which are partly the consequence of these advances,
and partly the sequel to revolutionary discoveries in physical science,
make it difficult for even the most assiduous to follow progress.
In order, therefore, to give the student an idea of the places
in which he may expect to find the results of investigations and
also to help him in studying more thoroughly the work of the past,
a short bibliographical note is appended to each chapter.
At the outset it is desirable to give brief definitions of the chief
terms used, leaving to an appendix more technical questions of
* And in a lecture delivered in the 'sixties of last century, Sir John Herschel re-
marked, in connection with recently determined parallaxes of a few stars, that
"A stepping-stone is thus laid for another upward struggle towards the infinite
to the nebulae, the remotest objects of which we have any knowledge, though the
stride here is too vast, as it may seem, for the limited faculties of man ever to take"
("Familiar Lectures on Scientific Subjects/' p. 181, 1867).
f The number of fairly reliable trigonometrical parallaxes (of course, ^not quite
the same thing as well-established distances) has grown as follows : in 1840, 3 ;
1880, about 20 ; 1900, about 60 ; 1915, nearly 200 ; 1925, close on 2000 ; 1935,
nearly 7,500.
2 Stellar Astronomy
derivation and explanation. It is assumed that the reader is
familiar with the meaning of the commoner terms such as "trigono-
metrical parallax/' "stellar magnitude," "proper motion/' and so
forth and also with the main features of stellar spectroscopy.*
In other words, this book is meant for readers with slightly
more knowledge than that necessary for perusal of "popular"
astronomical literature. But it will be found that no advanced
mathematics is involved, all that is essential being an acquaintance
with logarithms and with very elementary trigonometry.
Only the chief terms are given in the following paragraphs.
Appendix A gives fuller explanations and derivations of formulae.
Absolute magnitude is defined as the apparent stellar magnitude
which any celestial object (e.g., star, cluster of stars or nebula)
would have if placed at a distance of ten parsecs, the "parsec" being
the distance corresponding to a parallax of one second of arc.
Bolometric magnitude is the stellar magnitude corresponding to
the total energy radiated, and is a measure of the total intensity
in the same way that visual magnitude is a measure of luminous
intensity, and photographic magnitude a measure of photographic
intensity, which may be photovisual (with yellow light filter), or red
(with red filter). Bolometric magnitude is so adjusted numerically
as to give the same value as visual magnitude in the case of a star
of about 6500K effective temperature. It is consequently nearly
the same as visual magnitude in the case of a GO type star such
as the Sun, which has an effective temperature of 5800K.
Radiometric magnitude is sometimes referred to. It is a measure
of the radiation from a star which reaches the earth's surface, the
zero being chosen to agree with the visual magnitude of type AO.
It differs from bolometric magnitude in this respect, and also from
the fact that the earth's atmosphere reflects and absorbs part of a
star's radiation.
Effective temperature is "a conventional measure, specifying the
rate of outflow of radiant heat per unit area ; it is not to be regarded
as the temperature at any particularly significant level in the star"
(Eddington).
Colour index is the difference between photographic and visual
magnitude, the hotter bluish or white stars having a negative value
of this factor, the yellow and red cooler stars having a positive
value.
Surface brightness is usually given in stellar magnitudes. It is
the measure of average brightness per unit of radiating area, com-
pared with that of the Sun, and it is not to be confused with Lumin-
osity which is a measure of the total light received from a star.
* A short glossary of some of these and of other important terms is appended
at the end of the book.
Introductory 3
Other terms of less frequent occurrence will be explained as they
arise.
With regard to Designation of Nebulae, there are two systems of
nomenclature current. The older is that of the catalogues of
Messier (1730-1817) who listed 103 bright clusters and nebulae,
mostly found during his comet hunting ; they are referred to by
the use of M and a number (for example, the Orion Nebula is M42).
The other is by the numbering of the New General Catalogue or the
Index Catalogues of Dreyer (1852-1926) which contain 7840 and 5386
objects respectively; the letters NGC or 1C are used with the
appropriate number.
Although the progress of so intricate a subject as stellar as-
tronomy must necessarily be the result of work by trained profes-
sional specialists, yet the writer feels that something of minor
importance may be achieved in this branch by amateurs, even if
they are only acting as sources of suggestion to those better qualified.
It is partly in this hope, as well as with the purpose of providing
a useful outline of astrophysical knowledge, that these chapters
have been written.
An attempt has been made throughout to give concisely by
tabular presentation, wherever this is practicable, some of the
data from which the theories of astrophysics have been constructed.
For the sake of consistency the unit of distance used throughout
is the light year, a unit based on a fundamental physical constant
the velocity of light.
Readers of the first edition of this book will find that this is
practically a new work, owing to discoveries of the past twenty
years, such as the rotation of the galaxy, the absorption of light
by interstellar matter, the establishment of the status as external
galaxies of the extragalactic nebulae, and the development of the
pulsation theory of stellar variability, all of which are dealt with
in the following pages.
The author is indebted to Dr. Martin Davidson, F.R.A.S., who,
although not responsible in any way for errors of fact or opinion
which may exist in the book, has read the manuscript and made
some valuable suggestions.
Part I The Individual Star Observational Data
CHAPTER I
DIMENSIONS, LUMINOSITIES AND MASSES OF THE
STARS
ONE of our greatest authorities once remarked that "it does
not seem too sanguine to hope that in a not too distant
future we shall be able to understand fully so simple a thing
as a star." This rather optimistic remark was based on the cir-
cumstance that the high temperature matter of which a star is
composed is thought to be the simplest kind of substance that a
mathematical physicist can study ; simpler than material at terres-
trial temperatures which has complex properties certain to be very
difficult to deal with. Nevertheless astronomers are not yet agreed
on any comprehensive theory, although there are some points upon
which there does not seem to be any substantial difference of
opinion.
As a necessary preliminary to a description of modern theory,
sections giving the data of observation are first submitted, covering
as far as possible in the space at disposal the observed results for
dimensions, movements, luminosities and other physical properties
of individual stars and multiple systems.
THE DIMENSIONS OF THE STARS
In the very earliest times the anthropocentric trend of human
thought was displayed in the attribution of small dimensions to
the Sun and still smaller sizes to the stars. On the other hand,
astronomical distances were underestimated to a yet greater degree,
the fixed stars being considered by Tycho Brahe and his sixteenth
century contemporaries to show to naked-eye observation diameters
of a minute or two of arc, although Hevelius in the seventeenth and
Cassini in the early eighteenth century thought they had found a
diameter for Sirius of five or six seconds. These were, however, only
spurious images formed by small telescope apertures, and were
suspected to be such by Horrocks and Halley because of the in-
stantaneous disappearance of stars when occulted by the moon.
After unsuccessful attempts at parallax determination it became
evident that stellar distances were so great that the apparent angular
diameters of the stars could be only a few hundredths of a second
6 Stellar Astronomy
of arc, unless stellar dimensions were very much greater than those
of the Sun.* That remarkable astronomical theorist, the Rev. John
Michell (1725-1793) pointed out in 1767 that even in the case of the
brightest star, Sirius, the apparent angular diameter must be less
than "the hundredth, probably the two-hundredth part of a second,"
although he thought that "it is not unreasonable to suspect that
very possibly some of the fixed stars may have so little natural
brightness in proportion to their magnitude as to admit of their
diameters having some sensible apparent size" ; and he further
considered that this "natural brightness" would be according to
colour, the white stars having the brightest surfaces. The largest
telescopes having failed to show any sensible disc to the brightest
or reddest stars, it became necessary to attack the problem by some
method other then that of direct vision.
Each star image on a photograph is a cluster of silver grains
which is enormously larger than any real stellar disc. Even if
there were a supergiant star like a Herculis (see Table 1) as near to
us as the nearest star (a Centauri, 4.3 light years), its real diameter
on the scale of a photograph where the moon was six inches in
diameter, would be less than a fiftieth of an inch. There is no such
large star within a distance many times as great ; and as stars are
generally much smaller and further away, the true stellar dimensions
on photographs are very greatly less. For instance, on the scale
of Plate 7b, the brightest fixed star Sirius would be one two-hundred-
thousandth of an inch. In fact, it may be shown (see page 27)
that if all the stars of our stellar system were concentrated into one
stellar disc its size would be less than a two-thousandth of an inch
on the scale of the plate mentioned, the area of which plate covers
less than a ten-thousandth of the whole sky.
The application of spectrum analysis resulted in schemes of
classification by Secchi (1818-1878), Vogel (1842-1907), Norman
Lockyer (1836-1920) and E. C. Pickering (1846-1919), which,
although arbitrary and empirical, have formed the foundation upon
which theories of stellar constitution and evolution|have been built.
Into the modern Harvard system, now definitely adopted univer-
sally, the main features of over 99 per cent, of stellar spectra fall in
a continuous linear sequence, O, B, A, F, G, K, M, where is the
Wolf-Rayet, B the helium star, A the Sirian, F the type of Canopus,
G the Capellan, K the Arcturian and M the red stars with banded
spectra and sometimes bright lines (in the case of Long Period
* In his "System of the World " (1727), Newton showed, assuming that the planet
Saturn rejects a quarter of the sunlight on it, that the Sun, if removed to a distance
from which it would shine as a star of Saturn's stellar brightness (about l m .O with
the rings edgewise), would have a disc a very small fraction of a second in diameter.
(It would be 0*.0056).
Dimensions, Luminosities and Masses of the Stars 7
variables). There is also a relatively small number of stars of
R, N and S types (see Appendix B) f .
The existence of a great diversity in luminosity and size among
the stars has long been obvious from the composition of star clusters.
There was, however, no knowledge of any systematic trend until
in 1905 Professor Hertzsprung pointed out that the absolute mag-
nitudes of the redder stars, derived from trigonometrical parallaxes
and proper motions, were divisible into two distinct classes, one of
great luminosity and the other relatively faint. As these stars
are of similar colour and spectra and presumably therefore of about
the same surface brightness per unit of area, they must be of very
different sizes to account for the great inequality in the luminosities
of the two classes. The names "giant" and "dwarf" were therefore
adopted to indicate this disparity in dimensions. In 1913, H. N.
Russell independently reached the same conclusion as Hertzsprung.
An extract from his summary of the facts follows :
"The surface brightness of the stars diminishes rapidly with
increasing redness The mean density of the stars of classes
B and A is a little greater than I/ 10th that of the Sun. The den-
sities of the dwarf stars increase with increasing redness from this
value through that of the Sun to a limit which cannot at present
be exactly defined. This increase in density, together with the
diminution of surface brightness, accounts for the rapid fall in
luminosity with increasing redness among the stars. The mean
densities of the giant stars diminish rapidly with increasing redness
from l/10th that of the Sun for class A to less than l/20,000th of
the Sun for class M. This counteracts the change in surface bright-
ness and explains the approximate equality in luminosity of all
these stars."
This statement is founded on observational results, described
more fully later, study of eclipsing binary systems, considerations
of the relation between surface brightness and colour and also on
the work of the physical scientist. In the laboratory the relations
between temperature and radiating power have been determined
for fairly high temperatures and the distribution of energy in the
different wave lengths has been ascertained. These have given
laws of radiation which are exact when applied to a perfect radiator
or "black body." Material which is blackest when cold, shines
brightest and radiates most heat when it is hot, i.e., its emitting
power is large if its absorbing power is great. The perfect radiator
would appear absolutely black when cold ; its radiative properties
are the simplest possible and can be derived theoretically and
experimentally. The distribution of radiative energy* in the
spectrum of most stars is found to be similar to, or not very dis-
similar from, that of this theoretical black body and consequently
8
Stellar Astronomy
the effective temperatures of the stars can be fairly closely
estimated. (See Appendix G). The approximate amount of light
radiated per unit of surface may then be computed, and if we know
the star's distance and the amount of light received from A ", the
diameter can be calculated. Sizes calculated in this way are found
to agree with the giant and dwarf grouping, giving great difference
between M giants and dwarfs and progressively less disparity with
increasing temperature through K, G, F, to A and B type.
Another and more direct method of enquiry has been developed
by means of an application of the principle of light interference.
An "interferometer" at Mt. Wilson Observatory has enabled as-
tronomers to measure the apparent angular diameters of certain
giant stars as given in the table, Sirius and the Sun being added for
comparison. The diameters in miles are derived from the angular
diameter and the parallax by the formula :
Angular diameter
Diameter in miles = - x 93,000,000
Parallax
Star.
aHerculis
Betelgeuse ...
Mira Ceti
Antares
a Ceti
p Pegasi
j8 Andromedae
Aldebaran
Arcturus
Sirius
Sun
* Maximum value :
Table I
Angular
Spectrum. Diameter.
M5
0-030
M2
0-047*
M5#y
0-056*
cMO
0-040*
MO
0-012
M5
0-021
MO
0-016
K5
0-020
KO
0-020
AO
0-0065
GO
variable
diameter.
Parallax,
n
0-004
0-012
0-017
0-015
0-011
0-020
0-033
0-059
0-092
0-376
Diameter
in miles.
700,000,000
363,000,000*
307,000,000*
248,000,000*
97,000,000
97,000,000
45,000,000
31,000,000
20,000,000
1,600,000
864,000
The first nine of these stars are giants, the two last are main
sequence stars. The difference in diameters is a striking confirma-
tion of the giant and dwarf grouping, although it must be appre-
ciated that the diameters in the first half of the table are not close
values owing to the uncertainty of parallaxes of such small amount.
Studies of the grouping of the stars by spectral types and ab-
solute magnitudes were at first largely dependent on directly
measured trigonometrical parallaxes, or on distances derived from
Dimensions, Luminosities and Masses of the Stars 9
proper motions. More recently, however, the quantity of data has
been much enlarged by modern methods of estimation of distances
(see Appendix D). Fig. 1 shows' the results for more than 2000
stars, as plotted by H. D. Curtis.
BLUISH WHITE
WHITE
YSH. WHITE PALE YELLOW YELLOW ORANGE
FIG. 1 THE GROUPING OF STARS INTO GIANTS AND DWARFS (after
CURTIS),
showing the results of measurements of 2375 stellar distances and brightnesses. The
stars are all plotted for the magnitudes at which each star would shine if placed at a
distance corresponding to a light journey of thirty- two and a half years (parallax
one tenth of a second of arc), so that their true relative brightnesses are as shown.
The grouping into two branches, one of very bright stars averaging nearly one
hundred times the Sun's luminosity and the other branch of stars diminishing in
light with increasing redness of colour, is well brought out. In the diagram the
dots and circles indicate the methods by which the parallaxes (on which the absolute
magnitudes are based) were determined
. = modern direct (photographic only). o = spectroscopic only.
. = direct and spectroscopic or dynamical. dynamical only.
Most of the naked-eye stars are giants, the proportion of dwarfs
increasing generally as the limit of apparent brightness is reduced.
It will be noted in Fig. 1 that the difference in average luminosi-
ties of the two classes of stars, giant and dwarf, varies from nearly
ten magnitudes (a ratio of 10,000 to 1 in light output) in>the case
of M stars, through about four magnitudes (a ratio of 40 to 1) in
G type, to zero in the hotter stars.
10
Stellar Astronomy
MEAN ABSOLUTE MAGNITUDES.
The relationship between absolute magnitude and spectral type
has been the subject of much research by astronomers who have
published mean figures based on parallaxes found by all methods.
Their results are given averaged in Table 2 and graphically in
Fig. 2, the latter showing mean lines for the values of Fig. 1.
Spectrum.
O5
BO
AO
FO
GO
KO
M
Table 2
Giant Branch.
-0-6
+0-3
+0-6
0-0
Main Sequence.
-4*5
-24
+ 0-6
+ 2-6
+ 44
+ 6-2
-f-9-8
The averages for the giant branch cannot be usefully stated for
types hotter than F, owing to relatively great scarcity and dispersion
of values. Curves are also given in Fig. 2 for the corresponding
bolometric magnitudes.
The dwarf branch is now more frequently referred to as the
"main sequence," a name due to Eddington. One great value of
these mean absolute magnitudes will appear in considering the
indirect methods of estimating celestial distances. (See Appendix D) .
Certain stars are characterised by very narrow and sharp lines
in the spectrum ; these stars are denoted by the use of the letter c.
5PEXTRA
S~ 5
-
z
l+*
4f
6
V \
Fuuv.
U1NC&-
FIG.. 2 ME*N ABSOLVE
~ 5
J
o 2:
D
+ 5$
(D
<
*|Q
Dimensions, Luminosities and Masses of the Stars 11
Typical examples are e Canis Majoris (c Bl), oPersei (c F5) and
a Scorpii (c MO) ; such stars are known to be luminous super giants.
The prefixes g and d are used to denote giant and dwarf stars
respectively ; as, for example, Arcturus, g KO, and Procyon, d F5.
STELLAR MASSES AND DENSITIES.
The mass of a star is ascertainable directly only if it is a member
of a binary system of which the parallax and orbit are known.
From Kepler's harmonic law,
where m l and m% are the masses of the two stars of a pair, P the
period in years, a the semi-axis major of the orbit, and TT the parallax
in seconds of arc. The combined masses m^ + m 2 are known for
a considerable number of pairs, but for the individual stars of pairs
there is not so much information.
By means of measurements showing the mutual perturbing
action of the components, the masses of a number of binary stars
have been calculated, and for components of eclipsing binary pairs,
and (by statistical methods) for spectroscopic binaries, with varying
degrees of accuracy. This showed a marked correlation between
mass and luminosity, and when Eddington and others derived from
theoretical considerations formulae giving bolometric magnitude as
a function primarily of mass and secondarily of temperature, corres-
ponding fairly closely to observed results, a very great step forward
in astrophysics was achieved.
Simpler empirical formulae have been published which connect
luminosity with mass, one of which, derived by the writer, of some
value for quick estimation of approximate masses or luminosities,
is as follows :
10 M
Log Mass (Sun - 1) - K (2 -2-05)
K being 0-31 when M is visual absolute magnitude, and 0-26 when
bolometric values are employed, the use of the formula in the latter
form being preferable.
There is a class of stars which do not conform to this mass-
luminosity relationship. These are the "white dwarfs/' about 80
of which are listed. The best known are the companion of Sirius
and the B component of o 2 Eridani. When distance and inass are
known (the latter for such as are components of a binary), diameters
can be estimated, using the surface brightness appropriate to the
12 Stellar Astronomy
spectral type, which is usually that for stars whiter and hotter than
the Sun ; the densities are then computed and values of the enormous
order of 50,000 times that of the Sun are found.
In the case of Sirius B (mass 0-96 of the Sun's) the absolute
bolometric magnitude for its mass would normally be of the order
of +5, but it is found to be +11-3 or about 300 times fainter than
the normal. The spectrum is between A5 and FO and the diameter,
calculated as in Appendix E, is only about 24,000 miles, giving a
mean density 45,000 times the Sun's or about one ton per cubic inch.
These extraordinary figures were confirmed by Adams at Mt. Wilson
Observatory and later by Moore at Lick Observatory. According
to the general theory of relativity a large mass acts on light emitted
from it so as to increase its wave length. This effect is not great
enough to be observed in an ordinary star, but in one of large mass
and relatively small diameter it should be possible to measure it.
For Sirius B the displacement should be that corresponding to a
velocity of 12 miles per second and exactly that amount was found
by Adams and by Moore.
The white dwarf companion of o 2 Eridani mentioned above is
of about the same luminosity as Sirius B (absolute magnitudes
+ 11-1 and +11-3 respectively). Its spectrum is of a hotter type,
AO, and the diameter corresponding is 16,700 miles, which with a
mass of 0455 of the Sun, gives a mean density still higher 63,000
times the Sun's. Even greater densities seem probable for certain
other white dwarfs, the masses of which have been estimated on
the assumption that part of their radial velocities is a "relativity
shift/'
White dwarfs must be quite frequent, particularly as they are
not easy to find and identify owing to their low luminosity. In
fact, Luyten considers that perhaps one in twenty or thirty stars
will prove to have white dwarf characteristics, which would make
the class one of the commonest in space.
A number of stars of an abnormal sub-dwarf kind have recently
been noted. With spectra similar to those of white dwarfs (A and
F), their absolute magnitudes fall between the main sequence and
the white dwarfs on a Russell-Hertsprung diagram (as Fig. 1).
Their diameters are of an order of a third or a half that of the Sun
or about ten times that for white dwarfs, but their densities, although
certainly abnormal, are much less.
At this stage it will be of interest to present in tabular form
figures which give a rough idea of mean figures for absolute magni-
tudes, mass, diameter and density for the commonest star of each
type, ba3ed on the observational data and empirical mass-luminosity
relationship of the*preceding pages. Table 3 gives these particulars
for giants and main sequence. The absolute magnitudes are as in
Dimensions, Luminosities and Masses of the Stars 13
Table 2 and Fig. 2 ; mass is estimated by means of the empirical
formula, using bolometric magnitude ; diameter is calculated from
the formula *
log diameter (Sun-1) - 0-2 (/+4-9-M)
(See Appendix E).
For mass, diameter and density (mass/diameter 8 ) the units are
the values for the Sun.
Table 3
ABSOLUTE MAGNITUDES, MASSES, DIAMETERS AND DENSITIES OF
STARS OF VARIOUS SPECTRAL TYPES.
GIANTS.
Spect.
M vis .
Mboi.
Mass.
Diam.
Density.
BO
AO
FO
-0-6
-0-7
3-9
7-9
0-008
GO
+0-3
+0-2
3-0
9-5
0-0035
KO
+0-6
+ 0-0
3-2
21
0-00035
MO
0-0
-1-5
5-6
75
0-000013
MAIN SEQUENCE.
Spect.
MVJS.
M bo] .
Mass.
Diam.
Density.
BO
-2-4
-4-6
27-5
6-6
0-10
AO
+0-6
+0-3
2-9
2-5
0-19
FO
+2-6
+2-5
1-6
1-8
0-27
GO
+4-4
+4-4
1-1
1-3
0-50
KO
+ 6-2
+5-9
0-85
0-95
0-99
MO
+9-8
+8-4
0-6
0-6
2-8
Researches on the 0-type stars indicate a mean visual absolute
magnitude of about -4-0, and masses of about 30 to 50 times the
Sun's. But it may be noted that the relativity effect mentioned
earlier appears to have been observed in certain O stars of high
luminosity and mass inf galactic clusters, and from their probable
surface temperatures, luminosities, and observed shifts of spectral
14
Stellar Astronomy
lines to the red as compared with the fainter and less massive stars
of the clusters, Trumpler has derived diameters of 7 to 20 times
and masses of 75 to 300 times the Sun's. Mean densities of the
order of 0-04 to 0-25 of the Sun's seem likely. The N and R types
appear to be of considerable luminosity and mass, averaging about
-2 and -0-5 absolute magnitudes respectively while the S stars
are of the order of -1-5.
REFERENCES PART I CHAPTER I
Author.
Rev. John Michell,
H. N. Russell,
H. C. Wilson,
W. H. Adams,
A. S. Eddington,
L. Goldberg and
L. H. Aller.
Publication.
Subject.
Phil. Trans. Royal Socy., Hypothetical
1767 and 1784.
dimensions and
distances of stars.
Giant and
dwarf theory.
Interferometer
description.
Popular Astronomy,
22, 19.
Popular Astronomy,
29, 189.
Proceedings of the Ameri- Companion of
can Academy of Science Sirius.
11, 382.
"The Internal Constitu- General.
tion of the Stars."
"Atoms, Stars and General.
Nebulae."
CHAPTER II
THE MOVEMENTS, NUMBERS AND DISTRIBUTION OF
THE STARS.
STELLAR MOVEMENTS
THESE may be divided into two observational categories,
apparent angular motions (proper motions) and velocities
in the line of sight spectroscopically measured (radial veloci-
ties) of both of which many thousands are now known. The motion
of a star may be in any direction in space, but only that component
at right angles to the line of sight will be the cause of apparent
displacement in the sky relative to other stars. Proper motion
is compounded of the angular displacements caused by the star's
own movement and by the movement of the solar system in space.
Large proper motion usually means proximity rather than great
space velocity ; on the average the brightest stars, being nearer
than the fainter ones, have larger proper motions. Nevertheless,
when individual stars are considered, it is found that the biggest
motions belong to rather faint stars, as will be seen from the following
short list to which some similar examples discovered lately could
be added.
Table 4
Annual proper
Star. Mag. motion.
H
Munich 15040 9-7 10-3
Cordoba V h 243 9-2 8-8
Groombridge 1830 6-4 7-0
Lacaille 9352 7-4 6-9
Cordoba 32416 8-3 6-1
61 Cygni 5-4 5-2
Wolf 359 13 4-8
Lalande 21185 7-6 4-8
clndi 4-7 4-7
Lalande 21258 8-6 4-5
o 2 Eridani 4-5 4-1
Wolf 489 13 3-9
^Cassiopeiae 5-3 3-8
aCentauri 0-0 3-7
Washington 5583-4 8-5 3-7-
Cordoba 29191 6-7 3-5
e Eridani 4-3 3-2
Uf Stellar Astronomy
In mo$e than 200,000 measured annual proper -motions, the
following are found :
2" or more, at least 50 stars.
* *>
0*5 ,, ,, ,, ,,
One proper motion worthy of special reference is that of Arcturus
(magnitude 0-2). From its movement of about a degree of arc
and that of Sirius of half that amount, since the time of Ptolemy,
Halley, in 1718, discovered the proper motions of the stars.* Arc-
turus moved at the rate of 2"-3 per annum or 115 times its own
diameter of CT-02 as found by the interferometer. This movement
is due to a relatively great velocity, at right angles to the line of
sight, of 74 miles per second, as its distance is about 35 light years
from us. The annual proper of Sirius is l"-3.
THE SUN'S MOTION IN SPACE
The motion of translation of the Solar system with reference to
the stars in its neighbourhood (i.e., within about 1000 light years),
first discovered in 1783 from the directions of proper motions of
only 13 stars by Sir W. Herschel, shows itself by an apparent re-
cession of the stars from a point in Hercules, and a closing up of the
stars towards the part of the sky diametrically opposite, the co-
ordinates of these two points, the Solar Apex and Antapex, being
R.A.18 h Dec. 30 North, and RA. 6 h Dec. 30 South, respectively.
The line of sight velocities of the stars also show clearly the same
direction of motion of the Sun, most of the stars in the hemisphere
towards which the motion is directed having radial velocities of
approach (i.e., negative values), while in the other half of the sky
they are recessive (positive values). This is well shown in the
illustration, Plate 1.
By means of stellar radial velocities the rate of motion of the
solar system with reference to the surrounding stars can be best
found, and this may be taken as about 12-5 miles per second. In-
vestigations have shown, however, that both the direction and
velocity of the solar motion seem to depend on the magnitudes of
the stars to which they are referred and also to some extent on their
spectral type. The velocity appears to be greater when faint stars
are employed, being considerably greater than the figure given
above when only dwarf stars are employed in the calculation.
* The tremendous increase in accuracy of measurement of stellar positions, on
which proper motions depend, since the earliest times, is shown by the following
estimates, of average errors : Hipparchus (2nd cent. B.C.), 4' ; Tycho Brahe (16th
cent), 1'; Flamsteed (17th cent.), 10"; Bradley (18th cent.), 2*; Bessel (helio-
meter, early 19th cent.), 0"*2 ; first photographs (mid-19th cent.), 0"'l ; modern
long-focus photographs, 0"'025. Before Flamsteed's time telescopes were not used.
Movements, Numbers and Distribution of Stars .7
PROPER MOTIONS, RADIAL VELOCITIES AND SPECTRAL CLASS.
The table gives averages for the brighter stars ; the radial
velocities are corrected for the effect of the Sun's motion.
Table 5
Spectral Mean Annual Spectral Mean Radial Velocity
Class. Proper Motion. Class. miles per second.
Seconds of arc.
OandB 0-028 BO-B5 4-6
A 0-05 B8-A3 5-0
F 0-079 A5-F2 7-7
G 0-052 F5-GO 9-8
K 0-057 G5-K2 9-6
M 0-050 K5-M3 10-3
There is a rough general correspondence in these proper motions
and radial velocities. The O and B stars are highly luminous ; and
on the average at great distances, their proper motions being thus
very small. The increase in radial velocities with advance in
spectral class is marked by a progressive reduction in mass, the more
massive stars moving more slowly.
THE K-TERM' IN RADIAL VELOCITIES
Professor W. W. Campbell, of Lick Observatory, found in his
radial velocity determinations that there appeared to be a
systematic recessive motion of the stars from the Sun, shown by an
excess of positive over negative values, which is greatest in the case
of the B type. This apparent movement of expansion seems
a priori very unlikely, and has led to explanations being offered
other than movement of the stars in space, such as downward con-
vection currents in stellar atmospheres, a relativity effect , greater
in stars of large mass or high density shifting the spectral lines
towards the red, and systematic errors in the wave lengths of the
spectral lines employed. The amount of the K-term in B stars is
about 3-5 miles per second recessive, and the probabilities seem
to be that it arises from a complex cause in which are to be found
downward currents in the stellar atmospheres (which appear to be
greatest in hot stars like B type), relativity shift (also great in the
B type stars which are massive and relatively small in diameter as
compared with cooler giants), with perhaps systematic space motion
and some effect of erroneous wave lengths of the spectral lines. The
opinion is held generally, however, that this K-effect requires
careful further study both observationally and analytically.
18 Stellar Astronomy
KINETIC ENERGIES OF STELLAR MOTION
When the space velocities of stars are derived from radial velo-
cities and motions at right angles to the line of sight, corrected for
the Sun's movement in relation to neighbouring stars, kinetic
/ velocity \
energies of motions, (mass x / J ), can be computed,
using mean masses appropriate to the spectra or luminosities of the
stars concerned. Some investigators have found that these energies
appear to be fairly constant for several of the different spectral
types. There are notable exceptions, however. The B type have
smaller values than usual, while for K and M giants they are some-
what greater and for short period Cepheids they are much larger.
Uniformity of kinetic energy would indicate equipartition of energy
among the stars, but it is perhaps too much to expect equipartition
of energy in a mixture probably composed of interpenetrating
systems, which in themselves might show more approach to equi-
partition if the necessary segregation of stars could be made for an
investigation. Only in a system composed of stars which have
been neighbours practically from their origin, does it seem reasonable
to expect equality of kinetic energy between the more massive and
less massive stars, the former moving more slowly. A mixture of
systems might easily conceal any such tendency, especially if the
mean masses of the stars in the systems were not similar in amount.
On the other hand, these individual space velocities, relative to
the neighbouring stars as a frame of reference, are probably only
the more or less random differences among stellar orbital motions
round the centre of the Galaxy, which will be referred to in a later
section of this chapter.
PARALLAXES FROM PROPER MOTIONS
As already stated, part of a star's angular proper motion is due to
the solar motion in space, and in order to ascertain the motions
of the stars at right angles to the line of sight, it is necessary to
separate the component which is caused by the Sun's movement.
This component is called the "parallactic motion," and is usually
referred to as the ^-component. It is that component which is
on the great circle passing through the solar apex and the star.
The other component, at right angles to this, is the r-component.
Each gives a method of finding the average distance of a group or
class of stars or other objects. Using the parallactic motion, the
individual random motions are assumed to cancel, and the average
parallax results as follows :
Movements, Numbers and Distribution of Stars 19
v sin A
Mean parallax = 294 zzzz:
F sin 2 A
FO being the solar velocity, A the angle between the solar apex
and the star, and v the parallactic component of the annual proper
motion in seconds of arc. The bar over the quantities indicates
that averages for the group of stars are to be employed.
In the case of the r-component,
Mean parallax = 2-94
V
V being the mean of the radial velocities, corrected for the solar
motion, in miles per second, of the stars concerned. In both for-
mulae 2-94 is the velocity in miles per second corresponding to a
motion per annum of one astronomical unit (mean distance from
earth to Sun).
Should the mean corrected radial velocity be less than about
eight miles per second, the ^-component method gives the better
results, but for stars of greater velocity the use of the r-component
is to be preferred.
From studies of proper motion, Seares finds that the solar motion
varies with the magnitudes of the stars employed in the calculation,
so that
Solar velocity in miles per second = 8-0 + 0-75 m,
where m is apparent visual magnitude. Seares's latest values of
mean parallax for stars of visual magnitudes down to the 13th,
are given in Table 6. The second column is according to the above
formula, the third is for a constant solar velocity of 12-5 miles per
second.*
Table 6
MEAN PARALLAXES OF STARS OF GIVEN MAGNITUDES
Using 12-5 miles
Mag. Using formula. per second.
Seconds of arc. "
1 0-0830 0-0580
3 0-0376 0-0307
5 0-0175 0-0164
7 0-0082 0-0087
9 0-0039 0-0045
11 0-0018 0-0024
13 0-0009 0-0013
* The figures are averages for the whole sky. For Milky Way regions tjjey are
about an eighth smaller ; near the Galactic poles a third greater. These differences
are due to the greater proportion of stars of lower absolute magnitudes found among
stars of a given apparent magnitude as Galactic latitude increases.
20
Stellar Astronomy
It will be appreciated that .these figures can only be taken as
averages, since the stars of a particular magnitude in any star field
are of very different luminosities and therefore range over a con-
siderable distance. But they may be useful for a number of stars
in an area, and, for instance, in correction of relative trigonometrical
parallaxes to absolute values by their application to the comparison
stars used. And they are also of value when counts of numbers of
stars to different apparent magnitudes are being utilised to obtain
some idea of distances for involved objects such as nebulae or
obscuring clouds. (See page 111).
FIG. 3 TAURUS MOVING CLUSTER
More than forty stars are known to have apparent converging movements towards
a point not far from the bright red star Betelgeuse. By these movements and the
velocity in the line of sight measured by the spectroscope, the distance of the group
has been found to be such that light takes 130 years to travel from these stars to us.
(The lengths of the arrows correspond to motion in about 65,000 years).
THE MOVING CLUSTERS
It has been known for a long time that there is community of
motion amongst certain stars for which physical connection would
not otherwise be clear. In 1869, Proctor pointed out that five
stars in the Plough had parallel proper motions and he also drew
attention to the same features for certain stars in the Hyades. Later,
work by Boss, Eddington, Kapteyn, Rasmuson and others indicated
the probability of connection in these and a number of other groups.
The chief are the Taurus (Hyades) cluster, the Ursa Major group,
Movements, Numbers and Distribution of Stars 21
the Perseus cluster, the Scorpio-Centaurus group, the Stars in Coma
Berenices, a group of which 61 Cygni seems to be a member, and the
stars in Orion.
In the Taurus group there are nearly 80 stars, ranging from
about 3'5 to 6*0 magnitude and spectra A to K, the proper motions
of which strikingly converge to a point in the sky about 6 east
of Betelgeuse (see Fig. 3). The receding radial velocities of a
number of these stars being measured spectroscopically, the
true paths can be computed, assuming that they are really parallel
in space, by a simple trigonometrical calculation ; the conver-
gence being thus assumed only apparent and due to the recessive
movement from us. The parallax can also then be derived as
about 0".025, a value confirmed by several other methods. The
diameter of this cluster is about 50 light years, or roughly 40 per
cent of its distance from us.
The Ursa Major group is a very large and scattered one, dis-
covered by Hertzsprung, who found that it contained stars in all
parts of the sky, including such prominent members as Sirius,
j8 Aurigae, /? Eridani and a Coronae Borealis, as well as the five
stars, J8, y, S, and Ursae Majoris. More than 40 stars are
believed to belong to it, and it has a flat disc shape disposed
perpendicularly to the galactic plane, 130 light years in its largest
diameter, and moving as a whole parallel to the Galaxy.
The Perseus group, discovered by Kapteyn, Boss and Eddington
almost simultaneously, has at least 45 stars in it, from second
magnitude to below sixth, nearly all of B type. Most of the
stars in this group lie in an extended chain formation in the sky,
which may indicate a flat disc shape as in the Ursa Major group.
In this cluster the motion, according to Rasmuson, is also parallel
to the Galactic plane and the distance is roughly 330 light years.
The Scorpio-Centaurus group contains more than 150 members,
mostly of B type, scattered over the sky in a zone about 50 wide,
from 8 h to 18 h R.A., the width of the zone increasing somewhat
in the direction of Right Ascension. Such prominent stars as
a and /3 Crucis, ft and T? Centauri, /? Scorpii and possibly Antares
seems to be members, the average distances varying from about
160 to 250 light years, the narrow end of the zone apparently con-
taining the nearer objects. Some of the stars in the Southern Cross
and its vicinity belong to this group and are at a distance of about
230 light years. The motion of the cluster is also nearly parallel
to the Milky Way plane and is in the direction of its own longest
axis.
The Coma Berenices group contains at least 75 stars* from
about 4-5 down to 9-0 or fainter, situated between ll h and 15 h R.A.
and Dec. 10 to 50 North, all moving nearly westward in the sky.
22 Stellar Astronomy
The distance to the centre of the cluster is roughtly 240 light years.
The 61 Cygni group is composed of about 60 stars scattered all over
the sky from about the third to the eighth magnitudes. It is
marked by three sub-groups of F, G and K type stars. The physical
connection of the stars in Orion is considered to be shown by
their similar radial velocities, on an average about 13 miles per
second recessive. As their situation is roughly directly opposite
to the direction of the solar motion towards Hercules at about the
same speed, this shows only the reflex effect of that motion. The
distance of the group (much nearer than the great Orion nebula)
is about 600 light years.
The exact status of some of these extended moving clusters has
recently been shown to be very doubtful. A few of them are
Certainly connected groups moving together with reference to the
surrounding "field" stars. Although those of Taurus, and Ursa
Major are undoubtedly real, there appears to be not the same cer-
tainty for the groups of Scorpio-Centaurus, Perseus and Orion,
which are perhaps composed only of field stars with small individual
motions.
ROTATION OF THE GALAXY
As might be anticipated, the flattened form of our Galactic
system suggested by the Milky Way zone, has in the past led to
conjectures that it is in rotation in its own plane. The motion of
the Sun with reference to its surrounding stars discovered by
Herschel, was surmised (erroneously) by some to be an orbital
movement round the centre of the Galaxy. Following the analogy
of the planets revolving round the Sun, several have speculated on
the possibility of the existence of a central sun of enormous mass.
Kant thought that this might be Sirius, while Herschel put forward
the idea that the great globular cluster in Hercules (M 13) or, alter-
natively, the "compressed parts of the Milky Way," might be the
governing mass. Madler believed, however, that the ruling power
is not concentrated in any single mass, but that it is situated at the
centre of gravity of the whole system of the stars. From certain
indications of stellar proper motions he conjectured that this point
is in the vicinity of the Pleiades cluster. These speculations were
all (except HerscheFs alternative) ruled out ; in the case of Sirius
by inadequacy of mass, and for the Hercules cluster and the Pleiades,
by positions much too far out of the Galactic plane in which the
rotation might be supposed to occur. If there is rotation and the
control- is principally by a concentration of mass at the centre, the
speeds of the stellar motions round the centre will decrease with
distance from it, just as in the Solar system, with the mass con-
Movements, Numbers and Distribution of Stars 23
centrated in the Sun; we find the orbital motions of the planets to
be slower for those farthest from it. In the case of a system of
stars of more or less uniform distribution, the greatest attraction is
found at the outside parts, as there the mass of all the stars is acting
in the one general direction. As we pass inwards the attraction
towards the centre is acted against by outward attractions and at
the centre there is a balance of forces. In this case the bodies
on the outskirts would move the most rapidly. Evidence for or
against rotation may be sought in proper motions and also in the
differences of velocities in the line of sight connecting the star and
observer.
If the stellar system rotates as one body so that the stars,
although moving among themselves, keep on the average the same
relative positions to each other, there will be no possibility, except
by reference to the ''Invariable Plane " of the Solar system (see
B.A.A. Journal, 39, 167), of discovering rotation of the system by
means of relative changes in their positions or differences in their
radial velocities. To use a homely illustration, if a number of
people were situated on the spokes of a large rotating wheel at
various distances from its axis, none of them could see any altera-
tions of apparent position among themselves which would indicate
rotation. On the other hand, if the rotation were such that the
speeds decreased outwards, as is found in the planets of the solar
system, then by study of tlie apparent cross motions and line of
sight movements, rotation might be deduced and measured.
Among the most remarkable of recent achievements in astronomy
may be placed a demonstration by such methods of a Galactic
rotation of this nature. Stellar proper motions, and line of sight
velocities of 0, B, N type stars, Cepheid variables, c stars, planetary
nebulae and inter-stellar diffused matter, all objects with distances
ranging out to 2000 light years and more, have been studied by
Lindblad, Oort, Plaskett, Joy and others, and results of such great
consistency obtained as to leave no doubt that our Galaxy is rotating
in its plane, in a clockwise direction as seen from the northern side
of that plane, with great velocity, the speeds of revolution of the
stars decreasing from the centre outwards. This centre is in
exactly the same direction and at about the same distance away
from us in the constellation Sagittarius, as is suggested by the
distribution of stars and other objects in the Galactic system, and
also by the disposition in space of the globular clusters surrounding it.
The velocity of revolution for the stars in the Sun's neighbour-
hood is found to be about 150 or more miles per second with a period
of rotation of about 200 million years, which would require* a con-
trolling mass of the order of two hundred thousand million times
that of the Sun. Strong support is given to these conclusions by
24 Stellar Astronomy
consideration of the line of sight velocities of globular clusters. The
system formed by these objects is much less flattened than the
denser parts of the Galaxy itself and is presumably rotating more
slowly if at all. The rotational general motion round the Galactic
centre of the system of stars can therefore be related to this globular
cluster system as a frame of reference, and is then found to agree
with that derived from the motions of the Galactic stars. In fact,
it can be shown quite simply from the radial velocities of the globular
clusters that this is probably the case. Of twenty-one velocities
(18 of them are given in Shepley's "Star Clusters/' page 199), eight
are recessive from the Sun, twelve are approaching, and one is zero.
Seven of the eight recessive values are for clusters with Galactic
longitudes in the half of the Galactic circle between 155 and 335
longitude, and eleven of the approaching twelve are in the other half.
Two of the three remaining are at longitudes relatively near the
accepted centre of rotation and the third (the zero one) is almost
exactly at it.
As this centre in Sagittarius (longitude 330) is close to the
chosen point of division for the two halves of the Galactic circle
(335) this disposition of the radial velocities, which has been
obtained by simple inspection, is what might have been
expected for the centre of the rotation, and its direction, as de-
termined from stellar motions. Or, alternatively, it might almost
have been predicted* from the radial motions of the globular clusters
alone, that the Galaxy would be found to rotate about a point in its
brightest region in Sagittarius, the direction of rotation being so that
the part in our neighbourhood is at present moving towards a goal
beyond that region of the sky in which a Cygni is situated.
Study of the velocities of stars with speeds greater than about
60 miles per second, by Oort and others, led to the discovery that
these bodies appear to be streaming systematically in the direction
of the constellation Argo (R.A. 8 h , Dec. 44S), the opposite part
of the sky, in the direction Aquila - Cygnus - Cassiopeia, being
strictly avoided by them. The explanation of this is to be found
in the rotation of the Galaxy ; and in fact this preferential motion
constitutes in itself a corroborating fact.
It appears that most of the stars near the Sun have orbits round
the Galactic centre of an approximately circular shape. Some
(e.g., the high velocity stars mentioned above, and other fast-moving
bodies such as the short-period Cepheids and Long Period variables)
probably have long elliptical orbits, crossing the Sun's orbit at a
large angle, on their way into, or out from, their "peri-galactic"
position. They will appear, as a class, to be moving rapidly back-
* The prediction would scarcely have been any bolder than that of Herschel's
first determination in 1783 of the motion of the Solar system (see page 16).
Movements, Numbers and Distribution of Stars 25
wards towards Argo, which is 90 in Galactic longitude from Sagit-
tarius, as compared with the Sun whose path crosses their orbits
in its track round the Galactic centre ; those ahead of the Sun
having in general approaching line-of-sight velocities and those
behind receding speeds. They will thus seem to have high space
velocities, the Sun's speed in its orbit being, as stated, 150 miles or
more per second.
This provided a satisfactory explanation for the high-velocity
stars, but for the generality of stars in the Sun's vicinity another
remarkable phenomenon had been discovered by J. C. Kapteyn
earlier in 1904. This consisted of a general systematic motion
suggesting two streams of stars passing through each other, each
stream moving on the whole in a certain direction, although indi-
vidual stars have movements relative to one another ; the Sun,
for instance, having a motion towards Hercules with regard to the
neighbouring stars of about a twelfth the rate of its velocity of
Galactic rotation. The streaming motion discovered by Kapteyn
can be shown to be a natural consequence for the stars with orbits
round the Galactic centre that are not circular. These stars are
moving in elliptical orbits which, in the Sun's neighbourhood, have
an inward or outward trend as compared with the average of the
more circular motions of the nearby stars. When these outward
and inward differences are considered, a preference is shown by them
for a direction towards or away from the centre. This is what was
found by Kapteyn a direction lying nearly in the plane of the
Milky Way in a line joining Scutum and Orion. Between this and
the line from the Sun to the Sagittarius centre there is an angle of
only 15, a deviation no doubt capable of explanation on the ac-
cepted theory when further knowledge of the stellar movements
concerned has been obtained.
NUMBERS AND DISTRIBUTION OF THE STARS.
Important determinations of the numbers and disposition of the
stars over the sky were made by Scares and van Rhijn. The value
of such data has been recognised since the gauges of the Herschels
made between about 1780 and 1838. This work was continued by
others, notably Seeliger, Pickering, Chapman and Melotte, Kapteyn,
and Seares and van Rhijn. Progress in stellar photography has
led to extensions of the counts to larger sky areas and to lower
limits of brightness, and also to improvements in the accuracy of
the stellar magnitude scales. It is in the last-named factor that
the chief difficulty in the way of accuracy has lain, the problem
being one of photometry of a range of brightness covering over
20 stellar magnitudes and therefore involving the setting up of
accurate standards over an interval ranging in intensity more than
26 Stellar Astronomy
100,000,000 to 1, which is about the same as the ratio between the
width of the Atlantic in our latitudes and a couple of inches. The
difficulties are particularly great when visual methods are employed,
large errors then occurring, but the introduction of photography,
using a scale of stellar magnitudes defined by a field of stars near
the North Pole of the sky, the " Harvard North Polar Sequence/' has
produced much more dependable results than formerly.
Down to ninth or tenth magnitude the numbers of the stars in
each magnitude grade are known, all such having been catalogued.
For the fainter stars, the numbers have been obtained by counts
in sample areas.
Table 7 is the result of such methods applied under the direction
of Scares and van Rhijn. The figures are for the whole sky (41,253
square degrees) down to the twenty-first visual magnitude the
limit visually of a telescope about 250 inches in aperture corrections
from photographic to visual magnitude having been made.
Table 7
TOTAL NUMBERS OF STARS BRIGHTER THAN A GIVEN
VISUAL MAGNITUDE.
Mag.
Number.
Ratio.
Mag.
Number.
Ratio.
3
11
865,000
3-7
2-6
1
11
12
2,280,000
3-6
2-5
2
40
13
5,700,000
3-6
2-4
3
144
14
13,600,000
3-5
2-3
4
510
15
32,000,000
3-2
2-2
5
1,620
16
71,000,000
3-0
2-1
6
4,860
17
150,000,000
2-9
2-0
7
14,300
18
299,000,000
2-9
1-9
8
41,300
19
560,000,000
2-8
1-8
9
117,000
20
990,000,000
>
2-8
1-7
10
330,000
21
1,690,000,000
2-6
Movements, Numbers and Distribution of Stars 27
It will be noticed that the ratio between the numbers of stars
down to successive magnitudes steadily becomes smaller with
decrease in brightness. It was thought that if this continued, as
indicated by the run of the numbers, there could not be many stars
fainter than about the thirtieth magnitude and that the total number
of stars in our stellar system would be roughly thirty or forty
thousand millions, i.e., about 20 per human inhabitant of our globe.
Seares and van Rhijn also found that the total light of the stars is
equivalent to 1092 first magnitude stars and that 98 per cent of this
light is from the stars brighter than 21st magnitude.
THE AMOUNT OF STAR-OCCUPIED SKY.
In view of the enormous numbers in Table 7, it is surprising to
note the very small part of sky surface occupied by the stars of our
system. An idea of this may be obtained as follows. The aggre-
gate light is, as stated above, equal to 1092 first magnitude stars.
This is equal to one star of -6-6 magnitude, and it is obvious that
the total disc area of the stars will be between that of, say, one
B star or one M star of this visual magnitude, closer to the latter
owing to the great preponderance of later spectral types. From
the formula in Appendix E it can be found that the angular dia-
meters of these hypothetical stars are 0"-04 and 1"-0 respectively.
There will not be much wrong therefore in a statement, meant
merely to indicate the smallness of the fraction of the sky, that an
area substantially less than that of a disc a second of arc in diameter
is occupied by the luminous stellar material of our Galaxy. That
is to say, less than the area covered by a half -penny at a distance of
over three miles.
Loss OF LIGHT IN SPACE.
If the stars were equally distributed in space at all distances
from us and if there were no loss of light in space, there would be a
constant ratio between the numbers of stars brighter than successive
magnitudes. The light ratio being 2-512 for one magnitude differ-
ence, the ratios of distances and spherical volumes corresponding
are 2-512* (1-585) and 2-512* (3-98) respectively. The ratios of
Table 7 being progressively less than this figure (3-98), there must
be either a progressive thinning out of stellar light or a loss of light
in space, or both. If there is a loss of light in its passage through
space to us from the stars, then the density of stellar distribution
does not necessarily decrease as we go outward from the Sun / which,
moreover, need not occupy a central position in the space populated
by the stars counted, as might otherwise be assumed.
28 Stellar Astronomy
It is now thoroughly established that there is interstellar ab-
sorption of light. The exist enfce of dark Galactic nebulae near
the central axis of the Milky Way has long been known. But what
is perhaps more important in connection with the present discussion
is the possibility of a more general presence of obscuring matter.
Such a general obscuring medium has long been suspected* and has
now been demonstrated to exist.
During the early years of the present century a number of
investigations were made on the possible loss of light through
reddening by interstellar material, without much in the way of a
definite result. As regards general absorption an enquiry was
made by Trumpler in 1930, using 100 Galactic or "open" clusters as
his material. He assumed that clusters of the same physical type
(see Table 22) would be of the same real diameter and the same total
luminosity on the average.
According to these assumptions, clusters of a given angular
diameter should have had the same apparent stellar luminosities,
but he did not find this to be the case. The relative distance
corresponding to apparent angular diameter came out less than the
observed luminosities indicated, a general obscuration of 0-67
stellar magnitude per 3260 light years (1000 parsecs) being required
to remove the discrepancy. Confirmation of a value of this order
has been found by Joy, van Rhijn and others by different methods ;
and Hubble's counts of the nebulae outside our Galactic system at
varying angles above the plane of the Galaxy (Galactic latitudes)
have pointed to the existence of a layer of absorbing material in the
central plane, extending to a distance of at least 6000 light years
from the Sun, about 3000 light years thick, which would cause an
obscuration in a path perpendicular to the plane of about half a
stellar magnitude (photographic). This layer adds its effect to that
of the obscuring clouds where these are found. (See p. 109). De-
tailed study of the effects indicates, however, that the absorptive
material is not uniformly distributed and that the reductions in
apparent brightness caused by it vary somewhat in different direc-
tions in space.
* The following passage from Newton's " System of the World" (1727) is of
interest : "Some may, perhaps, imagine that a great part of the light of the fixed
stars is intercepted and lost in its passage through so vast spaces and upon that
account pretend to place the fixed stars at nearer distances, but at this rate the
remoter stars could be scarcely seen. Suppose, for example, that three-fourths of
the light perish in its passage from the nearest fixed stars to us .... the fixed
stars that are at a double distance will be 16 times more obscure, viz., 4 times more
obscure on account of the diminished apparent diameter ; and, again, 4 times more
on accouut of the lost light. And .... at a triple distance will be 9x4x4, or
144 times more obscure .... at a quadruple distance 16x4x4x4, or 1024 times
more obscure " Newton evidently did not favour the idea. But the
absprption he supposes in his example is very much greater than generally found.
Movements, Numbers and Distribution of Stars 29
Study of the colours of B stars andf other objects bright enough
for study at great distances, has shown that they appear redder
than the fnormal of the same types nearer to us. The effect as
expressedtin stellar magnitudes (see later section, on colour indices),
amounts to from about a fifth to as much as a half of the total
general absorption. The absorbing clouds responsible for the
reddening probably float within the general stratum of absorbing
matter.
The great effect on estimates of distance which are based on
apparent magnitudes of stars of known luminosities situated in the
absorbing layer referred to, will be evident when it is stated that,
with Trumpler's figure for the absorption, an apparent distance of
1000 light years has to be reduced by 8 per cent, one of 5000 light
years by 29 per cent, and of 10,000 light years by 42 per cent. Even
with a smaller absorption, which there is some reason to believe
may be the case, of say O m -5 instead of O m -67 per 3260 light years,
these percentages would be 6, 24 and 36 respectively. The effect
becomes considerable therefore beyond, say, a thousand light years.
INTERSTELLAR LIGHT SCATTERING AND ABSORPTION.
The obscuration by dust clouds referred to is caused chiefly by
small particles, the total interstellar mass of which is relatively
small. Ability to redden starlight entails sizes of particles smaller
than about a thousandth of an inch in diameter ; others of larger
dimensions simply obstruct the light without changing its colour,
although the obstructed light is absorbed and later re-emitted as
unobservable "heat" radiation. The deflection of light by the
smaller particles is known as "scattering/' and the bluer rays are
those concerned, much as the light of the Sun is scattered by the
earth's atmosphere, resulting in the blue sky and a yellowed or
reddened Sun. Interstellar space also contains many atoms and
molecules of gas which have little dimming effect, although their
aggregate mass is larger than that of the bigger dust, or even greater
sized, particles. This interstellar gas has been revealed by the
spectroscope which has shown fine absorption lines caused by atoms
of calcium, sodium and other elements such as potassium, titanium
and iron, and recently some lines have been noted which are due
to molecules of the hydro-carbon (C H), sodium hydride (Na H),
and cyanogen (C N). The strongest of these lines were first found
in the spectra of distant spectroscopic binaries, as "stationary lines,"
which did not change their position in the spectra, as did other lines
because of orbital motion in the binaries. These distant staA were
necessary for the discovery, a very great length of path through the
gas being essential to produce sufficiently strong absorotion lines
30 Stellar Astronomy
to be visible. As a consequence of the great tenuity of the inter-
stellar gas which produces them, the* lines are fine and sharp, be-
coming stronger as the distance of the star is greater, and thus
providing another useful measuring rod for estimating distances.
Within the last year or two it has been possible to discover,
from the doubling (or even trebling or quadrupling) of the calcium
lines, the pxistence of more than one intervening cloud each with a
different radial velocity.* Another useful result from the measure-
ment of velocities of interstellar gases is a definite confirmation of
the rotation of the Galaxy, and its speed of revolution, as found
from stellar radial velocities and proper motions. In all proba-
bility most of the elements found in the Sun and stars have atoms
in some part of interstellar space, but usually so rarefied as to be
undetectable, or of elements having spectral lines only in that part
of the spectrum (the extreme ultra-violet) which is cut off from our
study by the absorbing action of the earth's atmosphere. In fact,
it has recently been found, by means of a specially-designed spectro-
graph, that bright lines of hydrogen and ionised oxygen are detectable
in regions of the Milky Way ; the hydrogen lines are often apparently
associated with O type stars, and no bright lines of the kind are
evident in areas of the sky away from the Milky Way zone.
CONCENTRATION OF STARS TO MILKY' WAY.
The crowding of stars towards the Milky Way zone has long
been a familiar fact. This concentration in spite of any effect of
obscuration in the lower Galactic latitudes, increases very much in
the fainter stars, as will be seen from Table 8, which shows numbers
of stars per square degree for different angular distances from the
centre line of the Galaxy (Galactic latitude).
Table 8
APPROXIMATE NUMBERS OF STARS PER SQUARE DEGREE
AT DIFFERENT GALACTIC LATITUDES.
Down to Whole
visual mag. sky. 20 45 90
6-0 0-12 0-21 0-13 0-08 0-06
8-0 1-0 1-9 1-2 0-7 0-5
10-0 8-0 19 10-5 6-2 4-0
15-0 775 2100 f870 350 160
20-0 25,000 80,000 22,500 4,200 1,750
* Oort considers that, on an average, the light from a star about 3000 light years
away, irill traverse five of these clouds on its way. There seems to be two classes
of gaseous cloud, one of which has more of the molecules in its composition than
the other ; in other words, broadly speaking, we may refer to molecular and atomic
clouds of interstellar gas.
Movements, Numbers and Distribution of Stars 31
The increasing Galactic concentration in the fainter stars is
brought out by the ratios between the numbers for and 90, which
vary from 3-5 at 6 m -0 to 46 at 20 m -0. It is also strikingly illustrated
by Seares's conclusion that 95 per cent, of the thirty or forty thousand
million stars in our system are situated on the sky within 20 of the
centre line of the Milky Way zone.
In the southern Galactic hemisphere the distribution is in general
somewhat richer than for equivalent northern latitude. In Galactic
longitude the stars down to eighteenth magnitude are concentrated
about four times as highly in the direction of the Sagittarius region
as in the opposite hemisphere of the sky. The brighter stars (down
to about the ninth magnitude) are concentrated more towards Argo
Navis than in the opposite parts of the sky.
As regards the relation of particular types of stars to the Galactic
plane, the high luminosity and B types are strongly concentrated ;
and inside 15 degrees on either side of the centre line are to be found
more than 90 per cent, of the Cepheid variable stars of period greater
than one day. The Long Period variables show little or no con-
centration (see next chapter for a description of these variables).
COLOUR INDEX AND APPARENT STELLAR MAGNITUDES.
It has long been known that mean colour index or photographic
minus visual (or photovisuaj) magnitude (m p -mv), increases gener-
ally in the fainter stars. The reason for this has been variously
explained ; for instance, as due to a greater proportion of late red
dwarfs, or as caused by selective absorption of stellar light in space.
Whatever be the explanation, the quantity is important for the
purpose of transforming photographic magnitudes into visual
magnitudes in the case of the fainter stars, for which only m? is
usually known. Seares gives the following formulae :
Average colour index (whole sky) = + 0-50 + 0-029 mv
and = - 0-18 + 0-071 m p
The correction (for the whole sky) for transforming star counts for
a grouping according to photographic magnitude into one according
to visual magnitude, is = - 0-16 - 0-050 m p . For example, what
is the visual magnitude corresponding for the whole sky to 17-0
photographic ?
From the formula m = 17-0 - 0-16 - (0-050 x 17-0)
= 16-0
Colour index for a given magnitude is greater on the average
with increase in Galactic latitude, the stars being therefore generally
bluer in Milky Way regions ; this is owing to the greater concentra-
32 Stellar Astronomy
tion of the hotter B and A type stars there. Results by Kreiken
show that the average colour index for the whole sky is somewhat
less than that given by Seares, but that in any case the values are
about half a magnitude less for Milky Way regions. In higher
latitudes and also in parts of the Milky Way where there is evidence
of the existence of dark clouds, the colour indices are roughly of the
size given by Seares's formula.
THE LUMINOSITY LAW.
That stars vary very much in luminosity has been obvious ever
since the recognition of co-existence in physically-connected clusters
of stars of very different brightness. The most luminous star so
far known seems to be the eclipsing binary S Doradus, situated in
the large Magellanic Cloud, for which star we find an absolute
magnitude of about -8 for each component. One of the faintest
known stars is the 1 1th magnitude companion of a Centauri (Proxima
Centauri), which is about +15 absolute magnitude.* This range,
23 magnitudes, means a ratio of light output of 1600 millions to one,
or from about 160,000 times to about one ten-thousandth of the Sun.
To ascertain the relative frequency of occurrence of stars of
different luminosities (the "Luminosity Law") has been the object of
many investigations by Kapteyn, van Rhijn, Seares, Luyten and
subsequent astronomers.
The first estimates by Kapteyn and others gave numbers, down
to about 12th or 13th absolute magnitude which later investigations
have found to be considerably too small at the fainter end, and the
most recent results indicate many additional faint dwarf stars.
It is now thought that the greatest star frequency is at about the
12th or 13th absolute magnitude (visual), and the faintest stars
are perhaps of the twentieth absolute magnitude or thereabouts,
i.e., of a millionth of the Sun's luminosity. The true range of stellar
luminosities is perhaps therefore a hundred times that mentioned
above. The table gives an approximate idea of the distribution of
the stars as a function of spectral class and visual absolute magnitude
according to recent research.
Part A of the table gives the relation of absolute magnitude to
numbers ; the figures in brackets are extrapolations which take
into account, without accuracy in detail, the great number of faint
dwarf stars. Part B shows the distribution by spectral types.
* About the faintest star observed so far is a companion to the dwarf red star,
BD -f 44048, which is several magnitudes fainter than Proxima.
Movements, Numbers and Distribution of Stars 33
Table 9
NUMBER OF STARS PER MILLION CUBIC LIGHT YEARS
NEAR THE SUN.
A
Absolute Magnitude
Absolute Magnitude
(Visual).
Number.
( Visual). Number.
O'O and brighter
4
10-0
240
1-0
8
11-0
270
2-0
20
12-0
300
3-0
40
13-0
310
4-0
62
14-0
(290)
5-0
88
15-0
(260)
6-0
115
16-0
(200)
7-0
150
17-0
(140)
8-0
185
18-0
(60)
9-0
215
19 - and fainter
(20)
B
Spectral
Mean Abs.
Spectral
Mean Abs.
Type. Number.
Mag.
Type. Number.
Mag.
( Visual)
(Visual)
BO-B9 4-7
0-0 g
GO -g G9 0-4
+0-5
AO-A9 34
+ 2-5 g
KO -g K5 7
+0-5
FO-F9 68
+3-5
gMO 1
0-0
dGO-dG9 128
+6-0
N 0-01
0-0
dKO-dK6 484
+ 7-5
R 0-01
+0-5
d MO + 2250
+ 14
S 0-0003
-1-5
The mean absolute magnitudes given allow for the increasingly
greater main sequence frequency as spectral type becomes later.
The total number of stars in Table 9 is 2977 or, say, one star per
300 cubic light years roughly.
SPECTRAL TYPE AND APPARENT STELLAR MAGNITUDES.
The Henry Draper Catalogue of Stellar Spectra contains particulars
of the spectral classifications of somewhat more than 225,000 stars.
It is practically complete down to about 8 m -75 for the southern sky
and to 8 m *25 for the northern hemisphere, the difference being due
to the clearer atmosphere at the observatory at Arequipa, Peru,
as compared with Cambridge, Massachusetts. The catalogue can
be taken as complete therefore for the whole sky at 8 m -25 ^photo-
graphic), to which limit there are nearly 60,000 stars with the
following percentage distribution :
34 Stellar Astronomy
Table 10
SPECTRAL TYPES OF STARS BRIGHTER THAN 8 m -25 (PHOTOGRAPHIC),
Type. Percentage of Total.
B (BO - B9) 11
A (AO - A5) 22
F (FO - F8) 19
G (GO - G5) 13
K (KO - K5) 31
M (Ma Mb Me) 3
O, R, N, S 1
The K, A and F stars are the most numerous, accounting for
nearly three-quarters of the total. More than half of the apparently
brighter stars are of types hotter than the Sun, but of naked eye
stars it is found that those of class KO are the most frequent. Class B
contains a large proportion of the brightest stars, but the percentage
for it decreases very rapidly among the fainter stars. With regard
to disposition in the sky, the B and A type are closely confined to
the Galaxy, but there is no marked concentration for F and G types,
although for K and M there is a slight tendency to greater frequency
in low latitudes. In general, it may be said that the types of
greatest space-velocity are, as perhaps might have been expected,
found to be dispersed farther than others from the Milky Way zone.
It may also be said that on the average the stars of greater luminosity
and larger mass are concentrated towards the Galactic plane.
The greater concentration as a whole of the fainter stars of early
type spectrum towards the Galactic zone, is brought out for the
tenth to eleventh magnitude stars of two Milky Way regions centred
at about 40 and 160 longitude, using Harvard Observatory material
in diagrams published by Shapley. These show about 44 and 56
per cent, respectively for stars hotter and for those cooler than FO
type in the first of these regions, and 35 and 65 per cent, for the
other, in spite of the reduction in percentages of B types generally
among the fainter stars as mentioned above.
SPECTRAL TYPES AND DISTANCES
Using the material of the Draper Catalogue, average absolute
magnitudes such as are given in Table 2, and counts of the number
of stars: found on 2300 square degrees of sky in fields at all longitudes
along the central line of the Milky Way, Shapley has found the
limiting distances and numbers of stars given below.
Movements, Numbers and Distribution of Stars 35
Table II
Spectral Surface number Distance limit No. per million
Type. per square degree, in light years, cubic light years.
BO - B5 29-7 2860 0-13
B8 - A3 96-9 1100 7-2
dA5 - dF2 18-7 455 19-6
d F5 - d GO 26-0 230 220
gG5 -g K2 69-0 1140 4-3
g K5 - g Me 17-5 1400 0-6
The table does not take into account such relatively infrequent
stars as Cepheid variables, or abnormally faint A stars, and is not
continued to dwarf K and M type stars, which are much more
numerous even than the dwarf F5 - GO stars. Shapley concludes
that for every BO - B5 star there are about five giant M stars and
seventeen hundred dwarfs like our Sun.
It is of interest to note that the aggregate luminosity and mass of
the stars in Table 9 can be roughly computed to be equal to those of
1300 and 1400 Suns respectively. This indicates that the average
unit of stellar mass in the million cubic years round the Sun radiates
light at much the same rate as the same unit of solar mass. This
is noteworthy in view of the great disparity in rates of radiation
per unit of mass between a highly luminous star and a dwarf (see
page 78).
DISTRIBUTION IN GALACTIC LONGITUDE.
Attention has often been drawn to the high degree of concentra-
tion towards the Galactic plane of particular types of stars, and
occasionally references are made to the nature of the distribution of
various objects along the approximate great circle of the sky marked
out by the Milky Way. A detailed investigation of this distribu-
tion is much to be desired and although what follows can hardly
be taken to be such in any adequate sense it is put forward as a
compilation of data which may be of some value.
In Table 12 ten classes of object are shown in percentages
according to their distribution in quadrants of the Galactic circle,
the zero of longitude being situated at R.A. 18 h 40 m where the circle
crossed the celestial equator, the values of longitude increasing
towards the east. The region of the Milky Way in each quadrant
is indicated by the names of the constellations, although, of course,
many of the objects are in other constellations of higher north or
south latitude.
Classes (c} 9 (d), (h) and (/) are notably concentrated towards
the Milky Way zone ; particularly the novae, for which the mean
36 Stellar Astronomy
latitude without regard to sign is only 9 degrees, with the fainter
ones more numerous towards Sagittarius. This concentration is
also a feature of the distribution of Cepheid variable stars with
periods longer than about three days, which it is noteworthy have
considerably smaller space velocities than those of shorter period.
Concentration towards the Galaxy is also fairly well marked in the
case of eclipsing binaries. Galactic novae are all the temporary
stars other than those objects appearing in certain spiral nebulae.
The quadrant of greatest concentration is shown by the figure
in heavy type ; the interpretation of these concentrations will be
discussed in a later chapter.
The progression in longitude of the most favoured quadrant
suggests concentration of the nearer bright objects towards the
centre of the supposed Local Cluster, and of the more distant to-
wards the Galactic centre in Sagittarius. (See Part III, Chapter I).
Movements, Numbers and Distribution of Stars 37
o
eia
Longitud
0-90
Aquila
to
Cassiope
gitude
0-360
ntaur us
to
ittarius.
eo
S
J3 ,3 fc 5 *>
H ^ ^ O r S
O
o
CM
rt
HH
P^
H
c/)
W
O
H
W
W
PH
38
Stellar Astronomy
REFERENCES PART I CHAPTER II
Author.
Scares and van Rhijn,
H. Shapley,
H. Shapley,
A. S. Eddington,
W. W. Campbell,
Various Authors,
Bok and Bok,
R. J. Trumpler,
Russell, Dugan and
Stewart.
Publication.
Mt. Wilson Cont.
No. 301.
Harvard Coll. Obs.
fr Circular, No. 226.
Harvard Coll. Obs.
Bulletin, No. 792.
"Stellar Movements and
the Structure of the
Universe/'
"Stellar Motions,"
"Splendour of the
Heavens."
"The Milky Way/'
Publications Ast. Soc.
Pacific, 57, 244.
"Astronomy"
Subject.
Number of stars.
Numbers and
spectra.
Density of distri-
bution.
General.
General.
General.
Galactic rotation.
"The Motions of
the stars/*
General.
CHAPTER III
BINARY STARS, VARIABLE STARS AND NOVAE
THE VISUAL BINARY STARS
THE surveys of double star observers, such as the Herschels,
Dawes, Dembowski, the Struves, Burnham, Hough, Hussey,
Aitken and others, enabled the last-named astronomer to
make a statistical review of the data for pairs which are sufficiently
far apart on the sky to show as separate stars in our telescopes and
yet be within limits of angular separation which suggest physical
connection. A brief summary of Professor Aitken's conclusions is
given below.
Adopting limits of angular separation according to the formula
log separation (seconds of arc) = 2-6 -0-2 m, where m is the com-
bined stellar magnitude of the components, which gives a range of
from 250" for l m -0 to 2"-5 for ll m -0, his counts led him to the con-
clusion that one star in every eighteen brighter than 9 m -0 is visible as
a double star within the resolving power of the largest modern
telescopes. The significance of this in regard to real physical
connection between pairs is brought out by the fact that if all the
stars down to this magnitude were scattered at random over the
sky, the chances are that in not more than about six or seven cases
would two stars be as close as 10" apart.* Aitken's limiting value for
a combined magnitude of S^O is 6"-3. Of the stars catalogued
83 per cent have a separation of less than 2", 62 per cent less than
1", and 29 per cent less than 0"-5.
The proportion of stars that are double is ascertained to be
greater in Milky Way regions than in the rest of the sky ; and that
this is not merely a perspective effect, due to greater extension of
the stellar system in the Galactic plane, is shown by the fact that the
ratio of close to wide pairs is not greater there than in higher latitudes.
Professor Aitken also considers that the increase which is observed
in numbers as angular separation diminishes is a real augmentation
in the number of physically close pairs with smaller orbital dimen-
sions. With regard to distribution by spectral types, the following
refers to nearly 4000 pairs, classifying them by the spectra of the
* It has been remarked by A. Berry ("History of Astronomy," p. 342), that the
odds against two stars of the magnitudes of the components of Castor (of which
magnitudes he assumes there are 50 and 400 respectively in the sky), being by mere
chance as close as the 5" of arc which divides them, are more than 300,000 to one
against.
40 Stellar Astronomy
primaries where the types of both stars are known, and, if not, by
the composite spectrum of the two stars.
Table 13
SPECTRA OF DOUBLE STARS PERCENTAGE NUMBERS.
B. A. F. G. K. M.
Visual pairs, 8 31 29 19 12 1
All stars brighter than
8 m -25, 11 23 19 13 31 3
Spectroscopic binaries, 35 29 11 9 14 2
The percentages from Table 10 for all stars brighter than 8 m -25,
and those for over 600 Spectroscopic binaries are tabulated for com-
parison. It will be noticed that in the M and K types the visual
pairs are relatively scarce as compared with the stars generally,
while they are numerous in G, F and A types. This may be chiefly
an effect of selection of the stars of types which are brighter ab-
solutely, the K and M pairs being largely main sequence stars. A
more valuable comparison would take into account, as far as possible,
the giant and dwarf classification of the stars, so that it could be
ascertained whether the differences between the relative numbers
of binaries and single stars are most marked in the giant or main
sequence stars. This would possibly throw light on the question
of the origin of binary systems. Meanwhile it may be of value
to draw attention to the apparently relatively great frequency of
pairs of which the primary is a giant of F type and the companion
a star of A type spectrum, the writer having found, that in pairs
with a giant primary, more than 40 per cent have this spectral
relationship. Shajn has also found from a study of several hundred
stars with composite spectra, that the maximum frequencies of
spectra are F for the primary and A for the secondary, these objects
being evidently close double stars. Recently it has been shown
that some at least of these pairs are composed of an F type normal
main sequence star and an A type sub-dwarf of a density greater
than ordinary dwarfs although not so dense as a white dwarf.
The number of visual pairs in which an orbital motion is known
to be present, although often very slow, exceeds fifteen hundred.
Orbital elements have been computed for several hundred systems,
the reliability diminishing in general with increase in the period of
revolution, which varies from a few years to seven hundred years.
When t the particulars of an orbit and the parallax are known with
sufficient accuracy, the total mass of the system in terms of that of
the Sun can be derived by the formula given in Part I, Chapter I.
Binary Stars, Variable Stars and Novae 41
The known values vary with luminosity and spectral type. By
statistical methods, Russell has found the average total masses
to vary from about 7 to 10 in giant systems of all spectral types, and
in dwarf pairs to range from 5 or 6 in the hotter down to 0-7 or 1-0
in the cooler classes. This agrees very well with the values for a
nuiiber of dwarf or main sequence pairs, as found directly from the
formula mentioned. The average value for the combined masses
of all visual binary systems is about 1-8 times that of the Sun, the
fainter component being generally the less massive. The eccen-
tricities of the orbits increase, on the average, with period of re-
volution (see Table 14), the mean being about 0-50 against 0-06 for
the orbits of the eight major planets of the solar system. This
relationship of period and eccentricity must, it is considered, have a
physical significance.
As regards the frequency of companions to stars, a short in-
vestigation by Williams and Vyssotsky appears to indicate that a
very large proportion of stars have distant companions. In fact,
these workers conclude that the evidence already available shows
the likelihood of as many physical stellar companions at a distance
from their primaries of more than 1000 times the separation between
the Sun and the earth, as ordinary visual close companions.
MULTIPLE SYSTEMS
The occurrence of pairs or multiples among the stars in the
Sun's neighbourhood may perhaps be taken as giving some idea of
what is usual throughout the stellar system. Of the 250 known
stars within about 30 light years distance from us, more than forty
per cent are certainly members of binary or multiple systems, and
another five per cent apparently belong to the same category ; six
of the systems are triple and one is quadruple.
Within the past few years a new kind of member of a stellar
system has been found from measurements, on photographs of very
high accuracy, of the proper motions of certain stars. By these
measurements it has been demonstrated that the binary 61 Cygni
has a third component of small mass (only 16 times that of the
planet Jupiter) and that 70 Ophiuchi has an even smaller attendant
(about 10 times Jupiter's mass). Russell has investigated theoreti-
cally the probable physical characteristics of the former of these
two bodies and considers that his results indicate a body of planet-
ary type but with an internal constitution resembling that of a
star and not of the major planets ; not hot enough at its surface
to be self-luminous, shining therefore by reflected light and un-
observable with present optical means. It appears quite likely
that many stars may have similar attendants.
42 Stellar Astronomy
THE SPECTROSCOPIC BINARIES
More than a thousand stars are known to consist of two or more
components revolving under their mutual gravitational attraction
so closely together as to be inseparable by ordinary telescopic means,
but revealed by the periodic displacement or duplication of the lines
in their spectra. Elements have been derived for the orbits of
about 400. In general, the known periods are short, ranging from
a few hours upwards, more than half being less than 10 days, and
the orbital eccentricities, which also increase on the average with
period of revolution, are smaller than in the visual binaries, the
computed values averaging about 0-20 (see Table 14). There is a
gap between the longest periods of the spectroscopic pairs and the
shortest of the visual binaries, which is probably due to observa-
tional selection, in the circumstance that the displacement of spectral
lines in the slow-moving pairs is too small for discovery by that
method, while the stars themselves are nevertheless too close for
separate visual detection. The application of the interferometer
to discovery of very close doubles may provide the means of bridging
this gap, which has grown narrower as instrumental means have
improved.
As shown in Table 13, the distribution of the spectroscopic
pairs by spectral classes shows a preponderance in the B and
A types, in which 64 per cent of the total are found. The spectro-
scopic binaries are chiefly naked-eye stars ; a large proportion of
these are stars of high luminosity and more than average mass*
and to this circumstance may be due the great number of stars
discovered to be double by means of the spectroscope something
like two in ever five or six so far examined in this way. As Aitken
says, "We do not yet know whether that percentage will hold among
the fainter stars, but on the evidence before us we may venture the
suggestion that perhaps the stars of larger mass, and hence pre-
sumably greater luminosity, are the ones which have developed
into binary systems." The periods of revolution are generally
shorter in the hotter type stars, a fact which may be partly due to
their greater mass. The masses of spectroscopic binaries can only
be determined in individual systems when the angle of inclination
of the orbit plane to the line of sight is known (i.e., in eclipsing pairs).
As stated earlier, in the paragraph dealing with stellar masses,
average values corresponding to a mean angle of inclination can be
estimated, however ; and when these are grouped according to
* Although dwarf stars are much more numerous than giants in space generally
this does not apply to any aggregate of stars brighter than a given apparent magni-
tude. In fact, about four-fifths of the naked -eye stars are giants or early type main
sequence stars brighter than +1 absolute magnitude and at least twice the Sun
in mass.
Binary Stars, Variable Stars and Novae 43
spectral type, the hotter stars turn out to be decidedly the more
massive, just as has been found to be the case in the visual pairs.
When the spectra of both components are visible, the relative dis-
placements or "doublings" of the lines enable astronomers to obtain
relative masses of the components, and in such cases it has been
ascertained that almost without exception the fainter bodies are
the less massive, the disparity increasing with the difference in
brightness of the components.
THE ECLIPSING BINARIES
There are more than 1000 of these now known, a large proportion
of which are faint and therefore difficult to study spectroscopically.
It will be appreciated that, given the knowledge that the light
variation is the result of mutual eclipses of two stars revolving about
each other, it is possible to decide from the shape of the light curve
the ratios of the sizes of the stars to the diameters of their relative
orbits. Surface brightness, and particulars of orbital eccentricity
and inclination of the orbit plane to the line of sight can also be
calculated.
If, in addition to the shapes of the light curve, curves of orbital
radial velocities have been obtained, and if the spectra of both
components are observable, not only relative but actual dimensions,
masses and densities can be computed. Because of this the de-
termination and classification of the spectra of eclipsing pairs is of
great importance in the study of the physical character of the stars.
Among the spectra observed and classified, about half are of class A,
20 per cent of class B, 15 per cent of F and the remaining 15 per
cent or less are G, O, K and M. The predominance of A and B
is due to their being more easily discovered because of great lumin-
osity as a class compared with the fainter main sequence G, K and
M stars. Assuming that the volume of space through which eclip-
sing binaries are known is that in which the A type stars are visible,
there would be a very much higher number of the later types, G, K
and M than has been observed, if all types in the volume could be
ascertained. *
A valuable addition to the methods of study of eclipsing pairs
has been provided by the discovery of what is termed the "rotation
effect." This is due to the effect of the eclipse of the brighter
component on spectroscopically measured radial velocities. R. A.
Rossiter has described the phenomena as follows, the rotation of the
primary in such close pairs being almost certainly, through tidal
action, in the same direction and with the same period as th3 orbital
revolution : 'The spectrum lines of a star are symmetrically broad-
ened by the rotation of one limb away from us and of the other with
44 Stellar Astronomy
equal velocity toward us, since in one case the effect is of increasing
the wave length of the light and in the other case of decreasing it.
The resulting displacement in opposite directions would broaden
the lines, and equal opposite velocities would symmetrically broaden
them. When the bright star is entering eclipse, one limb is gradually
covered by the eclipsing star and consequently the lines from the
bright star are fully broadened on one side only because of the
velocity of the one wholly visible limb. When these lines are
measured for determination of radial velocity, the centre of density
of the line will be shifted toward the broadened edge, and away
from the centre of the symmetrical line that would be observed if
both limbs were visible. When the star is entering eclipse, the
receding limb is visible, and the approaching limb is covered. The
measured centre of the line is displaced toward the region of longer
wave lengths, and will give radial velocities too large positively.
At the centre of eclipse the lines are symmetrical, and are bisected
where they normally should be. When the star is emerging from
eclipse, the receding limb is covered, and the approaching limb is
visible and consequently the measured centre of the line is displaced
towards the region of shorter wave lengths. The radial velocities
are then too large negatively."
From these discrepancies it is possible to obtain the duration
of the eclipse in a manner quite independent of the curve of light
variation, and also to get ratios of masses and dimensions for the
component stars. From the range of the discrepancies in radial
velocities, which, as explained, are due to the rotation of the primary
the equatorial speed of rotation of that star can be calculated.
Multiplying this by the period of rotation, which may (as stated
above) be taken to be the same as the period of revolution (i.e.,
period of light variation) the circumference and hence the diameter
of the primary star may be derived. Knowing the ratios of dimen-
sions and masses the diameters and masses of both components
follow. By this method, McLaughlin has found the following for
the Algol system :
Diameter. Mass.
(Sun = 1) (Sun = 1)
Bright body, 3-1 4-7
Faint body, 3-7 1-0
Distance between centres, 6,500,000 miles.
These dimensions are larger than the values previously adopted
for Algol, but are no doubt more accurate, the mass agreeing very
well with the average for a B8 type main sequence star such as the
primary of ^ Algol seems to be. (See Table 3).
There is a third component C, which is brighter than B. A and
B together revolve round the common centre of gravity of the triple
Binary Stars, Variable Stars and Novae 4i
system in a period of just under 2 years. This was discovered fron
the variations in the radial velocity of the centre of gravity of th
system.
In many eclipsing systems the two stars are so near togethe
that the surfaces facing each other reflect the light of the othe
component so strongly as to affect the shape of the light-curve. Th
stars have then reflection phases which are superposed on the effect
due to eclipse. The shapes of the stars themselves are in such case
flattened spheroids and the total light received from the system i
affected by the rotation of these spheroids which, through tida
interaction, is almost certain to be in the same direction and perio<
as the orbital revolution. Methods of study of the light curv
(assisted by the great accuracy of the photoelectric photometei
which can measure brightness to the hundredth part of a magnitude
are so refined as to be able to disentangle these effects and give value
for the surface brightness of the faces which are turned toward;
each other and of those turned away from the centre of the system
together with the ellipsoidal shapes of the stars themselves. Ii
fact, there are several non-eclipsing binaries known whose ligh
variation can be ascribed to their ellipsoidal shapes alone ; but s<
far no single star has been found to vary because of rotation of j
non-spherical shape.
ECCENTRICITIES AND PERIODS OF DOUBLE STAR ORBITS.
The average increase of eccentricity with period, found in al
classes of binary systems, is shown by the mean values below :
Table 14
Average Average
Period. Eccentricity.
3 days. 0-05
I 8 ,/ 0-16
Spectroscopic / 14 0-22
pairs \ 31 0-35
103 0-30
1177 (3-2 years) 0-31
<O43
0-40
73 0-53
0-57
0-62
46 Stellar Astronomy
The foregoing eccentricities are derived from systems with known
orbits. Some information may be obtained, however, regarding
the shape of orbits of wide slow-moving pairs by statistical methods.
It is easily seen that if all orbits of such pairs were really circular in
shape, as real motion of the companion would be at right angles
to the line joining it and its primary, there would be an excess of
apparent motions perpendicular to this line in spite of the effects
of foreshortening. This effect would be least in orbits of high
eccentricity, Russell has thus found an average eccentricity of
0-61 for more than 500 pairs of average period estimated at about
2000 years and 0'76 for 800 others with average period of something
like 5000 years. These are in accordance with what would be
expected from the values above. The periods of binary systems
increase steadily on the whole with spectral type in the order B, A,
F, G, K and M, which seems to be due partly to the decrease in
average mass of the stars in this order down the main sequence.
COLOURS AND SPECTRA OF DOUBLE STARS.
F. C. Leonard has found that in visual pairs almost invariably,
if the primary is a main sequence star, the secondary is a cooler and
redder main sequence star, while if the brighter star is a giant the
companion is usually hotter and bluer. This is clearly brought
out when the spectra are studied, but is somewhat obscured in the
case of colours by the effect of contrast, which tends to make the
fainter star of a pair appear bluer than it really is. These re-
lationships of colours and spectra are so general as to provide a
reliable criterion as to whether a system is composed of stars of the
main sequence or has at least a giant primary. This is supported
by the fact that in eclipsing pairs the fainter star has been found
to be usually of the same colour as, or redder than, the brighter
component whenever it has been possible to determine the spectra ;
while in spectroscopic non-eclipsing binaries the fainter has been
noted to be generally bluer in colour. It is probable that the former
are more usually dwarfs or main sequence stars, while the latter,
because of observational selection, are more often giant systems.
The eclipsing pairs are found from variation of light and are thus
easier to remark even when of fainter apparent magnitude.
THE VARIABLE STARS.
There is as yet no really satisfactory classification of variable
stars, Ifor, except in the case of eclipsing systems, we do not certainly
know the cause of variation which would be necessary for a completely
reliable scheme. The following is a provisional one which, in broad
Binary Stars, Variable Stars and Novae
47
outline, defines the chief types of the 20,000 or so variable stars
now known :*
Class 1 Eclipsing Pairs.
2 Cepheid Variables.
3 Long Period Variables.
,, 4 Irregular Variables.
5 Novae, or Temporary Stars.
CLASS 1 ECLIPSING PAIRS. As these stars are really not
variable in the sense of true physical change of light output, they
have been partially dealt with in the preceding pages as double stars.
Before the refined methods of modern photometry were applied, the
presence of a secondary minimum was only known in the case of
systems such as /3 Lyrae, in which the two stars are more nearly
equal than usual. A light curve of this type, that for /? Lyrae, is
shown in Fig. 3, while that for Algol is given in Fig. 4.
3-3
35
37
1
35
37
3-9
41
43
,
x"-
-^x,
s
/-
"^"
^N
/
H
N
,*
^
s
S
N
/
N
/
S
*~l 1 T
S
S
/
\
4-1
M
41
/
\
/
\
/
1
^_
'
^
It/1
<T5
od
B>
1
&
J 4 5 7 ft 10
1 12 1
FIG. 3 OBSERVED LIGHT CURVE OF ft LYRAE
The much more prominent secondary minimum is noticeable
in Fig. 3, also the more gradual nature of the light changes due to
the large ellipticity of figure of the two components, so that, even
though the eclipse may be large or even total, the light does not
remain constant at minimum. These systems generally consist of
two stars of early type and low density revolving about one another
nearly in contact with tidally distorted elliptical figures.
* The growth in number of known variables was very slow at first. At the
beginning of the 18th century four only were known Mira (1596), Algol (1669),
R Hydrae (1670) and x Cygni (1686). No more were found until 1782, another
seven being added before the end of the century. By the end of the 19th century,
about 400 were listed. The extraordinary increase to the figure quoted above,
during the present century, is the result chiefly of photographic search at Harvard
Observatory and elsewhere.
48
Stellar Astronomy
a
in
Me
020
040
050
aco
010
0-80
aso
too
1.10
.10
1.30
10
30
From "Variable Stars").
FIG. 4 LIGHT-CURVE OF ALGOL.
(By C. Furncss.
In every eclipsing binary system the secondary is really in all
probability a luminous body. The ratio of brightness of the two
components is greatest in the Algol type.
There is a classification into three broad types. Algol gives
its name to one in which the light remains practically the same
between the minima, a relatively small secondary minimum being
produced by the eclipse of the substantially less luminous secondary.
Those with secondary minima of some amplitude and light curves
of a more rounded form, with components elongated in shape by
their mutual gravitational attraction, are called Lyrae stars. A
third type having light curves conspicuously convex upwards
between eclipses, a range of secondary minimum greater than two-
thirds the range of primary minimum, composed of two much
elongated rather dense dwarf stars later than spectral type AO,
revolving almost in contact and with periods of less than a day and
a half, are given the designation W Ursae Majoris stars. The table
gives some statistical data for the three divisions, based on infor-
mation in "The Story of Variable Stars," by L. Campbell and L.
Jacchia.
Binary Stars, Variable Stars and Novae 49
Table 15
ECLIPSING PAIRS.
Amplitude of Commonest Range of
Type. Number. Variation. Period. Periods.
Algol, 800 Up to 4 m -0 2 to 3 days 0-2 to 9883 days.
ft Lyr., 140 Rarely exceeds f-day 0-5 to 199 days.
l m -0.
W Urs., 120 Average O m -65 4-day 0-2 to 1-3 day.
The range in length of periods is, as will be seen, very considerable
in the first two types, however ; and there are, of course, systems
of intermediate character among the total number. The eclipsing
variable of longest known periods are e Aurigae, 27 years ; V V
Cephei, 20 years ; HV 6990, 18 years ; HV 7021, 13J years and
Aurigae, 2| years.
CLASS 2 CEPHEID VARIABLES. These stars are named after
8 Cephei, the best known of the type. There are about 1250 known,
with periods ranging from several hours* to more than 40 days,
and there are also many hundreds of similar variables known in
globular clusters, the periods of about 600 of which are generally less
than a day. Cepheid variables of long period have also been found
in the Andromeda spiral nebula, M31, the spirals M33 and M101,
the irregular nebula NGC 6822, in the Magellanic Clouds, and in
several other stellar systems.
The light variation of a Cepheid seldom exceeds l m -2 (visual)
and is characterised by a rapid rise to maximum and a rather slow
decline in the case of stars of period similar to the type star 8 Cephei
(see Fig. 5). In this star the increase to maximum is such that the
light doubles in about 30 hours, while in many of the short period
"cluster type/' of about half a day or less period, the light actually
more than doubles in 30 minutes. A progressive change with the
length of period in the characteristics of the curve was found by
Professor Hertzsprung. For periods of about 2-3 days, and also
for those 10-12 days, the curve tends to be symmetrical, but pro-
gressively unsymmetrical (as in 8 Cephei) between these two groups.
The radial velocities are also variable in the same period as the
light, with the maximum velocity of approach occurring at about
the same time as, or later than the maximum light ; and the maxi-
mum velocity of recession at about the light minimum. According
to Joy of Mt, Wilson Observatory there is, however, a lag of the
velocity curve, with respect to the light curve, which increases with
* About the shortest period known is 100 minutes for a star in the constellation
Pyxis which varies from 14 m *5 to 15 m *8, and there is one of even shorter period
(C Y Aquarii) of 88 minutes.
50
Stellar Astronomy
Mfc
tri
\
Days I
3
From "Variable Stars"). (By C. Furness.
FlG . 5 LIGHT-CURVE OF DELTA CEPHEI
This curve is typical of those of "Cepheid" variables. It shows a rapid rise,
followed by a slower fall of light, and these changes are repeated indefinitely
with perfect regularity.
Km/sec,
-70
-80
90
Mag.
7-2
7*4
7-6
7-8
Days.
0-0 0*1 0-2 0*3 0*4
0-5
00
\
FIG. 6 VELOCITY AND LIGHT CHANGES OF A SHORT-PERIOD
CEPHEID.
The lower curves represent the changes of light as observed at two different
Observatories. The upper curve shows the corresponding velocity of the star
or its atmosphere, as revealed by the spectroscope. The lowest point on
this curve indicates the maximum speed of approach, which is seen to coincide
very closely in time with the star's greatest brightness, as shown in the lower
curve. The reverse holds good for the time of least brightness. This corres-
pondence shows that the variability of the Cepheids is intimately connected
with motion of some sort.
Binary Stars, Variable Stars and Novae 51
period from zero to a considerable fraction of the period ; and there
are relations between length of period and amount of light variation,
and length of period and range of radial velocities, so that as periods
increase from about 1 day to 45 days the photographic light change
varies from about O m -6 to l m -8, and the range of radial velocity from
20 to 33 miles per second.
The spectra range from A to K type with increase in length of
period. They also alter during the period of light variation in the
case of the individual star, by about one spectral type. This
alteration indicates a higher effective temperature at maximum than
at minimum, and this is shown also by a greater range in the photo-
graphic than in the visual magnitude changes.
It will be convenient to summarise here the characteristics which
are observed to vary in a general way with length of period.
Spectral types, from A to K.
Shapes of light curves, symmetrical at 2-3 days
Range of and 10-12 days, unsymmetrical otherwise.
period, Change of brightness, 0-6 to 1-8 photographic
from about magnitude,
one to 45 days. Ranges of radial velocity, from about 20 to 33
miles per second.
Lag of velocity curves with respect to light curves ,
from zero to a considerable fraction of periods.
One of the most remarkable discoveries of modern times is that
the luminosities of Cepheid are fairly closely related to the period
of variation, This, the Leavitt-Shapley Period-Luminosity Law,
is due initially to the work of Miss Leavitt on the variables in the
smaller Magellanic Cloud, and later mainly to Dr. Harlow Shapley,
who showed from parallaxes derived by various methods (chiefly
proper motions in the nearer objects) that this relationship holds
for Cepheids in all parts of the sky, including the globular clusters.
The Table gives the relationships.
The absolute magnitudes are "median" values, i.e., the arith-
metical means between the brightest and faintest absolute magni-
tudes of^the average star of the period tabulated :
Table 16
THE PERIOD-LUMINOSITY RELATION
Period (days] Absolute magniti4de (photographic)
0-5 0-0
1-0 - 04
5-0 - 1-4
10-0 - 1-9
20-0 - 2-6
50-0 - 3-5
Stellar Astronomy
It will be obvious that such a relationship must be very significant
in any theory of Cepheid variation. It is also of great importance
from another aspect, as when once the period of any Cepheid is
known its luminosity follows and consequently a good estimate
of its distance, from the formula M =m +5 + 5 log 77, (see Appendix
A), however far it may be away from us.
The lengths of periods of Cepheids are very regular, although
there have been indications that they may change periodically or
progressively, particularly in the case of those of short duration ;
but a study over a long interval of time will be necessary to deal
satisfactorily with the matter.
CLASS 3 LONG PERIOD VARIABLES. These are of low tempera-
ture spectrum, chiefly of M0 (see Appendix B) types, with a number
of S, R or N type. Their periods range from about 100 to more than
600 days, with a marked concentration in the interval 200 to 400
days. The longer periods are associated jointly with the later spectra
(in the M type the range is from Mle to about M80, with increase of
period) and with the largest amplitudes of variation. The variation
of brightness is about three to over eight magnitudes, averaging
about five magnitudes. The variation bolometrically, as measured
at Mt. Wilson with a thermo-couple and the 100-inch reflector is,
however, very much less ; the variation in heat output in x Cygni
is only about six-tenths of a magnitude as against eight magnitudes
visually, and in o Ceti 1-3 magnitudes bolometric, corresponding
to 4-5 magnitudes visually. The bolometric range is therefore
similar to that of the shorter period Cepheid variable in which,
owing to higher effective temperature, bolometric and visual magni-
tudes are more nearly the same. The periods of the Long Period
stars are not regular; maxima or minima may be some weeks
before or behind their expected times. A few stars have even
shown definite changes in length of period : R Hydrae, from 500 to
400 days in 280 years, and R Aquilae 350 to 300 days in 80 years,
are two examples.
From study of their proper motions and radial velocities, Gerasi-
movic has found a relationship between period and visual absolute
magnitude as below. It will be noted that the relation is the
reverse of what has been found for Cepheids.
Period (days) Absolute Magnitude.
90 to 250 - 2-3
251 to 340 - 1-1
Greater than 340 + 0-3
Wilson and Merrill also find the same relation, which is connected
with the average spectral types ; in the M variables, M \e for the
Binary Stars, Variable Stars and Novae 53
short period to M8e for the longer period stars. With the Se type
variable the relation is from absolute magnitude -2-2 for about
150 days period, and -2-7 for 175 days, falling off at 450 days or
thereabouts to +0-6. When the motions of these Long Period
variables are referred to the stars in the Sun's vicinity they are
found to trend towards a point at right angles to the Galactic centre
as in the case of the high-velocity stars. The mean space velocity
is about 46 miles per second, but this ranges from higher to lower
values with increase in period of variation.
About 1300 variables of the type are known ; 90 per cent have
M type spectra, the remainder being of S, or R or N types. All have
bright emission lines in their spectra.
Classifications of these variables, by the shape of the light curve
have been made by Phillips, Turner and Leon Campbell. The
classification of Phillips is by means of elaborate harmonic analysis
of the light curves of more than 80 stars from which two groups
were derived. A later classification by Campbell of nearly 120
light curves, all reduced to a uniform scale longitudinally and
vertically for purposes of comparison, shows a regular progression
from those with broad maxima and narrow minima to those of wide
minima and steep narrow maxima. Seven progressive types are
somewhat arbitrarily fixed by him. There is a steady increase of
period in his II to VII types, which means that the stars with broad
Table 17
CAMPBELL'S CLASSIFICATION OF LONG PERIOD VARIABLES
Average range Aver, period Description of
Type, in visual mags. in days. Curve.
II 3-8 234 Max. fairly broad : min.
narrow.
III 4-3 280 Symmetrical ; nearly a sine
curve.
IV 4-9 273 Max. somewhat narrower than
min. Rise slightly steeper
than fall.
V 5-5 341 Max. still narrower than min.
Rise rather steeper than
fall.
VI 5-0 348 Max. much narrower than min.
Rise somewhat steeper
than fall.
VII 4-3 363 Broad min. ; steep nairow
max. Rise steeper than
fall.
54 Stellar Astronomy
maxima and narrow minima have in general shorter periods than
those with steep narrow maxima and broad minima. Type I does
not fall into this relationship and is also different from the others,
in that the maximum of the curve is somewhat irregular, showing
a tendency to a double maximum. Table 17 gives the characteris-
tics of Campbell's types, omitting as abnormal Type I (of which the
average range is 3-9 magnitudes, and average period 378 days).
Seven fairly representative stars of the types are, in order,
U Canis Minoris, S Ursae Majoris, S Bootis, R Trianguli, o Ceti,
R Tauri and S Tauri.
Study of the light curve of Mira by L. Campbell and Sterne has
revealed an interesting correlation. It appears that, if the time
between two arrivals, on the increasing branch of the curve at an
arbitrarily chosen point near half way in light between minimum
and maximum (6 ra -0 in this case) is shorter than normal, the maxi-
mum which follows is brighter than normal ; and vice versa. The
same correlation has been found in all but four of 29 variables of
the type, by C. B. Ford. By this means it seems possible to pre-
dict the approximate values of maximum magnitudes. This is
considered to be more than a mere geometric property of the light
curve, although the underlying cause is not clear.
Joy has made an exhaustive spectrographic study of o Ceti with
the Mt. Wilson 60-inch and 100-inch reflectors, and a number of
similar Long Period stars have been studied with much the same
outcome. Joy's results for Mira are given here in some detail as
indicating the observed surface phenomena of the class. The
spectrum varies with the light of the star. Bright high-temperature
iron lines are seen at maximum, and although at minimum there
are no emission lines, those of hydrogen appear soon after and reach
their maximum at maximum light of the star. Low-temperature
bright lines of iron, magnesium and silicon appear after maximum
is well past. The elements most prominent in the absorption
spectrum are iron, vanadium, chromium, manganese, calcium and
magnesium. Titanium bands vary with the light of the star, but
the lines of that element are weak. The bands give the same
radial velocities as the absorption lines of the spectrum. The striking
feature of the radial velocities from the dark lines is their regular
variation in a curve resembling the star's light curve, opposite in
phase to that of the Cepheid stars, since the maximum recessive
velocity in Mira occurs at maximum and the greatest velocity of
approach at minimum. Previous observers had thought the radial
velocity from absorption lines constant, but when observations are
made at all stages the variation is found to be from +40 miles per
second at maximum light to 4-32 miles per second at minimum.
The bright lines of the spectrum give a velocity curve which shows
Binary Stars, Variable Stars and Novae 55
outward motion relative to the absorption line curve, except at
light minimum, when the difference is zero, the greatest difference
being 12 miles per second 56 days after maximum light. The
intensities of the bright lines at their maximum depend on the
magnitude of the star. From certain lines in the spectrum an
absolute magnitude of -0-3 is obtained for the normal visual
magnitude at maximum of 3-5. (See Appendix D). This gives
a parallax of 0"-017, and with the angular diameter measured by
the interferometer, 0"-056, a linear diameter of 307,000,000 miles
and a surface brightness 7-5 magnitudes (1000 times) fainter than
that of the Sun. It was estimated by Joy that the temperature
varies between 2300K and 1800K. Measurements by radio-
meter at Mt. Wilson show a change in heat output, which would
be explained by a variation of 15 per cent in diameter. Owing
to the very great effect on visible radiation of variation of tem-
perature at the range mentioned, the change in light, between 6 and
7 magnitudes, is very much greater than the alteration in bolometric
magnitude, which is about one magnitude only, i.e., the Long Period
variables really change very much less in total energy output than
in light output. It has also been found that the energy maximum
occurs about 50 days (or, say a seventh of the period) later than the
light maximum, at a point when the visual brightness has declined
by l m -5, or to a fourth of the maximum brightness.
It will be noted that the change in bolometric magnitude is not
very different from that of the Cepheids.
The observed drop in magnitudes visually in the Mira type is,
however, greater than that calculated from the bolometric change ;
and this discrepancy has been attributed to selective absorption
by the bands of titanium oxide, and perhaps also obscuration by
clouds of particles of that substance formed at minimum.
The change in spectral type from A to K with lengthening
period of Cepheids is continued in the Long Period variables to M
type in a systematic and probably significant manner.
CLASS 4 IRREGULAR VARIABLES. There are some variables
which do not vary regularly. They are very diverse in character-
istics and include such quasi-periodic stars as Betelgeuse and
a Herculis ; SS Cygni, U Geminorum and SS Aurigae, stars ordinarily
faint which suddenly rise two or three magnitudes and then fade
gradually ; and R Coronae Borealis, RY Sagittarii and SU Tauri,
which remain for long periods at a fairly constant brightness, sud-
denly fading several magnitudes and varying irregularly until they
regain brightness.
In the case of Betelgeuse the radial velocities, the apparent
angular diameter (as measured by the Mt. Wilson interferometer),
56 Stellar Astronomy
and the light variation all seem to vary together in a most suggestive
way ; according to Pettit the light curve has a chief period of about
5J years with a range of O m -4, and there is an irregular period, of from
140 to 300 days with a range of O m -5, superposed. Stebbins finds
that the light maximum precedes the maximum radial velocity of
approach by about 0-8 years.
In SS Cygni two distinct forms of maximum are known, the long
and the short, and there is sometimes a third anomalous type. These
maxima are usually in the order short, long, short, long ; but the
anomalous form sometimes interrupts the series. R Coronae has
a peculiar spectrum of about GO type and is situated in rather high
Galactic latitude, the others of its class being in low latitudes.
The star 77 Argus is an irregular variable which is now of about
7th or 8th magnitude, but blazed up in 1843 to nearly - l m -0, that
is to about the same as Canopus. It has a peculiar spectrum with
bright lines and is situated in a nebula. It (and SS Cygni, U Gemin-
orum and SS Aurigae) should perhaps be classed with the novae or
temporary stars. Such parallaxes as have been obtained, although
small and rather unreliable, suggest that the Irregular Variables are
super-giant stars even brighter than most of the giant Long Period
stars ; the mean absolute magnitude is about - 2. A considerable
number of faint irregularly varying stars have been found in the
region of the Orion nebula M42. These appear to be dwarf stars,
even allowing several magnitudes for absorption of light by nebular
material, of about +5 absolute magnitude on the average.
Stebbins and Huffer have proved by photo-electric observations
that most red giant stars show slight variation of up to three or four
tenths of a magnitude (see page 93). There is, however, a type
of non-periodic variable of which eleven are known, named after
the best-known member of the class, T Tauri, and these are evidently
main sequence stars of F5 and G5 type. They are associated with
dark or bright nebulosity in or near the Milky Way dark clouds.
Five of them have been found to be double stars with companions
of the same order of brightness as themselves.
As Campbell and Jacchia state ("The Story of the Variable Stars,"
page 116), it is difficult to conceive of a really irregular phenomenon
in Nature, and "it is possible that these 'irregular' stars appear to
be so mainly because we have not been able to analyze the com-
plicated processes which concur to make them vary as they do."
CLASS 5 NOVAE OR TEMPORARY STARS. Well over 100 stars
of thq type known as Novae have been observed (exclusive of the
objects appearing in certain of the spiral nebulae), more than 70
of which have appeared in the twentieth century. A rather typical
Binary Stars, Variable Stars and Novae
57
10
to
30
40
50
(0
70
90
90
100
1(0
JD
24IS420
3
40
GO
30 STOO
40
GO
90
S60Q to
40
Prom "Variable Stars").
(By C. Furness.
FIG. 7 LIGHT-CURVE OF NOVA PERSEI, 1901.
This curve shows the very abrupt initial rise of light, amounting to over twelve
magnitudes in a few days. Then comes the fall, rapid at first, but more gradual
later. The remarkable series of undulations during a part of the fall is clearly
shown, but the latter part of the curve is much more smooth. The vertical lines
indicate intervals of ten days.
light curve of a bright Nova is given in Fig. 7. This shows the
exceedingly rapid rise to maximum.
It is now believed that the final magnitude is generally about
the same as the magnitude before the outburst, but irregular varia-
tion of light seems common in these later stages. The rise, amounting
to from ten to fifteen magnitudes, usually takes place in less than
a week. At this stage the colour is white and the spectrum, at
first apparently continuous, soon becomes similar to that of a giant
type A star with dark lines of hydrogen, iron, titanium and calcium
all displaced towards the blue end, the displacement varying as the
wave length and being best explained as due to a shell of gas moving
out from the centre of disturbance. The star then begins to fade
and becomes yellowish in colour, bright companion lines to the dark
lines appearing on their red side. These bright lines rapidly
broaden and show complex structure but are not displaced from
the normal positions of the lines identified with the absorption
companion?. After a few days, some of the lines, particularly those
of hydrogen, show a second dark companion displaced towards the
violet to a greater extent than the first dark lines. We may then
have present in the same spectrum lines displaced by an amount
corresponding to a velocity towards us of more than 500 miles per
second, and others of the same substance apparently giving a
58 Stellar Astronomy
velocity of 1000 miles per second in the same direction. This stage
is followed by an increase in brightness of the bright lines, although
the light of the star as a whole is still diminishing. The dark lines
then disappear along with the continuous background of spectrum ;
the bright lines are now the dominating feature and the colour of
the star is distinctly reddened by the strength of the red line of
hydrogen. Later on a fresh set of bright lines appears which is
much the same as those seen in the spectrum of a planetary nebula.
The hydrogen bright lines then slowly fade and the nova loses its
reddish colour becoming greenish white. The final stage towards
which most Novae seem to move is to a star, often of Wolf Rayet
(O type) characteristics, of the original pre-Nova brightness ; the'
time taken from the outburst until this stage ranges from about
10 to 30 years.
The foregoing briefly sketches the changes in light and spectrum
of a rather typical Nova. There have been objects, such as the
Novae in Aquila (No. 4), Aurigae and Herculis, which had a different
kind of light curve with a sudden rise but a long flat maximum,
and there have also been some of intermediate character.
The Galactic distribution has been referred to earlier, and it is
interesting to note that it is somewhat similar to that of the plane-
tary nebulae, apparently lending some support to the suggestion
that these objects may be the relics or residues of novae. The
light output at maximum of Novae is known to be very great. By
various methods, including direct parallax measurement for some
of them, combination of proper motions and radial velocities (based
on certain fine absorption lines not affected by the large displace-
ments described earlier), intensities of interstellar lines, and in
several cases by means of the measured angular expansion of
ejected nebulosity, the radial velocity of which is assumed to be
that given by the spectroscopic measurements of the bright bands,
a mean absolute magnitude at maximum of - 7-0 has been derived
which D. B. McLaughlin has found is the average of a range from
-8 to -3 according to the rate of decrease of light from the maxi-
mum, the stars that fade quickest being the brightest.
It seems probable that the initial luminosity before outburst is
of the order of +5 absolute magnitude, and that possibly a sub-
dwarf type of star has been concerned. But in the opinion of other
investigators the original star may have been of a more normal type.
In the case of a number of bright Novae (Persei 1901, Aquilae
1918, Cygni 1920, Ophiuchi 1919, Pictoris 1925 and Herculis 1934)
nebulosity has been observed to expand from them. Nevertheless
it docs not seem very likely that planetary nebulae are thus produced,
as the ejected nebulosity thins out and seems to disappear in most
cases. Besides this, the velocities of expansion of planetaries shown
Binary Stars, Variable Stars and Novae 59
by the spectroscopically measured radial velocities, are much smaller
than those of the Nova nebulosities ; and the number of planetaries
(about 150) seems to be much too small in view of the rate of occur-
rence of temporary stars in our system, observed and unobserved,
which seems probably 20 or more per annum. Even allowing for
the probable temporary nature of the existence as such of a plane-
tary nebula (the average life has been estimated on physical grounds
as about 30,000 years) there should be very many more planetaries
than are seen, if they are the relics of Novae.
A considerable number of Nova-like faint stars have been ob-
served in about a dozen of the larger spiral nebulae, more than 150
having been noted up to date in M31 alone, including that of 1885,
which reached 7th magnitude at maximum or nearly ten magnitudes
brighter than the average of the others in that system. The
similarity of the light-curves of these faint stars to those of Galactic
Novae showed that all are of the same class.
The 1885 Nova in M31 was the forerunner of more than 50
of an even brighter kind found in external galaxies. The average
ordinary Nova is 50,000 times as luminous as the Sun, but these
"Supernovae," as they have been called, have often a maximum
absolute magnitude of about - 15 or 100,000,000 times the Sun's
light. Several very bright Novae in our own system, namely, those
of the years 1054, 1572 and 1604, were almost certainly of the
Supernovae class, the luminosity of which is often comparable with
that of the entire stellar system in which it is found. The observed
radial velocities of ejection are of an order ten times greater than
those for ordinary Novae ; and it seems possible that these bodies
differ (to quote the Gaposchkins) "only in brightness and radial
velocity from a Nova that is, the phenomena differ in scale rather
than in kind. Possibly we may regard them as Novae that have
developed from giant, rather than from dwarf stars. The fre-
quency of Supernovae [according to Zwicky, one per average galaxy
per 600 years and therefore] perhaps about a ten-thousandth of that
of ordinary Novae, may well represent the relative commonness
of the giant and dwarf stars from which they originate." On the
other hand, Hubble has pointed out that the Supernovae appear in
all types of galaxies, including the ellipsoidal where no very bright
giants or supergiants are noted.
As stated above, Supernovae often reach a maximum of the order
of - 15 absolute magnitude or 100,000,000 times the Sun's luminosity.
It seems, however, that this order of brightness applies only to one
of two groups of Supernovae. In Group 1, the light curves are
similar in their light decrease to that of an ordinary Nova, but the
spectra have extremely broad emission bands that appear earlier
than the narrower bands of the ordinary Nova. Supernovae of
60
Stellar Astronomy
Group 2 reach maxima of the order of - 12 or - 13 absolute magni-
tude, or about 10,000,000 times the Sun's luminosity ; they have
conspicuous ' 'shoulders" on the descending branch of the light curve
and spectra similar to that of an ordinary Nova intensified.
REFERENCES PART I CHAPTER III
Author.
R. G. A^tken,
R. M. Petrie,
Publication.
"The Binary Stars,"
Pub. A st. Soc. Pac.,
54, 195.
E. T. R. Williams and ditto
A. N. Vyssotsky.
Aa. Strand, ditto
Subject.
Double Stars.
Composite spectra
and sub-dwarf
stars.
54, 260. Distant Companions.
55, 29. Small Companion to
61 Cygni.
H. N. Russell, ditto 55, 85. ditto
R. A. Rossiter and Astrophysical Journal, Rotation Effect.
D. B. McLaughlin. 60, 15.
F. C. Leonard, Lick Obser. Bulletin, Spectra of Double
343. Stars.
Monthly Notices, Royal
Astronomical Society,
82, 372. ditto.
Harvard Reprint, 21. Classification of long
period variables.
Mount Wilson Contri- Study of Mira CetL
butions, 311.
'The Story of Variable Variables and Novae.
Stars/'
ditto,
ditto.
Variable Stars/'
Pub. Ast. Soc. Pac., Supernovae.
53, 141.
Popular Astronomy, Light Curves of long-
50, 535. period variables.
P. Doig,
L. Campbell,
A. H. Joy,
L. Campbell and
L. Jacchia.
C. & S. Gaposchkin, "Variable Stars/'
P. W. Merrill, 'The Nature of
E. Hubble,
C. B. Ford,
Part II The Nature of a Star
CHAPTER I
A STAR'S SURFACE AND SURROUNDINGS
THE theory of a star's surface usually held until a generation
or so ago involved a photosphere, or light-emitting outer
layer, which was supposed to be composed of clouds of solid
or liquid incandescent particles of substances with high tempera-
tures of volatilization, such as carbon. Later research showed
that even the surface temperatures are usually too high to permit
of the existence of matter in any but the gaseous state. A star's
surface therefore consists of intensely hot gas, having a nearly
transparent atmosphere shading gradually into a photosphere of
gases opaque enough to obstruct radiation from the interior layers
and to emit a continuous spectrum.
The brightness of a star's photosphere varies from 200 times
that of the hottest part of the carbons in an electric arc in the B type,
to 10 times in a G type, down to one-third in an M star. In the
case of the Sun, the energy which is being radiated is equivalent to
4,700,000 horse power continually falling on the earth's surface
per square mile. According to the theory of relativity, energy
and mass are interchangeable, so that one can legitimately speak
of a pound of heat just as a pound of iron. Viewed in this way
the Sun is radiating 4,200,000 tons of heat per second.*
The Sun is the only star which can be studied in detail. The
radiation which comes from the middle of its disc is found to be
more intense than from the limb. This is because the rays from
the regions of the limb start on the average from higher and cooler
levels ; the path of the rays from the same real depth below the
photosphere is longer at the limb than at the centre, thus causing
more effective absorption. This explains also the falling off in
brightness of the Sun's disc at the limbs and also the redder colour
corresponding to cooler temperature which is found there. "Darken-
ing'' at the limb exists also in the stars, as is shown by studies of
eclipsing binary systems.
* In fact, it has been calculated that the mass of the radiated stellar" energy
contained in the volume of space which can be studied with the 100-inch Mt. Wilson
reflector is equivalent to that of something like 1000 galaxies of stars.
62 Stellar Astronomy
Approximate temperatures for matter in the Sun's surroundings
can be calculated by Stephan's Law (see Appendix C). Just outside
the photesphere a body coated with lamp-black (and therefore a nearly
perfect absorber and radiator) would normally have a temperature
of about 5000K, while at a height above the photosphere equal to
the Sun's radius the temperature would be nearly 2900K. The solar
atmosphere and immediate surroundings are therefore necessarily
gaseous and the same remark will probably apply to all but the
coolest type stars, at any rate for the atmospheres and adjacent
matter, the temperatures being usually above those of volatilization
for even the most refractory materials. The phenomena of the
corona, chromosphere and spots are probably persent at least in stars
of type similar to the Sun, but there is as yet no means if studying
these for even the nearest or largest star. For a detailed description
and explanation of these solar features the reader should consult
such works as Abbot's 'The Sun."
ATOMIC STRUCTURE AND SPECTRA
To follow the modern ideas of the constitution of stellar atmos-
pheres as revealed by spectral analysis, it is necessary to have in
mind at least a simplified theory of atomic structure. In the last
forty years it has been shown that although the chemical atom is
generally a remarkably stable unit of matter, it is not indivisible,
as was thought by the pioneers of atomic theory. Pieces can be
broken off, so to speak, and these pieces are found to be identically
the same whatever element is concerned, and are taken to be charges
of negative electricity or "electrons." The atom as a whole is
electrically neutral and consists of a central body called the nucleus,
with a charge of positive electricity ; this nucleus containing nearly
the whole of the mass of the atom, surrounded by a number of nega-
tive electrons conceived of as attracted by the nucleus and moving
about it in orbits like a complicated kind of miniature 1 solar system.
The positive charge of the nucleus is exactly balanced \ by the nega-
tive charges of the electrons, making the result neutral electrically.
The nucleus is believed to be very small, less than 10~ 12 inch in
diameter, the outer electron orbits which correspond to the overall
size of the atom, being perhaps twenty thousand times as large
or about 10~ 8 inch in diameter. The nucleus is very probably built
up of positive units of electricity, "protons," and neutral units,
"neutrons," bound closely together, except in the case of hydrogen ;
the nucleus in that element is composed of a proton only.
In the normal atom the total charge of positive electricity in
the nucleus is exactly equivalent to the total negative electricity
in the satellite electrons, and one element differs from another in
A Star's Surface and Surroundings 63
the amount of this electricity, or therefore in the number of electrons.
This number (the "atomic number") for hydrogen is one, for helium
two, for lithium three, and so on up to 92 in the case of the heaviest
element found naturally, uranium.* Many atomic characteristics
may be explained on the theory that the electron orbits in the more
complex atoms are arranged in successive layers, or shells, each
composed of orbits larger than the last.
At high temperatures the atoms move about with great velocities,
colliding with one another and loading each other's electrons with
energy which raises them to higher level orbits temporarily. When
they leave these orbits to lower ones they simultaneously give out
pulses or quanta of radiation, the wave-lengths of which are related
to the difference in energy between the two levels. If an outer
electron is actually removed as a result of high temperature and
agitation among the atoms, the atom is said to be singly "ionised"
and multiply ionised if two, three, or more electrons are lost ; atoms
with electrons removed are positively charged as a result. What
used to be called "arc spectra" of substances are produced by
neutral atoms, the "spark spectra" by ionised atoms. There is
thus a definite difference of origin between the two resulting in
almost as great a spectral distinction as that between two different
elements. Indeed the spark spectrum of any element strikingly
resembles in general appearance the arc spectrum of the element of
next smaller atomic number. For example, the spectrum of ionised
magnesium is very like that of sodium. Since both have eleven
electrons outside the nucleus, and only one outside the completed
shells, the inference is obvious that the general nature of a spectrum
depends on the number of electrons remaining in the atom outside
the complete shells (see Fig. 8).
Atoms are ionised at suf ficently high temperatures in the absence
of electrical disturbance. As temperature increases in a gas the
average energy possessed by the atoms gets greater. A proportion
of the atoms (increasing with temperature) loses electrons, and if the
ionised atoms could be kept clear from these free electrons, ionisation
would go on until the atoms were all ionised and no neutral ones
left. Sooner or later, however, each ionised atom, or "ion" meets
and captures an electron, becoming neutral again.
High temperature and the consequent agitation among the atoms
favours ionisation ; high density, on the other hand, provides a
better chance of neutralisation of atoms owing to the atoms and
electrons being closer together. The proportion of atoms ionised
therefore depends on a balance between temperature and density,
* Elements of even higher atomic number (Neptunium and Plutonium, etc.)
have been produced artificially in atom-splitting processes.
64
Stellar Astronomy
\ '
- . \ \
'-- ' '
\ V
---
/
/
P
1
\
\
\
1
1 s
** ^N
\
4
4 *
\
/
\
1
*
\ \
\ x
/
/
B
' / ,'"'X \ \
t 4 ** t :
\ \
\
\
FIG. 8 IDEAL STRUCTURES OF ATOMS
(A) Ordinary atom of magnesium. (B) Ionised atom of magnesium. (C) Ordinary
atom of sodium. (Diagrammatic). The number at the centre represents the positive
electric charge on the nucleus. In all ordinary atoms it is the same as the number
of surrounding electrons. It will be noticed that ordinary magnesium differs from
ionised magnesium only in the number of electrons, and ionised magnesium differs
from ordinary sodium only in the central charge.
A Star's Surface and Surroundings 65
and the spectra are consequently largely dependent on these two
physical conditions.
The temperature at which ionisation takes place is different for
the various elements. It is comparatively low for such as calcium,
but it is very much higher for helium, greater energy being necessary
to remove an electron.
SIGNIFICANCE OF THE SPECTRAL SEQUENCE
The linear nature of the spectral sequence, i.e., the fact that
there is a definite series of gradations between the spectral types,
shows that there is probably one chief physical cause, others pro-
ducing merely minor differences. Differences in chemical com-
position as the primary cause of differences in spectra are definitely
ruled out since in that case the properties of the various elements
could vary independently giving, in stars of the same general types,
says strong iron lines and weak sodium lines, or the reverse ; but
this is never found.
This principal cause is undoubtedly temperature in the stellar
photospheres and atmospheres, which entails different degrees of
"excitation" or ionisation of atoms, with the consequent differences
in obsorption lines. Taking the series O, B, A, F, G, K, M, we find :
in O stars (temperature about 30,000K) most of the lines produced
by multiply ionised atoms, even helium being ionised. In B stars
(20,000K) and A stars (10,500K) the degree of ionisation diminishes
steadily. In Type F (7400K) lines showing the presence of neutral
atoms appear, while in Type G (5200K for giants, 5800K for dwarfs)
and K (4000K for giants, 4700K for dwarfs) the neutral or ordinary
spectral lines predominate. Finally, in M (3100K for giants,
3300K for dwarfs) bands due to molecular compounds appear and
the neutral atom lines are very strong.
ELEMENTS IN THE SUN AND STARS
Out of the 92 elements found on the earth there are 31 which
show no identified lines in the solar spectrum. It does not follow,
however, that these elements are really not present in the Sun.
Only a tiny fraction of the Sun's mass, that in the layer above the
photosphere (the "reversing layer "), produces lines in the spectrum
and there are also many elements whose principal spectral lines lie
in ultra-violet regions of wave length to which the Earth's atmos-
phere is opaque (wave lengths less than A 2900).*
* Scares refers to this as follows, "The amazing performance of atmospheric ozone
still goes on. Equivalent in amount to a thin shell three or four millimetres thick
at sea-level pressure, it still effectively blocks practically all radiation on the short-
wave side of A 2900."
66 Stellar Astronomy
Elements such as bismuth, radium, tantalum, thorium and
uranium, all with great atomic weights, are not represented by lines
so far identified, and this is probably due at least partly to their
being so low in the Sun's atmosphere as to be practically absent
from the reversing layer. There is therefore no sufficient reason for
believing that any of the elements are not present in the Sun.
The order of relative abundance of the twenty most common
elements shown in the solar spectrum is as follows :
Table 18
Hydrogen ' Nickel
Helium Sodium
Oxygen Aluminium
Magnesium Zinc
Silicon Manganese
Nitrogen Chromium.
Sulphur Cobalt
Iron Potassium
Carbon Titanium
Calcium Copper
Hydrogen and helium account for slightly more than 98J per
cent and oxygen and magnesium for one per cent, leaving less than
half of one per cent for the remainder in the table. Most stellar
atmospheres have much the same composition as the Sun's. Some
have a relatively large amount of particular items such as carbon,
strontium, silicon or sulphur ; but these are mainly stars either of
low or very high temperatures. The relative strength of the lines
of different elements in stars of the same general type is very similar,
and it is now considered that, in general, uniformity of composition
of stellar atmospheres is an established fact. The observations on
abundance refer only to the stellar atmospheres ; but as marked
differences of internal composition might be expected to affect the
atmosphere to a noticeable extent, it is unlikely that any funda-
mental internal differences exist as regards the elements which are
actually present.
PRESSURES IN STELLAR ATMOSPHERES
The temperature at which a spectral line reaches its maximum
intensity depends on the pressure in the atmosphere of the star.
It is possible to find this temperature by observation (see Appendix
C) and from it, and the observed line intensity, the pressure can be
calculated. By these studies it is found that theoretically the
A Star's Surface and Surroundings 67
pressures in the reversing layers should be extraordinarily low,
ranging from about one-thousand millionth of an atmosphere at
the top to one ten thousandth of an atmosphere at the bottom. The
average distance through which the atoms would move between
successive encounters (the "mean free paths") can be calculated
to be about 1300 yards and a twentieth of an inch respectively for
these two theoretical densities, which refer to the average on giant
stars, and should be increased for dwarfs where the atmosphere is
much less extensive, the pressure gradient more rapid and the total
range probably somewhat less. The smallness of these values is
due to the outward pressure of radiation, which in a star is capable
of supporting atoms against gravity. Strictly speaking, perhaps we
should not refer to "pressure in the reversing layer/' for pressure,
like temperature, has a gradient throughout a star. This gradient
is steep at the centre, but becomes smaller towards the star's surface,
where radiation pressure and gravitation are of the same size ap-
proximately, till in the tenuous outer regions there is no appreciable
pressure gradient, and atoms are almost floating freely. Such
tenuity makes it at first difficult to understand how the photosphere
of the Sun, for instance, is opaque and definitely bounded at the
limb. The explanation is to be found in the extraordinary opacity
of ionised gases. As ionisation is greater at the higher tempera-
tures, the opacity is strongest in the hotter stars being, for instance,
20 times as great in the atmosphere of the A-type star Sirius as in
the G-type Sun. In giant stars, with more diffuse atmosphere,
the opacity is less but there it is also greater in the giant of higher
temperature.
DIFFERENCES IN SPECTRA OF GIANTS AND DWARFS
The effective temperature of a giant is lower than that of a
dwarf, but the pressure in the atmosphere of the latter is re-
latively greater. The effects on ionisation of atoms and the spectral
consequences are therefore to some extent compensatory, but for-
tunately not in complete detail ; on this depends the possibility of
"spectroscopic" parallax determination (see Appendix D) K The
net residual result of these two factors is that elements in which
ionisation is easy are more ionised in giant stars than in dwarfs,
and those in which it is difficult are less ionised. This is what
is found in the case of the lines used for determination of absolute
magnitude and parallax.
There is good reason to believe that a greater quantity of gaseous
material can be seen through when density is low, i.e., comparing
a giant and a dwarf of the same temperature, the quantity of matter
above the photosphere in the former is greater, although at lower
68 Stellar Astronomy
pressure and density. Spectral lines are therefore stronger in giants,
and because of the lower density, sharper also. These character-
istics are exhibited most strongly in the c stars mentioned in Part I,
Chapter I.
BRIGHT LINES IN STELLAR SPECTRA
Hundreds of stars are known of types ranging from Oe (or O6)
to A2, and probably there are more than 350 brighter than about
8 m -0, in which this phenomenon is noted. The ratio of numbers
of stars with bright lines to others of the same spectral type increases
steadily from about one in eight (O type) to one in more than 6000
(A type) and the proportion is also highest amongst the stars of
brightest apparent visual magnitude. It therefore appears likely
that the more luminous stars tend most strongly to develop bright
lines, which is supported by their concentration to the Galactic zone,
a feature of distribution of the more luminous stars. The most
conspicuous lines are always those of hydrogen, with sometimes a
few lines of helium and various ionised atoms and in many cases
these bright lines vary in intensity. The Long Period variable
stars also shew variable bright lines of hydrogen, iron, magnesium
and silicon. The existence of bright lines brighter than the con-
tinuous background means that the star's atmosphere or gaseous
surroundings has a more intense emission in the particular wave
length than the photosphere. That this is due to the possession
of extensive gaseous atmospheres has now been demonstrated for
the hotter type stars mentioned. They appear to have envelopes
which are expanding, rotating or pulsating. The Wolf-Rayet
stars (O type with bright lines) have continuous spectra with wide
bright lines superposed ; and there is probably a high temperature
central star with a rapidly expanding gaseous envelope the material
of which is continually being restored by atoms ejected from the
star.
There are other bright line hot stars such as the P Cygni and
the B types, all stars of high luminosity. They also are con-
sidered to have large atmospheric envelopes. The B type eclipsing
variable ft Lyrae has, it is suggested, an extended envelope sur-
sounding the two components, which is produced and maintained
as the result of the passing of a stream of gas from the more massive
to the less massive component ; some of this goes round the latter
star and partly back to the primary, but the remainder goes right past
the primary and swings round to form a large envelope surrounding
the system. The bright lines in the spectra of the Long Period vari-
ables are probably due to periodic pulsatory outbursts of hotter in-
ternal gases. One important recent development is the discovery
that many close binary systems have tenuous rings of hydrogen and
A Star's Surface and Surroundings 69
other gases, which revolve round the hotter and more massive
component in the same direction as the binary system itself. This
has been found by study of the bright lines in the spectrum which
originate in this ring. The larger, cooler, less massive and less
dense component first occults that half of the rapidly rotating
edge-on ring which is approaching the observer, then the whole ring
is completely or nearly covered so that no bright lines, or much fainter
ones, are visible, the primary star being itself covered, and the
approaching side is then uncovered and the receding side alone is
covered. It has been found that in eclipsing systems in which
the eclipse is total, one out of every four examined shows observable
features due to a ring of the kind. There seems good reason to
believe that many single bright-line B-type stars have similar rings,
the existence of which is of course not discoverable in a similar way.
The binary systems described may perhaps be regarded as a further
stage in the development of a binary of the /3 Lyrae type.
THE WIDENING OF SPECTRAL LINES : STELLAR ROTATION
The lines in the spectra of stars are broadened by various factors.
There is a natural width due to the fact that the atoms do not
radiate at one sharp frequency, and there are Doppler effects of
toward and from components of movements of individual atoms
in a heated gas and of large-scale movements of masses of gas in the
stellar atmosphere, and also magnetic and electric effects. In
some stars there are broadenings caused by the motion to and from
the observer of the limbs of the star in its rotation. These indicate
much faster rotational speeds than the Sun's. For example,
Altair (a Aquilae), a main sequence star of about +1-7 absolute
magnitude appears to have surface limb velocities of 160 miles per
second ; and this is a minimum value as the axis of rotation is
probably inclined to the line of sight, no rotation effect being obser-
vable if the axis is in or near the line of sight between the star and
the observer, the maximum effect being if the axis is at right angles
to that line. The diameter of this star is about twice that of the
Sun, and the period of its rotation must be about nine hours
or less, or not as much as a sixtieth of the Sun's. The stars
for which rotation has been noted in this way are B, A and F type,
but practically none of G type. They are generally of about
+2 absolute magnitude corresponding to masses about twice that
of the Sun. The reason for this restriction of observed rotation to a
somewhat limited range of stars is not clear.
THE CONSTITUTION OF A GIANT STAR'S ATMOSPHERE
The lines in the spectrum of a star are the result of absorption
at different levels by gases of various temperatures and densities.
70 Stellar Astronomy
Some idea of the constitution of a giant star's atmosphere may be
got from study of an eclipsing binary such as Aurigae. Here
there is a K 4 supergiant of very large diameter (200 times that of
the Sun) and small density, which, every 973 days eclipses a B 8
companion less than a sixtieth of its diameter for a period of about
60 days. Before the eclipse the spectrum is a composite of the
two, but as the small star goes behind the large one, its light is
progressively absorbed by the latter's atmospheric envelope and the
spectrum changes ; the B star fades away, like a planet setting in a
smoky atmosphere and disappearing before it reaches the horizon.
The spectrum at each state of the eclipse of the smaller star thus
gives an idea of the physical conditions in each layer of the K star's
atmosphere. The sequence observed is as follows. At the be-
ginning when the B star is shining through the primary star's upper
atmosphere, strong, narrow lines of hydrogen and lines of ionised
calcium are photographed. The next lines to show themselves
are of ionised metals with the hydrogen and calcium lines strengthen-
ing ; and as the denser strata are traversed neutral lines of metals
become prominent. Eventually the light of the B8 star is extin-
guished and the K4 supergiant spectrum remains. As the smaller
star reappears gradually, the phenomena occur in the reverse order.
It should be noted that solar eclipses show that hydrogen and calcium
extend higher than any other element in the Sun's atmosphere also.
But perhaps the most remarkable thing about the phenomena
observed is the extraordinary slow rate at which the giant's atmos-
phere gets thinner. It is calculated that for a star like Aurigae
the force of gravity at its surface is such that the density of its
atmosphere should get greater inwards much more quickly than it
seems to. The Sun's atmosphere is also more tenuous than it
should be in the same way ; and the cause of the phenomenon is
still unknown in both cases.
A Star's Surface and Surroundings 71
REFERENCES PART II CHAPTER I
Author. Publications. Subject.
Miss Cecilia Payne, "Stellar Atmospheres," General.
Russell, Dugan and Young's "Astronomy/' General.
Stewart.
Abbot, G. "The Sun/' Solar.
Goldberg and Aller, "Atoms, Stars, and General.
Nebulae."
0. Struve, Observatory, 66, 208, "Gaseous Rings in close
Binary Systems."
PLATE 2 THK SPliCTRUM OF NOVA GKMINORUM, 1912.
Photographed at the Cambridge Observatory, March 16- April 29, 1912.
No. 1 Mar. 15
12 Mar.
Nos. 1 and 12 are stationary enlargements, showing the eomparison
spectra of iron.
On No. 2 are seen many broad bright bands and narrow absorption
lines. In Nos. 3, 4, 5 and 6 the bright and dark hydrogen pairs have a
wider structure and are doubled.
The stronger absorption lines in Nos. 2, 3 and 4 are mostly hydrogen
lines or enhanced lines of iron and titanium characteristic of a Cygni. In
Nos. 7 and 9 the strong absorption lines other than the hydrogen Hnes are
nitrogen, .oxygen and helium lines typical of y Orionis. These are more
displaced than the enhanced metallic lines, but with the same displacement
factor as the more displaced component of the pair of dark hydrogen lines.
r MI
;c, if
K: 1 1
llI^^ ' : ' {
(Harvard College Ohscrvatury*
PLATE 3. -THE CHIEF TYPES IN THE HARVARD SPECTRAL
SEQUENCE.
Nearly all the recorded stellar spectra belong to the types represented in this
photograph, or to intermediate types. The characteristic lines of the B type are
those of helium. The strong hydrogen lines in the A type spectrum gradually
become weaker in the succeeding types. The increasing complexity of the spectra
after the F type is due to the appearance of many lines of the metals. Class M
spectra are not well represented in the region represented here.
Photo by]
E. E, Barnard.
PLATE 4. THE GREAT STAR CLOUD IN SAGITTARIUS.
Taken with the Bruce 24-inch photographic doublet. Shows distant star clouds
in the direction of the centre of the Galaxy, and some luminous nebulosity and
dark obscuring clouds closer to us.
PLATE 5a PLANETARY, NGC 7293.
Photo by]
(Max. Wolf.
PLATE 5b SPECTRUM OF THE DUMB-BELL NEBULA, NGC 6853.
This is a gaseous emission spectrum on a faint continuous background.
PLATE 6- NEBULA ROUND THE STAR v SCORP1I.
Photographed by Professor E. E. BARNARD with a Six-Inch Portrait Lens.
The nebulosity surrounding the star stretches for some distance, but its illumination
is probably due to the star itself and possibly one or two other bright ones in the
vicinity. The dark halo round the star is a photographic effect, owing to the plate
used being unbacked.
rom }
PLATK 7a OBSCURINC; ri.OUDS IN
( " A strophysical Journal"
OPH1UCHUS.
.ATK 7b -THIC DOUMLIC Cr.USTJCU, NGC 869,884, IN PERSKUS
PLATE 8a THE E-TYPE NEBULA, NGC 3115.
C k HK
PLATE 8b SPECTRUM OF THE NUCLEUS OF THE SPIRAL NEBULA
M81, NGC 3031.
CHAPTER II
A STAR'S INTERIOR
AT first sight it might appear unlikely that astronomers could
find out much if anything about the interior of a star. Direct
study is confined to spectroscopic and visual survey of the
conditions at the surface, whereby we are able to ascertain the
chemical composition and to some extent the physical state of the
layers near the surface. It is here that the mathematical physicist
comes to the aid of the astronomer and assists him to penetrate,
so to speak, into the inside of a star. In an outline work of this
description, however, it is only practicable to give a general idea
of the theories of radiation and internal constitution, commonly
accepted, and this will now be done.
As a star is a mass of intensely heated and highly ionised gas,
it is possible, for a particular distribution of internal density, to
calculate internal temperature and pressure at any point. This is
because the properties of a highly-ionised gas are very close to those
of a "perfect" gas, where, subject to some modification due to
pressure of radiation, the following relationship holds :
4> m
T =
Rp
T being temperature, p pressure due to atomic, etc., movement
(gas pressure), m the mean ''molecular"* weight, R a constant which
is the same for all gases and p the density. From the assumed law
of density, pressure follows, while m cannot be much different from
unity at the temperatures concerned.
This value m is near unity because of the stripping from all atoms
of nearly every one of their satellite electrons. For instance, a
hydrogen atom is split into two parts, a proton and an electron, with
an average molecular weight of 0-5 ; helium is divided into three
with the value 1'33 ( =43) ; carbon into seven, value 1-71 ( = 127)
and so on. Even with the heaviest element, uranium (which is
probably very scarce in a star) the value is only 2-56 ( =238-f-93).
As the proportion of hydrogen (and helium) in a star is high, the
mean molecular weight is thus never much different from unity.
In the case of the Sun, the proportion of hydrogen is considered to b&
* The term "molecular" weight is used, although only atoms, electrons, etc.,
are concerned, as it gives the mass divided by the number of particles resulting
from ionisation.
74 Stellar Astronomy
about a third to a half and m is usually taken as 1 -0. In the stars
generally, the proportion of hydrogen is believed to vary from about
an eighth to three-fourths, and m from 1-3 to 0-6.
The detailed structure of the material of a star may be sum-
marised briefly as follows. The central regions consist of a mixture
of bare nuclei and dissociated electrons. As we pass from the
centre the temperature falls, and atoms which are more nearly
complete as regards their satellite electrons are encountered. Close
to the surface the atoms are probably quite complete except for some
of their outermost electrons. At the surface itself, especially in
the cooler type stars, molecules may even be found, such as those
of titanium oxide, zirconium oxide, cyanogen and magnesium
hydride, which appear in M, S, N or R type stars.
From the foregoing it will be seen that, for an assumed law of
internal density, it is possible to calculate the values of temperature
and pressure at all points which will give a condition of mechanical
equilibrium throughout the star's interior. The true law of density
is not easy to determine, but various models have been assumed
for the purpose of calculation to see if they satisfy observational
results.
The rate of escape of radiation through the star's photosphere
(the measure of luminosity) may be calculated, the flow being
carried almost entirely by radiation, with only a small fraction due
to convection. This rate depends on the opacity of the stellar
material which can be approximately derived on reasonable assump-
tions. These assumptions rest on the idea that absorption and
re-emission of the energy throughout the star are primarily due to
processes involving interaction between the ionised atoms and
electrons, which are more frequent the more of these particles there
are in a given volume (i.e., the greater the value p/m), but less likely
to happen when they are moving fast (T great).
In the calculation of the luminosity of a star the chemical com-
position is involved in two ways. The heavier elements mean
greater opacity, and the average molecular weight depends, in the
manner already indicated, on the constitution. But, except for
hydrogen, and to a lesser extent helium, the result is nearly inde-
pendent of the constitution, as the increase of average molecular
weights with heavier elements counteracts the effect of increased
opacity. The amount of hydrogen or helium makes a great dif-
ference and where calculations of stellar luminosity are made,
based on the proportions of these elements which seems reasonable
from indications found in the outer layers of the stars, the results
correspond fairly closely to the observed values.
Although various assumptions have to be adopted (which are all
tested by comparison with the observed properties of the stars) the
A Star's Interior 75
position may be broadly summarised by the following extract from
a standard work :* 'The characteristics of the stars depend upon
the simplest and most fundamental laws of nature, and even with
our present knowledge might have been predicted from general
physical principles if we had never seen a star.
The laws of gravitation, of radiation, of atomic structure, and of
simple gases suffice as a basis for such prediction
For bodies massive enough to shine, the radiation would increase
rapidly with the mass, but would change but little with the diameter,
the smaller bodies (for equal mass) being hotter inside, but letting
only a little more heat leak out to the surface, than the larger ones ;
this, however, would keep the surface much hotter, on account of its
smaller area."
RADIATION PRESSURE.
It is essential to take into account this phenomenon, which is of
considerable importance in the question of stellar radiation. It is
known both from theory and experiment that radiation actually
has mass and momentum and exerts a pressure on any object
obstructing it. A star's interior has atoms rushing about in all
directions, because of high temperature, with speeds up to hundreds
of miles a second, and the energy of such moving atoms constitutes
a great store of heat contained in the star. This is only part of the
store, however ; the radiative heat constitutes another portion.
Waves of radiation are hastening in all directions inside a star.
They leak very slowly into space, the history of their careers consist-
ing in alternate absorption and re-emission by atom after atom, a
process which might last for hundreds of years until the wave reaches
the surface of the star to be emitted thence, the original radiation
being in the form of y or X-rays, which are absorbed and re-emitted
as temperature radiation by the time they reach the surface.
In bodies heated to the temperature possible in a terrestrial
laboratory, the heat is practically confined to the molecular move-
ments, a negligible fraction being radiation. In a star, however,
the quantities are more nearly equal, and because of the pressure
effect mentioned above there is a force tending to assist the elas-
ticity or gas pressure in resisting the inward gravitational pull of the
material. This has to be taken into account in calculating tem-
peratures ; its neglect has the effect of making too high the result
from theory based on gas pressure only. The mathematical
physicist can calculate this radiation pressure which amounts to
about
* "Astronomy/ 1 Russell, Dugan and Stewart, ii., 894.
76 Stellar Astronomy
17 tons per square inch at 1,000,000K ;
170,000 tons per square inch at 10,000,000K ;
being proportional to the fourth power of the temperature.
The proportion of radiation pressure to the total is dependent on
the mass of the star, increasing with it in a way that suggests that a
maximum value of mass is determined by it, beyond which a stellar
body could not exixt.
LANE'S LAW.
Before proceeding to an outline of recent ideas of the anatomy
of a star and of its production of energy and possible lines of evolu-
tion, it is desirable that a short account of the relations referred
to as Lane's Law and frequently mentioned in the literature, should
be given. The first investigations of the probable distribution of
temperature inside a star were made in 1870 by J. Homer Lane,
followed later by Ritter, Lord Kelvin, Emden, Schwarzschild and
others. Lane reached the apparently paradoxical result that a star
by losing heat and contracting actually grew hotter. A star
shrinking under gravitation to half its linear size and remaining
built on the same model, or "homologous" (i.e., the densities at two
corresponding points at any two stages remaining the same fraction
of the mean density) would be eight times as dense, and the internal
pressures would be sixteen times as great as the overlying material
is attracted four times as strongly and its weight is held up on only a
quarter of the area. From the formula connecting temperature with
pressure and density, given earlier in the chapter, it will be seen that
the temperature in this example would be twice as great. By such
reasoning, Lane concluded that as stars get smaller they grow hotter
to withstand gravitation and resist collapse. In all the pioneer
work it was assumed that heat was transported from the interior
to the surface by conduction or by convection currents, so that the
inside was thoroughly stirred and followed a similar law of thermal
equilibrium to that in the lower regions of the earth's atmosphere.
As already stated, it is now clear, however, that most of the transfer
of heat is by radiation and that the flow of radiation determines
the distribution of temperatures. There will be a tendency to a
different kind of distribution owing to the presence of some con-
vection, which must exist as otherwise the action of gravity would
produce a settling down of the heavier elements towards a star's
centre, leaving very little but hydrogen to be detected in the outer
layers. Such convection as does exist will be either in the form
of slow circulation of matter throughout a star or of turbulent
mixture, and there appears to be evidence of both types ; in the
Sun, for instance, from the phenomena of sunspots, solar granu-
lation, and eruptive prominences.
A Star's Interior 77
THE INTERNAL STRUCTURE OF A STAR.
The problem here set is to find the interior distribution of den-
sities, pressures and temperatures, given the mass, luminosity and
radius of a star, and using our knowledge of gravitation, radiation
and properties of gases. A helpful idea of the distribution of density
can be obtained by study of the light curves and radial velocity
curves of eclipsing binaries from which rotational movements of the
lines of the major axes of the orbits (the lines of apsides) and ellip-
soidal distortion of shape in close pairs are occasionally derivable,
such features being governed by the interior distribution of the
stars' densities. This study has thus shown that there is a rapid
increase of density towards the centre which was to be expected
for other reasons. A recent estimate for the Sun gives a central
density more than 100 times that of water, and the figures in this
model for a fifth, third and half its radius from the centre are
approximately 40, 10 and 1 respectively. As a star is only in a
stable condition if the superincumbent mass at each point is balanced
by the gas elasticity and radiation pressures, it is possible therefore,
knowing mass, radius and bolometric luminosity (total energy
produced) to calculate pressure, density and temperature at any
given depth in the star. The central temperature is of high im-
portance, as it is believed that it determines the rate at which
energy is generated ; and the chemical composition, which, as has
been already stated, affects the transparency or rate of flow of
energy to the surface and also affects the central temperature, is
another factor of great significance.
As described in the first section of this chapter, practically all
atoms are completely ionised in a star's interior, and the average
molecular weight, which depends on the proportions of elements
present, has a bearing on the temperature to be found. For example,
a star made entirely of nitrogen and one made of hydrogen (where
the "molecular" weights of the ionised atoms would be 1-75 and 0-5
respectively), alike in mass, density and radius, would have different
internal temperatures, as the nitrogen particles would require to
move with greater velocities than the more numerous hydrogen
particles to hold up the superincumbent layers. Consequently
stars are hotter if composed more of heavy elements than of hydro-
gen. As a result the first estimates of central temperatures by
Eddington and others, being based on a smaller proportion of
hydrogen than is now considered correct, were higher, 40,000,000
or so against about half that figure.
The probable composition is estimated by a process of trial and
error using various assumed proportions of hydrogen, helium and the
heavier elements and calculating the rates of increase of pressure and
78 Stellar Astronomy
temperature towards the centre, and the central temperature and
luminosity. Different mixtures are assumed and tried out until
the calculated luminosity equals that observed. In the case of the
Sun with the average molecular weight taken to be 1-0, the central
temperature is found to be about 20 million degrees.
With the assumption that all main sequence stars have the same
interior pattern (the same model) it is noted that the central tem-
peratures (Tc) vary from about ten million degrees for those of least
luminosity (M type dwarfs) up to thirty million for the most luminous
(B and O type). The range in the amount of energy produced is
very much greater. For instance, a faint star of small mass (say
an eighth of the Sun's mass) emits energy at a rate per unit of mass
about a twentieth that for the Sun, while each unit of mass in a
star of high luminosity (say of 30 times or more the Sun's mass) may
radiate several hundred or even more than a thousand times as much
as a unit of mass in the Sun. Using the data of Table 3 for bolo-
metric magnitudes (which are the measure of total radiation), and
for masses, it is found that the average ratios between total radiations
and masses are as follows for main sequence stars, in terms of the
Sun; BO, 210; AO, 22 ; FO, 5 ; GO, 1-3; KO, 04 ; and MO, 0-06.
For giant stars the values are : FO, 41 ; GO, 23 ; KO, 26 ; MO, 59.
For supergiants the values may be as high as several thousands.
The high luminosity giant stars, if they are of the same interior
pattern of structure as those in the main sequence, appear to have
relatively low central temperatures ; for Capella, about six million
degrees has been computed and for the redder giants it is believed
to be as low as a million degrees.
To summarise what are perhaps the present general ideas. Main
sequence stars are composed of matter which appears to behave
as a "perfect" gas throughout, with radiation pressure not large as
compared with gas pressure ; central temperatures are of the order
of 10 to 30 million degrees with the mean temperatures about half
the central value ; the density at the centre is generally from about
10 to more than 100 (water = 1), the mean density is about a fiftieth
or less of this, and the radiation per unit of mass ranges from about
a twentieth in M type to 200 times in B-type, in terms of the radia-
tion of a unit of Solar mass. Ordinary giant stars have similar
general properties, but central temperatures are from less than
5 up to 10 million degrees, and central densities are much smaller
about a tenth as much ; while radiation per unit of mass is more
uniform than for the main sequence, averaging about 40 times the
value for the Sun.
A Star's Interior 79
THE SOURCE OF STELLAR ENERGY.
All authorities are now agreed that the old hypothesis of gravita-
tional contraction as the source of solar or all stellar radiation is
quite insufficient. The age of the earth has been demonstrated by
evidence based on geological and other facts and also on the uranium-
lead ratio of the older rocks, to be of the order of 2000 or 3000
million years which is much greater than the maximum admissible
(about 20 to 40 million years) for its parent body the Sun, on the
gravitational theory. An age of at least as long seems to be re-
quired for the Sun and most stars, and therefore a much greater
source of energy is apparently necessary for this prolonged period
than that of gravitational energy released by contraction. Outside
sources of heat, such as collision with meteoric matter, are also ruled
out (at any rate as the sole means), the crux of the problem being not
merely the provision for surface radiation, but also the maintenance
of an internal heat sufficient to prevent collapse under gravitation.
For instance, to keep the Sun in its present condition of equilibrium,
a temperature gradient of from 6000 at the surface to about 20
million degrees at the centre has to be maintained, and it is clear
that this cannot be effected only by supplying heat at the surface
or lower end of the gradient.
Further evidence of the existence of some internal store of
energy appears when we consider the rapidity of evolution required
by the contraction hypothesis in the case of a giant star ; Eddington
calculated that a star of 11-5 times the mass of the Sun would take
less than 31,000 years to develop from type M to type G and not so
much as 72,000 years from M to A. Observation shows that most
of the naked-eye stars are in the giant, or high-luminosity main
sequence, stages ; and it is not easy to believe that so many of these
stars have changed from red to white in such a short period. Another
indication of the internal store of energy is found in the case of the
Cepheid variables, which are thought to be stars pulsating in a
period depending on their densities. If there is no internal source
of energy, contraction under gravitation would necessitate an
increase of density entailing, for example, a shortening of the period
of variation in S Cephei of 17 seconds per annum, which is certainly
not the case.
It therefore appears clear that the stars must contain within
themselves the energy which is to last their lifetimes.
The store of energy must be sub-atomic, that is to say, related
to the constitution of atoms and electrons. Three hypotheses have
been suggested :
(1) Radio-activity, or the breaking down of more complex
atoms into simpler elements.
80 Stellar Astronomy
(2) The building up from simple elements of some of more
complex atomic structure.
(3) Mutual cancellation of protons and electrons, i.e.,
annihilation of matter.
The first of these three involves the postulating of elements of
higher radio-activity and greater atomic weights than those known
to terrestrial experience. Even if the Sun were made of pure
uranium the radiation would be only about half what is observed
and its life only a fraction of what seems likely to have been the case.
In the case of (2) what is involved may best be illustrated by the
transmutation of hydrogen into helium which may take place inside
a star. The atomic weight of the hydrogen atom, which is com-
posed of a proton and one electron, is 1 -008 (oxygen's atomic weight
being taken as 16-00). When a helium atom is formed from four
hydrogen atoms, an atom consisting of a nucleus of two protons
and two neutrons, and having two electrons revolving round it, is
built up. The atomic weight is 4-004, not 4 x 1-008 or 4-032, as
might be expected, since the mass of both hydrogen and helium
atoms is practically all contained in the nuclei. There has thus
been a loss of 0-028 or 0-7 per cent of the mass ; the energy corres-
ponding to this mass must have been set free during the process of
combination.
The third hypothesis, unlike the first two, depends on the tem-
perature and pressure. This is because it involves the idea of
collision between a proton and an electron so that their electric
charges cancel each other and nothing is left but radiation of ex-
tremely short wave length, which soon becomes transformed into
longer waves of heat. Such collisions will be more frequent at high
temperatures and densities. It was contended, however, that stars
under such circumstances would be explosively unstable and that
the hypothesis was therefore unsound. It was also urged that the
interior temperatures, high as they are, are much too low to cause
mutual annihilation of matter and production of radiant energy,
as in hypothesis (3).
Recently hypothesis (2) has received support which has made it
favoured, although details may yet require considerable revision.
A possible source of the energy has been revealed by intensive study
of nuclear physics. The account which follows is based largely
on lectures by Sir James Jeans.
Rutherford's experiments showed that the nuclei of the atoms
of light elements could be transmuted into nuclei of different chemical
properties by bombardment with a -particles. At stellar interior
temperatures, a -particles, which are merely the nuclei of helium
atoms, are probably quite common, heat having completely re-
moved the orbital electrons.
A Star's Interior 81
Atomic nuclei and the atoms generally are bombarded by a -
particles and other swiftly-moving projectiles protons, neutrons
and the like. These reactions are called thermonuclear, and they
are mostly very sensitive to changes of temperature, so that each
reaction may be associated with a definite critical temperature below
which it occurs only very slightly, but above which in torrential
amounts. This critical temperature depends greatly on the com-
plexity of the' nuclei involved and it is consequently lowest
500,000 to 1,000,000 for the simple reaction of one proton with
another. In this a deuteron (positive electron and two neutrons,
the nucleus of a "heavy hydrogen" atom) is liberated. This
ejected positron then encounters an ordinary negative electron
with mutual cancellation and the production of radiation ; and the
deuterons also react with protons producing helium of mass 3 and
radiation.
When these processes (which take place at the first stage of a
star's life following the initial gravitational contraction stage)
have exhausted their possibilities, the star contracts owing to the
lessening of energy necessary to keep it at its former size. This
produces central temperatures of 2 to 9 million degrees, when
protons may react with the nuclei of the light elements lithium,
beryllium and boron ; and later, there is further contraction and
increase in temperatures. When temperatures at the centre of the
order of 20,000,000 are reached, there is the reaction of a proton
with a carbon nucleus of mass 12. The combination forms a
nitrogen nucleus of mass 13, but this is only the first of a series of
processes, of what is termed the "carbon cycle." The nitrogen
nucleus may capture a second proton, becoming an ordinary nitrogen
nucleus of mass 14, and then a third proton, becoming a nitrogen
nucleus of mass 15. This may capture yet a fourth proton, but the
result is not a nitrogen nucleus of mass 16 ; it is usually a carbon
nucleus of mass 12, together with a helium nucleus of mass 4.
The foregoing description of the carbon cycle has omitted some
minor processes which have no effect on the final result. The main
events consist of the carbon nucleus absorbing four protons one after
the other, and thereby being moved along the sequence of nitrogen
isotopes* until this road comes to an end. In this way 4 protons
are bound together to form a helium nucleus ; all the other nuclei
are unaltered. The carbon has acted as a sort of catalyst.
This transmutation may not appear to have any relation to the
supply of energy for the star's radiation. But, as has been referred
to above for hydrogen, there is a loss of 0-7 per cent, of mass which
* Practically all elements have varieties of their atoms identical in chemical
properties, but differing in atomic weight owing to additional neutrdns in their
nuclei ; these are termed "isotopes."
82
Stellar Astronomy
goes off as radiation of short wave ("soft X-ray") to be absorbed
and re-emitted by the interior material as longer wave "temperature"
radiation constituting the star's luminosity.
The various stages described are considered probably to provide
the causes of luminosity of the stars as they increase in temperature,
the carbon cycle being that which applies to most of the range of the
main sequence. Presumably the reactions characteristic of lower
temperatures take place, in minor amount no doubt, away from the
centre of a star, at points where the temperature, although lower
than that at the centre, is sufficient for the thermonuclear reaction
in question that is if there is any of the required element left.
A number of difficulties have yet to be overcome in connection
with this attractive hypothesis and there will probably be modifica-
tions, some of them important, particularly in the case of the red
giant stars and hot temperature high luminosity stars.
In connection with these hypotheses of transmutation of ele-
ments, it seems possible that, during the past history of the universe,
the elements have all been built up from hydrogen with production
of radiation. The fact that those of larger "atomic" number
(see p. 63) are scarcer generally is consistent with this view, although
an observed smaller frequency of elements with odd atomic numbers
has not yet been given an explanation.
REFERENCES PART II CHAPTER II
A uthor. Publication .
A. S. Eddington, "The Internal Constitu-
tion of the Stars."
A. S. Eddington, "Stars and Atoms,"
Young's "Astronomy,"
Russell, Dugan,
and Stewart.
J. H. Jeans,
G. Gamov,
L. Goldberg,
and L. H. Aller.
A. Holmes,
J. Homer Lane,
Nature, 1943, Jan. 2,
"The Birth and Death of
the Sun."
"Atoms, Stars and
Nebulae."
Benn's Sixpenny Library,
American Journal of
Science and Arts, 1870.
Subject.
General.
General.
General.
"Evolution in
Astronomy."
General.
General.
"The Age of the
Earth."
"On the Theore-
tical Tempera-
ture of the Sun."
CHAPTER III
THE EVOLUTION OF THE STARS.
THE duration of life of a star is so long that observation of
successive stages in stellar evolution in an individual star
is quite out of the question ; even in the periods of geological
time it is certain from geological evidence that very little change
can have occurred in our Sun. Among the millions of stars, how-
ever, it is possible to select specimens which seem to represent each
stage of the luminous life of a star. As the elder Herschel re-
marked, in connection with the nebulae and clusters : "Is it not al-
most the same thing whether we live successively to witness the
germination, blooming, foliage, fecundity, fading, withering and
corruption of a plant, or whether a vast number of specimens,
selected from every state through which the plant passes in the
course of its existence, be brought at once to our view ? " The
task of the astronomer is to arrange in this manner the various
classes of stars for which observational data have been collected,
in some systematic scheme of evolution and orderly development.
A great amount of information regarding the physical character-
istics of the stars, mass, density, luminosity, colour, spectrum,
temperature and so forth, has been collected by various methods of
research. In Russell's words, modified to allow for subsequent
progress, the central problem of stellar astronomy may be formulated
as follows : From the existing data, and from all further data which
may be secured by methods new or old, to deduce a theory of stellar
evolution, that is, of the changes in the temperature, density, bright-
ness, spectrum, and other observable characteristics of a star with
the progress of time, and of the dependence of these changes upon
such factors as mass, composition, and angular momentum of
rotation. Such a theory must satisfactorily represent the observed
properties of the majority of the stars, and the relative abundance
of the different types.
In addition to the main problem there are those of the source of
stellar energy (dealt with in a previous chapter), the origin and
evolution of binary and multiple systems, and the causes of varia-
bility of luminosity.
FORMER THEORIES OF EVOLUTION.
These involved the idea that stars generally are losing heat and
falling in temperature, the hottest stars being the O and B type
and the coolest the M type. It seems probable that astronomers
84 Stellar Astronomy
formerly did not conceive that the stellar spectrum could be produced
by a body diffuse enough to act as a perfect gas and therefore sup-
posed that Lane's Law (see previous chapter) did not apply in regard
to increasing temperature, except perhaps in some very early stage
of development. Bluish-white stars, such as Rigel or Sirius, were
considered to be the youngest, born from diffuse gaseous nebulae,
yellow stars like the Sun or Capella being further contracted under
gravitation and at an intermediate stage, and the orange and red
stars were thought to be passing towards a stage of extinction.
Certain facts of distribution, such as the observed association of
white stars with gaseous nebulae, and the reverse for the redder
objects, were believed to be confirmation of this order of evolution.
A progressive increase of space-velocity in the order of falling tem-
perature was also taken as support, although it was not at all clear
why velocity should get greater as a star grew older. Both of these
observational data have received explanation on grounds quite
different from those which were first believed in, and which were
accepted by most astronomers well into the present century, leading
to the use of the terms ' 'early " and "late" for the hotter and cooler
spectral types respectively.
THE GIANT AND DWARF THEORY.
One or two investigators had, nevertheless, doubted these almost
universally accepted ideas of development. The first rational
theory, taking into account Lane's Law, was based on the hypothesis
of maintenance of heat by gravitational contraction. A diffuse
giant red star was supposed to contract and become hotter, obeying
perfect gas laws until the density became so great that the molecules
of the gas came nearly together. The central temperature would
then reach its maximum and the star would cool down in the liquid
or solid state to extinction, the surface temperature, although not
passing through as great a range, following a similar course. In
principle, this was a revival of the ideas of Lane and Lockyer,
adapting them to the observational data of "giant and dwarf"
classification, described in an earlier chapter, so that the stars
could each be classified as rising or falling in temperature. Those
on the rising branch of M, K, G, F, A, B sequence of spectra would
be large and of low but increasing density. Those on the falling
branch of the order, B, A, F, G, K, M, would be smaller and of still
higher and increasing density. This theory, revived by Hertz-
sprung and Russell about 1913, seemed to account for all the facts,
both in general and in detail. It appeared possible to show, for
instance, that the highest maximum surface temperature would be
reached only by the more massive stars, and this was found to be
The Evolution of the Stars 85
the case for the B type. It was also thought that the stage of
difficult compressibility and departure from behaviour as a perfect
gas would take place at about the density of A type (about a fifth
that of the Sun). The configuration of spectral types and absolute
magnitudes, shown in a diagram such as Figure 1, also received an
apparently satisfactory explanation. The division into two distinct
classes, one of great, but of much the same order of luminosity
throughout the spectral types and the other progressively fainter
towards the redder stars, was to be expected. As the spectra were
substantially the same, type for type, in the two groups, the con-
clusion was that surface brightnesses per unit of area were similar
and that the difference in luminosity must be due to difference in
area of radiating surface, one group of stars being of very large
dimensions, the other composed of considerably smaller bodies.
The diminishing size in the order M, K, G, F, A, B in the giants was
counteracted by an increase in temperature and surface brightness,
resulting in a fairly constant luminosity ; while in the dwarf or main
sequence branch the luminosity fell off because of diminishing size
and also decreasing surface brilliance.
It is now known that the theory, as outlined, is certainly not a
sufficient one. The giant or ascending series may present no in-
superable difficulties, but the main sequence branch is not to be
explained after the manner suggested by Hertzsprung and Russell.
As we have seen, the conditions of ionisation in a stellar interior
are evidently such that the perfect gas laws continue to be obeyed
at very much higher densities than are experienced terrestrially,
the stars behaving as though constituted of perfect gas even with
densities greater than those of ordinary liquids.
PRESENT IDEAS OF STELLAR EVOLUTION.
It can be stated that there are not so far any very generally
accepted ideas on this subject.* But for the very earliest stage of
stellar evolution most astronomers take the view, which has been
current during the greater part of the present century, namely,
that a star begins its life as an enormous gaseous spherical mass of
exceedingly small density slowly contracting under gravity. The
clouds of dust and gas in the dark obscuring nebulae have been
thought to be possibly the material of which stars are made ; and
it has recently been suggested that any condensations in them will
tend to become pressed into spherical shapes by the external pressure
of radiation from surrounding stars, and that this will be assisted
* One well-known astronomer has recently remarked, "Of our present jumbled
ideas of stellar evolution the less said the better." Another states that "he
knew all about stellar evolution in 1923, less in 1925 and nothing at all since 1930."
86 Stellar Astronomy
by gravitational attraction of the enclosed material, with the for-
mation of stars of low temperature and small density in a period
of time calculated to be of the order of 100 million years. The
interior temperature is then much too low to start up any thermo-
nuclear processes ; but when the advancing temperature gets as
high as say half-a-million degrees at the centre, nuclear reactions
commence which, by increase of temperature and of gas pressure,
prevent further contraction.
As stated in the chapter on the source of stellar energy, the first
reaction is likely to have been the one in which deuterons are in-
volved. Following the exhaustion of the material for this reaction,
contraction and heating up take place until, with central temper-
tures of from two to about nine million degrees, the reactions with
lithium or beryllium atoms begin, and then those with boron atoms.
As these elements get used up there are more stages of contraction
rapidly passed through ; the radiation is derived from the energy
of gravitational contraction until the central temperature reaches
about twenty million degrees when the carbon cycle begins. During
the stages before that cycle is active, it is considered that the star
shows spectra of M, K, G and F type giant stars in succession, until
arrival at central temperatures of ten to thirty million degrees
brings it into the zone of the main sequence (see Fig. 1).
The most usual presentation of these ideas proposes that the
deuteron reaction marks not only the ordinary red giant or super-
giant M and K stage, but also probably the Long Period variable ;
and that the lithium and beryllium processes which occur in the
G and F type giants and supergiants are taking place also within
the Cepheid type of variable. The processes described entail great
increase in generation of energy as they are reached at stages of
higher temperature. The consequence may be that in each case
there isja rather sudden expansionary state reached with accom-
panying ^cooling and therefore a temporary reduction of production
of energy which creates a somewhat unstable condition. In such
instances circumstances appear to be present which are likely to
produce pulsating long-period or Cepheid variable stars. The
boron reaction is the next stage of the F type or A type giants before
they reach the main sequence.
According to these ideas, which are due to Gamov and others,
a star is considered to pass through the stages described with not
much enhancement of its luminosity until, when it reaches the main
sequence branch, it passes upwards along the branch to the B type
or to the O type, according to its mass, while the hydrogen atoms
are being meantime used up in the carbon cycle.
When the hydrogen is exhausted there does not appear to be
any source but gravitational attraction for the star to use in the
The Evolution of the Stars 87
production of energy (although there is perhaps the possibility of
some other thermonuclear processes, not yet identified, at tem-
peratures over twenty million degrees') and the star drops greatly
in luminosity to the white dwarf stage, perhaps more than ten stellar
magnitudes fainter.
Modern theory suggests that a star in its last radiating stage
is a small body of extremely great density and it is considered that
the white dwarfs may be in this very late part of the life of a star.
Their average densities are of the order of 50,000 or more times that
of water with central densities perhaps hundreds of times again as
great as that. The central temperatures are, however, not thought
to be very high as compared with those of main sequence stars
probably of the order of ten million degrees. The enormous den-
sities are due to the stripped state of the atoms through ionisation ;
nuclei and electrons are jammed tightly together. As the volume
of an atom has been calculated to be actually 10 14 times the total
of the volumes of its constituent protons, electrons, etc., complete
ionisation would in theory permit of compression to densities of the
order of 10 14 times ordinary matter, which is much beyond the mean
densities attributed to white dwarfs. But recent theoretical de-
velopments have shown that there is a limit to the compression, and
that at that limit there will be no energy available for radiation at
all, the white dwarf being thus an intermediate stage between a
normal and an "invisible" star. As already stated, the source of
the energy radiated in the white dwarf stage is thought to be pro-
bably gravitational contraction.
There are certain difficulties in the way of complete acceptance
of these ideas of giant, main sequence, and white dwarf stars. Some
of these difficulties will now be referred to.
Stars of large mass radiate so much energy per unit of mass that
they must evolve and live much more quickly than lighter ones.
They must, therefore, have been born at a relatively recent date,
or have existed in a state of very low radiation and luminosity.
Stars of large mass and very low luminosity have not been found,
and a stage of small luminosity for such bodies,Tproviding a longer
life, does not therefore appear to occur.
It has been suggested that such stars may be able to collect
enough hydrogen from interstellar space for nuclear reactions,
enabling them to shine for a longer time. But this would appear
to require an interstellar medium (see Appendix G) of greater
density than seems likely ; and it is moreover contended that such
collection of hydrogen might lead to unstable or even explosive
results.
Another difficulty is found in the need for an explanation of the
spectral relationship in the components of double stars (referred to
88 Stellar Astronomy
in Part 1, Chapter III). On the once current Giant and Dwarf
theory of a star's evolution, this relationship appeared to be natural
if stars in pairs are of simultaneous origin, and if the star of smaller
mass evolves more rapidly. In that event the fainter star in the
giant stage would be "earlier" in spectral type and evolving more
quickly, and when the pair is in the main sequence the companion
would naturally be of "later" type and be ageing more rapidly.
It is true that it can be said that on the new ideas of evolution, pairs
on the main sequence may both be moving upwards on the branch,
the more massive and luminous star evolving the more rapidly,
but a binary pair on the giant branch has the secondary of an
"earlier" type spectrum (unless it happens to be on the main sequence
when it is occasionally of "later" type) and therefore evolving faster
than the primary on the new ideas, although it is less massive.
Then there is the difficulty presented by the co-existence of
young giants with apparently old dwarfs in clusters, the stars of
which are presumably contemporaneous in their origin.
Another matter requiring consideration is the fact that if the
cooler giant stars owe their energy to terrestrially very rare elements
such as beryllium, lithium and also boron, they would require to
have been initially in the possession of much more substantial
quantities than are found in the earth or Sun. Otherwise they
would go through the giant stage so quickly by exhaustion of their
supplies, that the proportion of the numbers of such giants and
supergiants to the number of main sequence stars would be even
smaller than it is.
It may also be remarked that although the course for giant stars,
which appear to join the main sequence at about G, is clear on the
sketch of evolution given above, the formation of the main sequence
branch of stars hotter than G type being thus explained, the origin
of the lower end of the branch is not so well accounted for. There
seem to be very few stars fainter than the giants, and cooler than
G type, whose joining the main sequence at the bottom end would
similarly explain what will really turn out to be the most crowded
part of the sequence, i.e., the part composed of M and K stars
(see Fig. 1). It appears, however, to be quite possible that the gap
between the giant and dwarf K stars is not real, and that many stars
of intermediate brightness have yet to be found (see Martin, Obser-
vatory, 66, 82) ; and it may even prove that further investigation
will show a number of intermediate stars in the gap between giant
and dwarf M stars (see Jackson, Observatory, 66, 374).
One apparent objection relates to the increase of a star's lum-
inosity (of the order of 100 times) supposed to take place in passing
upwards in the main sequence after that zone has been entered,
The Evolution of the Stars 89
which looks like a contradiction of the mass-luminosity relationship,
since the mass actually becomes less (although only very slightly)
in the process of energy generation now believed to be probable.
The explanation given for this is two-fold. In the first place, the
suggestion is made that the stellar universe may be as yet very
young, with most of its stars still in their earlier stages, when mass
and luminosity may be closely related ; secondly, it is considered
that the time spent in the upward passage through the main sequence
may be rapidly passed through so that very few stars would be
caught at that stage. It is believed that support is given to this
idea by the fact that such stars as have been noted to be abnormally
luminous for their masses are usually found in these higher ranges
of the evolutionary path.
Although, as has been remarked earlier, the hypothesis of col-
lection of interstellar matter, chiefly hydrogen, as a factor of im-
portance in stellar evolution, is not thought a likely one in view of
inadequate density of such material, it may be nevertheless worthy
of further consideration on the lines advanced by Lyttleton and
Hoyle. These investigators find that the rate of accretion of mass
by a moving star through a medium of the kind is proportional
directly to the density of the medium and to the square of the
star's mass, and inversely to the cube of its velocity ; and they
suggest that, in regions of space where interstellar matter may be
much denser than the normal, slow-moving stars of greater mass
than usual would result, and that in other parts of space the more
rapidly moving dwarfs would be formed. The greater velocities
and smaller masses of later type main sequence stars (see Table 5)
and the greater lengths of periods of later type dwarf binaries would
be consistent with this. The relation of spectra of the components
of binaries does not appear, however, to be capable of explanation
by this hypothesis any more than by that already discussed ; but
the presence of early "young" giants and later type dwarfs, pre-
sumably of contemporary origin, in a star cluster, might not be so
difficult to undertsand. It is worthy of remark that the idea above
described appears to be somewhat like an earlier one advanced in
1918 by C. D. Perrine, that the "stars of classes A, B and 0, the
planetary and irregular nebulae, the novae and perhaps the Cepheid
variables, are confined to the galaxy because there the matter is
sufficiently plentiful to cause an increase of energy, the energy of
the matter swept up being in excess of the energy lost by radiation.
The direction of spectral changes in such conditions is towards the
nebulae. In the regions (distant or near) where there is little or
no cosmic matter, radiation will overpower the energy received
from external sources and the direction of change will be toward
the late types"
90 Stellar Astronomy
Readers will appreciate, however, that the statement made at
the beginning of this section, to the effect that there is, as yet, no
well-established, or even very plausible, comprehensive theory of
evolution of stars, is a correct one.
THE ORIGIN OF BINARY STARS.
There are three chief theories of the origin of binary and multiple
systems, which may be stated as follows :
1. By the chance encounter of two stars, resulting in their
revolution about a common centre of gravity (the capture
theory) .
2. By a previous existence in the original dust cloud or nebula
of independent nuclei separated by a distance comparable
with those now observed in visual systems, and by sub-
sequent condensation about such nuclei.*
3. By division of a single star into two components through
centrifugal, and possibly occasionally tidal, fission, in-
fluenced by radiation pressure.
The first of these does not seem likely to have been frequent,
taking into account the great distances which separate the stars in
the stellar system. Calculations based on reasonable assumptions
show that only about once in three billion years will there be an
approach between two luminous stars within a distance equal to
the radius of Neptune's orbit (see Appendix H). Another point
apparently adverse to the capture theory is to be found in the
relations of the spectra of the components of physical pairs, pre-
viously mentioned, which show that the companions in giant sys-
tems are bluer and in dwarf pairs redder than their primaries. This
could hardly be expected to be a general rule if the origin of pairs
were by capture. Methods 2 and 3 are perhaps both valid, and
may be the normal ones for the relatively widely-spaced visual pairs
of multiple systems and for the close spectroscopic and eclipsing
binaries respectively.
It should be noted, however, that from the researches of Kuiper,
a common method of origin, which he considers cannot be that of
fission, is perhaps likely for both, as the distribution of lengths of
major axes of orbits appears when analysed to be really the same
for all classes of binary. Kuiper also considers that fission is not
possible for the accepted model of a star's internal structure, or
even for stars less concentrated towards the centre ; and also that if
* One of the earliest to suggest this was Laplace, without, however, any mathe-
matical basis : "The condensation of nebulae, consisting of two nuclei, will form
stars very near to each other, revolving the one about the other like to the double
stars." ("Syst&ne du Monde," 1796).
The Evolution of the Stars 91
fission were a method of origin the distribution of the ratios of the
masses of the components would be similar for all classes of binaries,
which it is not.
The early stellar evolutionary process for the individual com-
ponents involved in method 2 is well described in the words of
W. W. Campbell, one-time director of Lick Observatory. "It will
happen that there are regions of greater density, or nuclei, here and
there throughout the structure, which will act as centres of con-
centration, drawing surrounding materials into combination with
them. The processes of growth from nuclei originally small to
volumes and masses ultimately stupendous must be slow at first,
relatively more rapid after the masses have grown to moderate
dimensions and the supplies of outlying materials are still plentiful,
and again slow after the supplies have been largely exhausted. By
virtue of motions prevailing within the original nebular structure,
or because of inrushing materials which strike the central masses, not
centrally but obliquely, slow rotations of the condensed nebulous
masses will occur. Stupendous quantities of heat will be generated
in the building up process. This heat will radiate rapidly into space,
because the gaseous masses are highly rarefied, and their radiating
surfaces are large in proportion to the masses. With loss of heat
the nebulous masses will contract in volume, and gradually assume
forms more and more spherical. When the forms become approxi-
mately spherical, the first stage of stellar life may be said to have
been reached."
If the method of fission is after all a possible one, further evolu-
tiomof close pairs sometimes produced from the larger masses formed
as by method 2, might follow. This might then provide a satis-
factory explanation of the frequency of B and A types among the
relatively very close spectroscopic and eclipsing binaries ; the
cooler type giants have not divided in considerable numbers, while
the F, G, K, and M dwarf pairs are not observed in large numbers
owing to lower absolute brightness.
As a result of this process of division the companion stars might
be expected to be less dense than the primaries, being possibly the
result of expansion of smaller masses with less gravitational con-
traction forces, or composed of outer and more tenuous layers of
the rotating parent masses. In this connection it may be noted
that most eclipsing binaries are found to have secondaries less dense
than their primaries. On the other hand the writer finds, from
the data for visual binaries where the necessary information of
spectra, parallaxes, orbits and relative masses of the components
is known, that, on calculating diameters based on the appropriate
surface brightness, the densities of the companions are found to be
generally greater than those of the primaries.
92 Stellar Astronomy
It should be mentioned that close binaries may become wider
pairs as the result of tidal interaction, but not to so great an extent
from that cause as to convert the separations which would result
from a process of fission into the distances found in visual pairs.
Perhaps mutual perturbations and tidal reactions may be able to
assist in this, in the case of multiple systems which are the eventual
result of a binary pair first formed by method 2, followed by division
of one or both of the pair by method 3. Tidal or other separative
force may also help to account for the observed increase of average
eccentricity of orbit with length of period, but the chief cause here is
perhaps the effect of approaches of passing stars. These tend to
make orbits more eccentric, and pairs of longer period, being also
on the average most widely separated, are more likely to be "knocked
about" by chance approaches.
It must be clear to the reader that there is as yet no satisfactory
theory for the origin of binary or multiple systems. It may be
that some theory of a catastrophic nature will prove to be the correct
one. For instance, E. A. Milne has proposed a nova theory, accord-
ing to which there is a certain stage in the evolution of a star at
which internal instability sets in, resulting in a "collapsed" dense
state accompanied by the liberation of much gravitational energy.
This, in the case of a rotating star, might be followed by division
into two or more components which would not necessarily remain
collapsed, with consequent birth of a binary or multiple system.
Although this idea involves a stellar model of great central con-
densation, different from that generally favoured, some catastrophic
theory of the kind may perhaps be found applicable even with a
model of the gaseous description. Something of the sort seems
required to explain the existence of binary pairs like Sirius, composed
of a normal star and a white dwarf.
REFERENCES PART II CHAPTER III
Same as for Part II Chapter II, also.
A uthor. Publication . Subject.
G. P. Kuiper, Pub. Ast. Soc. Pac., "Problems of Double
47, 121. Star Astronomy/'
E. A. Milne, Observatory, 54, 142. "Dense Stars."
R. A. Lyttleton & Observatory, 63, 40. "The Evolution of
F. Hoyle. the Stars/'
CHAPTER IV
THE CAUSES OF STELLAR VARIABILITY
WE are not yet in a position to state that the causes of light
variation in a star are certainly known, except for the
eclipsing variables which are not really variable in a physical
sense at all. As Russell has remarked, it is probable that if we
understood the physical causes of light variation in the stars we
should have advanced a long way towards the solution of the pro-
blem of stellar evolution.
A successful investigation of the question involves a study of
all the data on the subject that can be collected. Meantime, it may
be noted that work with the photo-electric photometer by Stebbins
and others has made it appear likely that a sensible proportion
of all the stars are slightly variable.*
A connection between luminosity and variability, and also
between redness and instability of light has been shown to exist
by Huffer from studies of 104 red giant stars by means of the photo-
electric photometer.
His results were as given below :
Table 19
Absolute Magnitude.
- 4-3 to - 1-2
- 1-1 - 0-5
-0-2
+ 0-1
- 0-4
-0-1
+ 0-2
+ 0-7
Spectrum.
MO
Ml
M2
M3
M4
M5
M6
Percentage Variable.
100
45
41
24
Percentage Variable.
7
24
30
64
100
67
* An enquiry made by Mrs. H. Shapley in 1915 led her to conclude that about
3 per cent, of the stars visible to the naked eye were known to vary.
94 Stellar Astronomy
This inconsistency of light in giant diffuse stars suggests an
unstable physical condition for the most luminous and reddest and
the idea finds support in the observed quasi-periodical variability
of the diameters of Betelgeuse and Ant ares. In the latter, a
diameter of (T-026 has been observed at Mt. Wilson with the inter-
ferometer, as well as the 0"-040 given in Table 1.
Stars of the main sequence are believed to be constant in light
over ordinary periods of time. It is interesting to note, however,
that in 1934, Sir G. C. Simpson (then Director of the Meteorological
Office) advanced a theory, to account for the Earth's Ice Ages,
that the Sun (a main sequence G type star) is variable with a range
of about O m -4 in a period of the order of 100,000 years, and that it
is now at about minimum.
With regard to the possibility of any secular change in the light
of the stars generally, a statistical investigation has been made by
Lundmark of the magnitudes of more than a thousand stars in the
Star Catalogues of Ptolemy (second century), Al Sufi (tenth century)
and Tycho Brahe (sixteenth century). Comparing the values with
modern photometric magnitudes and also grouping the stars accord-
int to modern colour indices he has reached the conclusion that
there has been no significant change in brightness or in relative
colours* in the period covered, or in the colour sense of the human
eye as has sometimes been suggested. He also concludes that the
reported increases or diminutions in brightness of certain stars are
all due to errors in the earlier estimates. It may be observed,
however, that the mean systematic error of these old naked eye
estimates as compared with the Harvard photometry values is less
than a fifth of a stellar magnitude.
A general survey of the statistics of periodic variables shows
three well-defined maxima in the numbers, grouped about the
following periods a half-day, a week (not so marked), and 300 days.
The first two are generally classified together as the short-period
variables and the third group as the Long-Period stars.
The short-period variables are the "cluster" and "Cepheid"
types, although the latter name is sometimes used to include both.
The characteristics of their light curves and also the changes in their
radial velocities and spectra have been described in the section on
Variable Stars. The relation between their periods and luminosi-
ties, and their distribution with reference to the Galaxy, have also
been referred to.
The causes of Cepheid variation have been the subject of much
investigation. The simultaneous changes of brightness, spectrum
The red colour attributed to Sirius by some classical writers was probably due
10 wie fact that in Mediterranean regions, selective atmospheric absorption makes it
red at rising and setting and reddish for some time after rising or before setting.
The Causes of Stellar Variability 95
and colour make it appear that the physical cause is concerned with
variation in effective temperature of the surface, however effected.
The usual shape of the light curve indicates that rotation of a star
with parts of its surface brighter than others cannot be involved,
and also shows that eclipses of one component by another are not
the explanation. All binary theories seem effectually ruled out.
First, because no spectral lines of a secondary have ever even been
suspected, and second, because consideration of the probable
dimensions of the systems shows that the stars themselves must
be larger than the orbits in which the components would move.
The greatness and rapidity of the light changes seem to indicate
a periodical transformation of heat energy to some other form of
energy and back again, little being lost by radiation in the com-
paratively small time interval concerned. The form of energy
suggested is gravitational energy, and the theory developed in this
connection is that of pulsation in the star, whereby a periodical
expansion and contraction takes place under the opposing forces of
gravitation and gaseous elasticity. The period of such a pulsation
should be inversely proportional to the square root of the density
(see Appendix K) and it should also depend on the law according to
which the pressure of the gas gets greater when the volume is
diminished.
THE PULSATION THEORY.
There has been remarkable progress in development of a theory
explanatory of stellar variation (Cepheid and Long Period) as due
to pulsation.
In Cepheids, differences in radial velocities between the lines
produced by high and low levels of the star's atmosphere are found.
The main effect is a lag in the phase of pulsation of the higher levels
behind that of the lower ones. The explanation proposed (first
advanced by M. Schwarzschild) is that there is a periodic wave of
:ompression of the star's material moving up from below the photo-
sphere into the higher atmospheric regions.
In the case of a Cepheid of short period (less than a day or two)
the maximum velocity of approach shown by the displacement of
the lines of the spectrum is at or near light maximum. In stars
rf longer periods this velocity of approach comes after the light
maximum at a progressively later phase, until in a Cepheid of long
period the star is at its brightest when the velocity curve indicates
that it is smallest, agreeing roughly with the original pulsation
theory. But in the case of the Long Period variable where the
velocity maximum occurs at light minimum, the star appears to be
lottest at too early a stage.
96 Stellar Astronomy
The difficulty of the original pulsation theory, as accounting
for the phenomenon of Cepheid variation, was that the star was
taken to be expanding and contracting with all its parts moving
outwards and inwards at the same time. The theory of Schwarzs-
child altered this by introducing the idea of an outer region of the
star in which moving waves of compression progressed outwards
to the surface. The central body of the star pulsates as one body,
but there are compressional waves in the outer parts passing out-
wards to the photosphere and from there into the star's atmosphere.
What is observed in light variation and radial velocity therefore
depends on the phase the wave is in at the radiating surface, i.e.,
at the photosphere. The maximum compression occurs at the
time of greatest speed of approach to the observer, that is, at the
moment of the greatest temperature and light maximum. For the
Cepheid with a steeply rising light curve, the maximum and mini-
mum of light both come when the star is decidedly smaller than its
mean size, and the total light variation is due to change of tempera-
ture and of surface brightness only. The alterations in diameter
modify the shape of the light curve.
The increase in the delay between maximum velocity of approach
and light maximum with length of periods is explained as follows :
The longer the period is the larger the star and the more extensive
its atmosphere both absolutely and relatively to the size of the star.
From this it follows that the time taken by the wave in moving
through the atmosphere is not only longer but also is a greater
fraction of star's period of variation. There should be a photo-
spheric velocity curve with maximum speed of approach towards
the earth (i.e., maximum speed outwards from the star) coinciding
with maximum light, this being at the moment the compressional
wave reaches the photosphere. But if the level of effective absorp-
tion is far above the photosphere, because of extensive atmosphere,
then there will be a lag in the velocity curve. In the Cepheids of a
few days' period the layer which absorbs is probably close to the
photosphere, but with greater periods the absorption takes place
at greater and greater heights, and the maximum speed of approach
to us occurs at progressively later stages relatively to the time of
maximum light. The extreme case in a pulsating variable is for the
Long Period class, where the delay is at its greatest.
Formerly it has been thought that the absorption lines in a star's
spectrum are produced close to the photosphere ; but this is evi-
dently not always so, at least for a pulsating star ; and it is now
considered that in the case of a Long Period variable star the velocity
curve from the bright emission lines is what has to be used in con-
The Causes of Stellar Variability 97
siderations of the theory of pulsation. In fact, if the information
for temperature and bolometric magnitude is used to compute the
star's diameter and its curve of light variation, and this is compared
with a similar curve based on the absorption line velocities, it is
found that there is no correspondence in phase. On the other hand,
if the velocity curve of the emission lines is taken, the phases are
found to agree with those of the calculated curve.
This revised pulsation theory, therefore, appears to give at least
a good foundation for explanation of the observed phenomena,
both for Cepheids and for Long Period variable stars. The question
as to whence comes the energy to maintain the pulsations has
not yet received a satisfactory answer, although variations in
connection with the production of stellar energy, referred to in a
section of the chapter on the subject, seem at least worthy of con
sideration (see page 86).
LONG PERIOD VARIABLES.
As stated earlier, these stars appear to be pulsating giants of
large diameter and low density and surface temperature, with
visual magnitudes at maximum ranging from about +0-5 to -2-5.
Estimates from the spectra give surface temperatures of about
1800 to 2300. Owing to the great effect on visible radiation of
change of temperature at this low range, the change in light (an
average of about five magnitudes) is very much greater than the
alteration to total radiation or bolometric magnitude ; this is about
one magnitude only. The meaning is that the Long Period variable
stars really alter very much less in their total output of energy than
they do in radiation of the wave lengths that can be photographed
or are effective visually. The observed discrepancy is partly due,
however, to excessive absorption by titanium oxide bands at mini-
mum light. It is thought that it may possibly also be partly a
consequence of the formation of cloudy veils of liquid or solid
particles condensing from the star's upper atmosphere ; such a
phenomenon might provide an explanation of the irregularities in
the amplitude of light variation as well.
IRREGULAR VARIABLE STARS.
Of the known irregular variable stars, all but those connected
with the Orion nebula and the T Tauri type seem to be giants of
* The original level of the bright line emission appears to be below that of the
absorbing (reversing) layer which produces the dark lines of the spectrum, suggesting
that "at a certain phase in the light cycle, masses of superluminous gas may appear
in or near the photosphere and, as the cycle advances, rise through the reversing
layer until they disappear at an upper level." (Merrill, Pub. Ast. Soc. Pacific, 1946,
October, p. 305).
98 Stellar Astronomy
large size and small density. The suggestion sometimes made
that the variation is caused by opaque interstellar clouds drifting
between us and the star may be the correct explanation for the faint
Orion variables, which seem to be probably, but not certainly,
dwarf stars they may be heavily obscured giants in or near the
nebula, or lightly obscured giants at a greater distance beyond.
The same hypothesis is not so suitable for the giant irregular variables
however, as there are spectral changes in these stars which suggest
some intrinsic cause. For instance, R Coronae Borealis, which
remains for years at about the sixth magnitude and rapidly drops
several magnitudes occasionally for an interval that may be short,
or may be several years, has a spectrum of GO type when at its
brightest, but shows enhanced metallic lines at minimum. Recently,
it has been suggested that the drop in its light is caused by clouds
of condensed carbon vapour in its atmosphere.
SS Cygni also has a variable spectrum with wide dark bands
due to hydrogen at maximum, but a bright O type spectrum at
minimum. The variation of a Orionis appears to be connected
with pulsatory changes in its diameter, as shown by interferometer
measurements at Mt. Wilson. The Veil theory of formation of
obscuring clouds in the star's atmosphere has been suggested for
giant red irregular types ; also that spots of the solar kind, but on a
gigantic scale, are responsible for the variation in light.
NOVAE.
The great suddenness and the enormous increase of light charac-
teristic of a Nova or Temporary Star, when considered in con-
junction with the spectra, seem to show that an explosive outburst
is concerned. For example, the increase in light output for five
conspicuous Novae of the twentieth century ranged from 1 1 to 13 J
magnitudes with a mean of 12| magnitudes, corresponding to a
hundred- thousand-fold change.
Several explanations have been put forward. These may be
divided into two types according as they account for the explosion
as due to outside influences or to causes chiefly intrinsic in the star
itself. The simultaneous presence of the bright line and absorption
spectra led to the idea of two stars colliding, or passing very close
to one another with resulting violent outbursts due to tidal dis-
turbances. This theory would account for the suddenness of the
phenomenon and also for the more gradual fading in the light. In
one form it would involve the hypothesis of one star with an absorp-
tion spectrum moving towards us with great velocity and another
star with a bright line spectrum moving from the Earth at a small
speed. This coincidence seems an extremely unlikely one and
The Causes of Stellar Variability 99
moreover the frequency of appearance appears to be much too great
when the enormous distances between the stars, even in Milky Way
regions where Novae are most frequent, is considered. (See
Appendix H).
Another objection is to be found in their return in the course
of a few years to their former level of brightness, a most unlikely
occurrence to any bodies concerned in a violent collision at stellar
velocities.
Practically all theorists have therefore of late favoured an
explanation of the phenomena of Novae as due to a sudden de-
velopment, or release, of sub-atomic energy somewhere beneath a
star's surface, causing violent expansion at speeds beyond gravita-
tional control. The star's surface layers swell but keep on radiating
like any other stellar surface, and they give a continuous spectrum.
This enlargement of radiating surface causes a very great increase
of the star's apparent brightness ; but later on the expanding shell
becomes thinner and transparent, and is then excited to shine more
strongly by the very short wave high energy radiations from the
inner regions of the central star, exposed by the loss of its lower
temperature surface material. The result much exceeds the light
of the star itself, which rapidly decreases, the bright lines or bands
from the moving envelope being very strong while the continuous
spectrum from the star is practically unobservable. As the ex-
panding shell thins out and dissipates in space, the bright lines fade
and disappear, leaving the continuous stellar spectrum of the star
at its eventual brightness. The spectral phenomena described in
an earlier chapter are in the main due to the moving shell ; this
produces absorption lines, displaced towards the violet where it
comes between the star and the observer, and bright broad lines or
bands from the other parts which have motions in all directions
with respect to the observer, varying from zero to large velocities of
approach and recession. It is suggested that there may be a zone
of instability under the surface of such stars as "explode" into
Novae. The slightest disturbance to a zone of the kind, either
from inside or outside of the star, would upset the state of convective
or radiative equilibrium of the star's interior and cause a sudden
outburst of radiation.
The idea has been advanced by McLaughlin and others that
Novae may be the result of repeated outbursts of a star. Several
Nova-like stars (e.g., T Coronae Borealis) are known which repeat*
the interval between the great increase in brightness being pro-
* The list of recurrent novae now includes T Coronae Borealis (1866, 1946),
RS Ophiuchi (1898, 1933), T Pyxidis (1890, 1902, 1920, 1945), Nova Sagittae (1913,
1946), Nova Sagittarii (1901, 1919), and U Scorpii (1863, 1906, 1936). These six
stars are possibly a group connecting the SS Cygni and U Geminorum type variables
with normal novae.
100
Stellar Astronomy
portional to the range of light change, and it is thought possible
that those of much greater range may really repeat at intervals of
several thousand years. If the phenomenon is not a recurring one,
to a particular kind of star, then it appears likely that most, if not
all, stars pass through a Nova stage, judging by the number which
appear and by the age of the stellar system.
The great gap between the luminosity of an ordinary Nova and
that of a Supernova, and the much greater radial velocities of
emission of the latter, have suggested that the causes are of a
different nature. The possibility that a collision of two stars may
be responsible for the Supernova has been discussed. Although
their frequency is of the order of a ten-thousandth that of a normal
Nova, it would seem (see Appendix H) that their frequency, if due
to collision, would be much less than every 600 years for an average
galaxy as estimated by Zwicky, or that suggested by the 1054,
1572 and 1604 Galactic Supernovae.
REFERENCES PART II CHAPTER IV
Publication.
'The Internal Constitution
of the Stars."
A. S. Eddington, "Stars and Atoms"
Russell, Dugan and Young's "Astronomy."
Stewart.
"The Story of Variable
Stars."
C. & S. Gaposchkin, "Variable Stars."
P. W. Merrill, "The Nature of Variable
Stars."
Popular Astronomy,
49, 292, 457.
Astrophysical Journal,
88, 529.
Author.
A. S. Eddington,
L. Campbell and
L. Jacchia.
D. B. McLaughlin,
F. Zwicky,
Subject.
General.
General.
General.
Variables and
Novae.
Do.
Do.
Novae and
Supernovae.
Frequency of
Supernovae.
Part III The Stellar Universe
CHAPTER I
THE GALACTIC SYSTEM
EVEN a cursory naked eye examination of the sky shows a
very evident tendency to grouping amongst the stars. Such
asterisms as Ursa Major, Orion and Scorpio, although loose
aggregations, seem closer together than random distribution would
produce ; and there is a gradation from these through clusters like
the Coma Berenices stars, the Hyades, the Pleiades, Praesepe, on
to those clusters which are revealed only by telescopic search. Of
greater structural importance may be many large and bright patches
in the Milky Way regions of the sky often several degrees in extent,
which a good telescope or a photograph of long exposure shows to
be composed of myriads of faint stars. On the other hand, their
outlines are perhaps often largely due to the effect of the obscuring
clouds found throughout galactic regions. The star clouds in
Sagittarius, Cygnus, Scutum, Argus and Auriga are the most pro-
minent of these bright aggregations.
As regards the physical connection of the stars in asterisms or
clusters, such as are referred to above, it is of interest to note that
in 1767 the Rev. John Michell showed that the probability against
their being chance dispositions is very great. For example, he
found in the case of the six brightest Pleiades, that the odds are
half a million to one that, out of the 1500 naked-eye stars as bright
as or brighter than they are, no six stars would be found within the
area of the sky occupied by them.
The Milky Way or Galaxy is in appearance a luminous belt of
stars of irregular outline and width, the centre line of which is
approximately a great circle of the sky. This centre line passes
the celestial North Pole at a distance of about 30, and runs through
Cassiopeia, Perseus, Auriga, Monoceros, Argo, Crux, Centaurus,
Scorpio, Sagittarius, Aquila, Cygnus and other constellations. It
is divided into two streams for about a third of its length by an
irregular dark band, the brighter of the streams passing through
Scorpio and Sagittarius and joining the other at Cygnus. Its width
varies considerably, from about 10 to 40, and the brightness is
also different from one point to another. It is at its brightest in
the star clouds of Sagittarius, but is also prominent in other regions
102 Stellar Astronomy
such as Aquila, Cygnus and Centaurus. In the areas of average
brightness, such as those in Cassiopeia, Perseus or Monoceros, its
light is equivalent to that received from about four to five stars
of the sixth magnitude per square degree.
Readers may be interested in the results of the work of the
Belgian nineteenth-century astronomer Houzeau. Observing in
Jamaica, he made careful drawing of the Milky Way and estimates
of its brightness to the naked eye. Of the seven brightest regions
only one (4 east of a Cygni) is north of the celestial equator. The
seven are as follows, roughly in order of brightness : 7 west of
Sagittarii ; 3 north of /z Sagittarii ; 2 north of y Sagittarii ; 3 east
of a Scutum ; 6 south of a Scutum ; 6 west of Arae ; 4 east of a
Cygni. It will be noted that the three brightest are near the
galactic centre in Sagittarius. Houzeau also recorded a number of
regions somewhat less luminous than these seven. In this next
grade of brightness there were twelve, and of these the following
seven are in the northern celestial hemisphere ; 3 north of /? Cassio-
peia ; midway between 8 Cassiopeiae and y Persei ; 3 west of 77 Gem-
inorum ; 3 east north east of /? Cygni ; 5 south west of y Cygni ;
9 east north east of a Cygni and 4 north west of y Aquilae. All
these positions are in or near the brightest Milky Way regions, as
shown in modern small-scale photographs.
According to van Rhijn's measures the luminosity of the Milky
Way zone is not very much greater than that of the other parts
of the sky, being less than twice as luminous on the average ; but
if that part of the general illumination of the sky*, due to permanent
aurora and zodiacal light, could be eliminated, the ratio of average
galactic to non-galactic brightness would be several times increased.
The observed centre line of the Milky Way is not a great circle,
but is about 1 south of the great circle which is taken as the galactic
equator. The galactic poles are in R.A. 12 h 47 m Declination + 27,
and R.A. O h 47 m Declination - 27, the former in Coma Berenices,
the latter in Sculptor. Galactic latitudes are measured from the
great circle of which these are the poles, and longitudes are measured
eastward from the point of intersection or ascending node of the
galactic equator on the celestial equator at R.A. 18 h 40 m , situated in
the constellation Aquila. Such co-ordinates are of great importance
in investigations of the structure of the universe, as the galactic
plane is evidently the fundamental plane of reference for our stellar
system, corresponding to the ecliptic in the solar system.
* The total general illumination of the night sky is caused by diffused Aurotal
and Zodiacal light plus stellar light and a faint background of starlight reflected
from interstellar matter. It is estimated to be about equal to that produced on
a surface by a candle, distant 185 feet, i.e., by a star about three times as bright
as Venus at its brightest.
The Galactic System 103
In Part I, Chapter II, the question of the concentration of stars
of different types with reference to the Galaxy has been dealt with,
from the point of view of galactic latitude and longitude, in Tables 8
and 12 respectively, and on pages 34, 35. The concentration in
latitude has long been recognised as suggesting a grouping in space
in the form of a flattened disc.
THE GALACTIC NEBULAE.
Leaving aside for the time being the consideration of the structure
of the galactic system, it is desirable to consider the various forms
of nebulae and clusters which are known to be scattered throughout
the system of the Milky Way. It was formerly frequently remarked
that there seems to be a clear distinction between nebulae situated
in Milky Way regions and those elsewhere in the sky. This was
hinted at by the classifications of the Herschels and is now accepted
by all astronomers. The galactic nebulae, comprising only a small
percentage of the many thousands of nebulous objects known, are
divisible into principal types as follows :
1 . Planetary.
2. Diffuse :
(a) Luminous.
(b) Dark.
Of the planetary nebulae, there are about a hundred and fifty
known. Their appearance is as round or oval masses of faint
nebulosity, very 'of ten with a central star and with a considerable
amount of detail, sometimes consisting of concentric shells of light
occasionally showing as a ring formation, which has a star in the
centre and is not completely dark.
R. H. Stoy has proposed a classification into six groups : a,
irregular, with several bright condensations and with or without
faint outlying nebulosity ; /?, a bright ring or sometimes two rings,
the outer broken and fainter, superposed on a fainter disc with a
more or less conspicuous centre star ; ^ , small and disc-like, with
uniform brightness or brighter towards the centre, the central stars
when visible being faint ; 8, stellar in appearance, but known from
spectra to be planetaries ; e, three specimens known from their
spectra as the "hydrogen nebulae," with conspicuous central stars ;
0, relatively large and with low surface brightness, but conspicuous
central stars. He thinks that judging by apparent galactic con-
centration, group 6 are nearest, next are group y, and furthest away,
group 8.
The sizes of the planetaries range from a few seconds up to 12'
in diameter, but most of them are less than about 1' across. The
104
Stellar Astronomy
central stars are generally fainter than tenth magnitude photo-
graphically, and being evidently very hot and bluish in colour are
still fainter visually. The fact that the apparent diameters are
smallest in general for those nearest the Galaxy suggests that they
may be roughly of the same order of size, the more remote ones
having low galactic latitudes as a consequence of their distance.
On this assumption, statistical investigation, using apparent angular
diameters together with proper motions, has provided an idea of
distances. These appear to range from about 1500 light years to
as much as 50,000 light years, mostly lying between 3000 and 30,000
light years. For the most part inside a stratum 10,000 light years
thick, the centre of which is approximately the galactic plane, they
are, as is shown earlier on Table 12, noticeably concentrated towards
the centre of the Milky Way system in Sagittarius. The following
table gives distances and dimensions of a number of these objects,
derived as above described, and therefore not likely to be more than
approximate.
Table 20
Designation.
NGC 1535
NGC 6543
NGC 6572
NGC 6826
NGC 7009
NGC 7027
NGC 7662
1C 418
Distance
(light years).
5600
3500
4000
3400
3000
7000
3900
5900
Radius
(astronomical units).*
15,500
10,800
8,600
13,600
8,400
10,600
10,000
10,800
Temperature.
10,000 K
6,000
9,200
7,200
9,500
9,500
10,300
6,800
(* Astronomical unit = radius of Earth's Orbit).
The fourth column gives the temperatures of the nebulae them-
selves derived from their spectra. The ultra-violet radiation of the
central stars, after absorption by the atoms of the nebulae, causes
the observed emission of light from the nebular material. The
photographic magnitudes of the nebulae range from about the same
as those of the central stars to as much as six or seven magnitudes
brighter ; the greater brightnesses are observed in the case of the
nebulae containing the hottest of these central stars, whose tem-
peratures range from about 25,000 to over 100,000. Rotational
velocities have been measured spectrographically, the lines being
inclined when the slit of the spectroscope is placed along the major
axes of the figures of the nebulae. From these velocities and
assuming appropriate distances and dimensions, masses equal to a
fraction of that of the Sun have been derived. With diameters
The Galactic System 105
of about 20,000 to 30,000 times the distance between the earth
and the Sun, planetaries are therefore what might be termed "glow-
ing vacua," thousands of times more tenuous than the best vacuum
obtainable in our laboratories.
The chemical composition of the planetary nebulae does not
differ essentially from that of a star like our Sun. Hydrogen,
oxygen, nitrogen and neon are abundant according to the spectra,
and small proportions of the metals are also part of their com-
position. The luminosity is produced by a process similar to
fluorescence. The total amount of photographic light radiated
ranges from as much as, to more than, 100 times that of the central
stars, whose high temperature means energy emitted as invisible
ultra-violet radiation. This is absorbed and re-radiated by the
nebular atoms, in longer wave-lengths, which can be photographed
or seen. The hydrogen atom is the chief agent concerned in this
transformation.
As regards the origin and evolution of the planetary nebulae,
the suggestion that they are the relics of Novae has already been
considered but not favoured (see page 58). A Nova perhaps always
passes through a quasi-planetary-nebula stage, but that stage does
not last. In normal planetaries the radial velocity movements, as
measured by the spectroscope, are of the order of 10 miles per second
as against fifty or more times as much in the case of Novae ; it
appears likely that they are the products of stars that reach a state
in which the energy generated is too much for the retention of their
outer layers, and the star blows off large amounts 'of matter until
it again reaches a state of equilibrium. Such a star would appear
surrounded by a luminous shell that would increase in size, starting
as a nebula of a bright condensed type and becoming one of a more
diffuse appearance with a bright ring or rings seen on a fainter
nebulous background. This line of evolution was suggested by
R. H. Stoy and appears to have much to commend it. It must
be remembered, however, that the two Supernovae of our Galaxy,
which appeared in 1054 and 1604, are believed to have left masses
of nebulosity in their places, one of which (the Crab Nebula), con-
nected with the 1054 star, has been classified (perhaps wrongly)
as a planetary nebula. Is it possibly the case that this happens
with a Supernova, although with an ordinary Nova the ejected
nebulosity thins out and practically disappears ?
The diffuse nebulae are irregular in shape and they range from
small wisps and streaks, only observable by means of long exposure
photographs, to such objects as the Orion nebula easily visible
without optical assistance. As in the planetaries, in most cases
diffuse nebulae are associated with stars in such a way as to suggest
that there is some relationship.
106
Stellar Astronomy
In 1912, V. M. Slipher of the Lowell Observatory, Flagstaff,
Arizona, discovered that some of the diffuse nebulae have dark line
spectra ; the Pleiades nebula round Merope, for instance, has a
spectrum similar to the one shown by that star (23 Tauri, 4 m -2,
B5 type). He suggested that the nebulae in this cluster shine by
light reflected from its stars, and photometric measures by Hertz-
sprung in 1913 gave support to the idea. This led to a new view
of the source of light of the gaseous nebulae. Later work by
Hubble|at Mt. Wilson gave the following results for planetary and
diffuse nebulae :
Type.
Small planetaries.
Large planetaries.
Diffuse with bright Usually
line spectra. wispy
Diffuse with con- Usually
tinuous spectra. smooth
and cloudy.
Table 21
Appearance. Associated Stars.
Less than 2' Bright line O type.
diam.
Over 2' dia. Between bright line
and Oe5.
Oe5 and BO.
Bl and later.
Remarks.
Nebulae
absorb
and
re-emit
radiation.
Nebulae
reflect
radiation.
Hubble has remarked that, since nebulae with bright line spectra
are more easily identified for a given surface brightness because of
the concentration of their light in the discontinuities of their spectra,
they are actually the less numerous, although about equal numbers
of bright line nebulae and nebulae with continuous spectra are
known. A detailed discussion showed that, with the exception of
about four objects, each nebula had associated with it one or more
stars of a type as given in the above table. This suggested that the
source of luminosity of the nebula is the radiation from these stars,
the nebulosity consisting of clouds of matter, molecules, dust or
perhaps larger particles not hot enough to be self-luminous, but
visible because of light excited by or reflected from the involved or
neighbouring stars. Adopting this hypothesis, Hubble has related
the brightness and angular extents of the nebulosities to the photo-
graphic magnitudes of the stars. Assuming that the intensity of
illumination varies inversely as the square of the distance from the
stars, and that the nebulae absorb and re-emit, or reflect, the radia-
tion falling upon them, he showed that, theoretically, for a constant
ratio of focal length to aperture and with 60 minute exposures,
m + 5 log a = 11-6 or 10*6, according as the line joining the star
to the nebulosity is perpendicular to it or has the mean inclination
The Galactic System 107
corresponding to random direction (m being photographic magnitude
of the star and a the maximum apparent angular extension of the
nebulosity from the star). When the values of m and log a for 82
diffuse nebulae are plotted, the points lie along a mean line, falling
between the two lines derived from the above formula, thus proving
the substantial correctness of the assumptions. In thirteen cases
the value a is greater than the maximum possible on this theory
for the magnitudes of the stars concerned, but a satisfactory ex-
planation seems to be that the stars are partially obscured by
nebulosity intervening between them and us, the excess of colour
for the spectral types being abnormally great in these cases. Hubble
also showed that for exposures of 160 minutes, with reflectors of
focal ratio 1 to 5, nebulosity would be photographed which is situated
at the following distances from stars of the photographic absolute
magnitudes given :
M . Distance in Light Years.
x 5 32
3
+ 5 0-3
+ 10 0-03
The nebulosity in the Pleiades shines by reflection of light from
the enclosed stars. In the case of nebulae with continuous spectra,
their colours have been found to be nearly the same as those of the
stars concerned, an outstanding example being the large reflection
nebula near the red supergiant Antatf3S. This nebula is about
a degree in angular breadth and is several light years in diameter.
The dimensions of the diffuse nebulae are often very great.
For instance, the Orion nebula, which is also nearly a degree in
diameter, and is approximately 980 light years away, is more than
14 light years across, while one nebula in the large Magellanic Cloud
must be (adopting Shapley's estimate of distance) several hundred
light years in diameter or sufficiently large if placed at the distance
of the stars in Orion more than to fill that constellation !
If stars or clusters are involved, distances and dimensions are
derivable. Trumpler has found the following values for several
well-known diffuse nebulae, all connected with galactic clusters :
Distance Diameter
(light years) (light years)
Pleiades nebula ... 500 50
"Trifid" nebula (M20) 3200 20
"Lagoon" nebula (M8) 3600 36 by 55
NGC2237 4400 75
M16 6700 40
108 Stellar Astronomy
The spectra of gaseous nebulae were found to be fairly similar
to one another, all the lines being sharp, as would be expected from
a gas of low density. The bright lines observed were of hydrogen,
helium, and (occasionally) singly ionised carbon and doubly-ionised
nitrogen, but the most conspicuous lines were those of a hypothe-
tical substance "nebulium," at wave lengths A 5007 and A 4959;
which were referred to as the N x and N 2 lines. There are a number
of other lines also and all of them vary in relative strength from
one type of gaseous nebula to another.
For some time it seemed to be certain that these lines are not
produced by a hitherto undiscovered element or elements, but by
the radiations of ionised atoms of known elements subject to physical
conditions not produceable in terrestrial laboratories. The spectra
o'f the light elements, which are thought to form the chief constituents
of nebulae, are well known and it was therefore considered probable
that some cause, such as a density much lower than can be produced
terrestrially, must be the reason for the unidentified radiations.
From considerations of physical theory based on laboratory ex-
periment, Bowen has shown that the extremely low densities pre-
valent in nebular matter and the consequent long intervals between
atomic collisions, provide the conditions for radiations of the wave
lengths concerned, from atoms which have lost one or more electrons.
When gases are at ordinary pressures, or even at the low pressure
of a so-called vacuum tube, the atoms collide very frequently, and
change the energy they contain at each collision. In the course
of these changes they pass occasionally through states known as
"metastable" conditions, in which they have given out nearly all
their energy, and do not radiate light under ordinary circumstances.
But at the extraordinarily low densities of the nebulae, a cubic mile
probably containing less gas than a cubic inch of our air at sea level,
collisions are extremely infrequent, (Bowen estimates the mean
interval as from 3 hours to 5 days) and the metastable atoms get
an opportunity to radiate before their condition is altered by a
collision. It has been found, for example, that the following
nebular lines are thus due to oxygen : a red line at A 7325, the
green "nebulium" lines at A 5007 and A 4959, the blue line at A 4363,
the ultra-violet one at A 3727 and possibly others in that region,
while those in the violet at A 3868 and A 3967 are similarly produced
by neon.
It is noteworthy that the explanation has been arrived at
through theory based on laboratory experiment, but not by actual
production of the spectral lines in question in a terrestrial laboratory.
Several nebulae are known to vary in shape and brightness. Two
of the most remarkable are NGC 6729 in Corona Australis and
NGC 2261 in Monoceros. They both resemble a comet in shape
The Galactic System 109
and each has a nucleus at the head, consisting respectively of the
irregularly variable stars R Coronae Australis and R Monocerotis.
The spectra of both these nebulae are continuous, with faint bright
lines superposed, and are somewhat similar to those of the nuclei.
Changes in the nebulosity take place with great rapidity, details
disappearing and reappearing as if subject to obscuration by moving
masses. NGC 6729 is in a region in which obscuring clouds have
been observed, and its distance has been estimated by Hubble to
be about 300 light years. As already stated, the luminosity of
diffuse emission nebulae is due to excitation of the atoms of gas by
radiation, but it should be borne in mind that it does not follow
that these nebulae are entirely gaseous in constitution. It may be
that only the gaseous portion can shine under the influence of the
radiation, and there is almost certainly also a considerable quantity
of dust and solid matter.
As regards the temperature of a diffuse gaseous nebula, if this
is measured in terms of atomic and molecular motion, it may be
said that at about a light year from the exciting star, the nebula,
however tenuous, has a temperature of thousands of degrees. The
temperature of interstellar space itself can be otherwise defined,
however. If measured by the equilibrium temperature of a small
meteoritic particle more than a light year or so from any star, it is
probably only two or three degrees above absolute zero (2 or 3K).
The line-of-sight velocities of diffuse nebulae with respect
to the Sun, as measured from their bright line spectra, are found
to be in general relatively small, e.g., Orion nebula (M42), zero ;
r/ Argus nebula, 3 miles per second approaching ; "Trifid" nebula
(M20), 14 m.p.s. receding ; and M8 and the "Omega" nebula (M17),
5 and 13 m.p.s., both receding, respectively.
OBSCURING CLOUDS IN SPACE.
The existence of "dark nebulae" or obscuring cosmic clouds is,
following Barnard's pioneer work, now known to account for most
of the dark markings in the Milky Way and for dark starless regions
in various parts of the sky. On the Franklin-Adams photographs
of the sky Lundmark and Melotte counted 1550 dark areas, covering
about 850 square degrees, most of which are probably due to ob-
scuring clouds, mainly in Milky Way areas. In some cases, as in
the region of the Pleiades, Orion and Ophiuchus, these dark clouds
merge into luminous nebulosity in the neighbourhood of certain
stars, showing that they are physically connected. The distances
of these stars are known, so that it is believed that the dark clouds
of Taurus, Ophiuchus and Orion are situated at about 500, 500 and
650 light years respectively. The dimensions of
110 Stellar Astronomy
axe very great, as much as 70 light years in length by about a
twelfth of that in breadth in the case of the dark lane east of p
Ophiuchi, while the dark cloud or clouds which produce the bifur-
cation of the Milky Way from Cygnus to Centaurus (nearly 120
long) is much larger in extent and in Cygnus it is estimated to be at
2000 light years distance. The cloud which produces the "Coal
Sack" near the Southern Cross is probably about 300 light years
from us.
There is good reason to believe that the obscuration of these
clouds is produced chiefly by dust, although other particles of some
size may be present. Fine dust, having a much greater surface
per unit of mass, is very much more effective in stopping light, and
an extremely small amount per unit of volume would be completely
opaque. Russell states that even a milligram per square centimetre
(less than a tenth of an ounce per square foot) whatever its thickness,
would be sufficient, which would mean an aggregate mass of about
a dozen times that of the Sun for a dark lane like that in Ophiuchus.
The clouds cannot be gaseous as the quantity of matter required
would produce dynamic effects, shown as motions of the neigh-
bouring stars, which are not observed. Finely divided meteoric
matter would behave in a field of stellar radiation as follows, assum-
ing the particles to be spherical, opaque and practically non-reflecting.
Except for light pressure, which is doubled if the particles reflect
perfectly, the effects produced are not much altered by changing
these properties. If the particles are larger than ten times the
wave-length of the light concerned, their power of stopping in stellar
magnitudes is very nearly equal to the sum of the cross sections of all
the particles in a given cylinder divided by its cross section. With
smaller sizes, this ratio has to be multiplied by from 1-0 to 2-5, this
factor increasing as the diameter decreases to about a third of the
wave-length. For still smaller particles, the factor decreases,
however, from 2-5 to nearly zero. Particles with a density of 2-5
times water and a diameter of a twenty-five thousandth of an inch
with a mass of about a fifteenth of an ounce per square foot, no
matter what the depth of space is, will reduce light by approximately
one stellar magnitude. In order to show the very much smaller
effect of absorption by gas, it may be here remarked that the earth's
atmosphere, which dims starlight at the zenith by less than half a
magnitude, has more than half a million times as great a mass as
this above each square foot.
As regards the effect of light pressure, since gravitational attrac-
tion and repulsion by light pressure both vary inversely as the
square of the distance, a particle for which repulsion exceeds gravi-
tational attraction near a star will be repelled from the star at all
distances. For* particles of a given density there are two values
The Galactic System 111
of diameter where there is a balance. Particles between these
limits are repelled, those outside the limits are attracted. The
limits depend on the luminosity and mass of a star and for a massive
star of low luminosity the limits may actually coincide, so that all
particles of any size would be attracted.
It has been suggested that the dust clouds may be accumulations
of material repelled by the radiation of the stars, but observation
of solar prominence phenomena seems to show that most ejected
material probably falls back on its surface.
COMPARATIVELY UNOBSCURED REGIONS.
The more obscured regions of the Milky Way have been given
considerable attention, several of them being referred to above, such
as the chief one of the kind, the great Rift from Cygnus to Centaurus
where the dark obscuring clouds are at 2000 light years distance in
Cygnus, although in the more southern parts of the Rift dense dark
nebulae show their effect 400 or 500 light years away. These
distances are obtained by various methods, including one involving
counts of stars down to given magnitude when deficiencies in the
numbers at particular magnitudes (the average distances of which
are known) point to the required distances of the obscuring cloud,
while the deficiencies in the numbers for the faintest magnitudes
indicate the total obscuration due to the absorbing material.
But in certain directions there appears to be a relative transparency,
notably towards the Milky Way star clouds in Sagittarius, Cygnus,
Cepheus, Auriga, Argus, Scutum and Aquila, where on the average
the obscuration does not seem to be more than the general one
described in Part I, Chapter II, that is, of the order of less than
one magnitude per 3260 light years (1000 parsecs).
GALACTIC CLUSTERS OF STARS.
These are sometimes referred to as "Open" clusters which
distinguishes them from the more condensed globular type. More
than 300 have been noted as the result of visual and photographic
work. They range in apparent size from clusters like the Pleiades
or Praesepe, on the one hand, to faint collections made up of a few
telescopic stars on the other. The stellar populations vary from
hundreds of members in such cluster as the double one in Perseus
(see Plate 7b) down to small numbers of stars which can hardly be
distinguished from chance groupings ; and the degree of concentra-
tion of the stellar contents to a centre varies widely. Distances and
dimensions have been estimated chiefly by means of the method of
' 'spectral parallax" (see Appendix D), the spectra of their stars
112
Stellar Astronomy
showing generally a well-marked correlation with magnitudes
similar to the configuration of Fig. 1. Trumpler has classified them
in accordance with the types of stars contained ; the following is
based on his classification. A typical cluster is given under each
heading :
Table 22
Clusters with stars
hotter than B8 type.
Clusters with no stars
hotter than B8 type.
Clusters containing only
stars of FO to M types.
GALACTIC CLUSTERS.
Clusters with no
yellow or red giants.
Pleiades.
Messier 34.
Clusters with both
giants and dwarfs.
Cluster round.
8 Carinae (Melotte
102).
Praesepe.
(Not observed through NGC 752.
faintness of constituent
stars ?)
Shapley's classification is on the basis of two main characteristics
numbers and concentration of stars, and distribution of spectral
types of the contained stars. For the first of these he gives seven
groups from (a] field irregularities, to (g) the richest and most com-
pact type. In practice, however, only (c) to (g) are used, all of
which are compact and increasingly rich and concentrated. The
other characteristic involves two principal groups based on spectra
or colours of stars, (1) the Pleiades type, with all its stars in the main
sequence, (2) the Hyades type, with yellow spectral classes (G, K
or M) of the same apparent brightness as the more common A type
stars in them.
The spacing of the stars in a galactic cluster must be consider-
ably closer than in the solar neighbourhood* and an observer situated
at the centre of one of them would probably see many stars nearer
to him than a Centauri is to the Sun, some shining more brilliantly
than Sirius does in our skies. Unlike the globular clusters, the
galactic type appear to contain very few variable stars, which is
probably a fact of some significance in the origin and history of
these clusters.
Since Trumpler's demonstration of the amount of absorption
of light, referred to in Part I, Chapter II, the distances found have
been always by methods which allow for the effect of this obscura-
* One investigator puts the density of stellar distribution as from 5 to 250 times
as great for the stars brighter than the limits of the photographs studied by him,
the real densities being therefore even greater.
The Galactic System 113
tion. In addition, study of the colour indices of the stars in star
clusters, for which excess of colour due to selective absorption in
space can be derived, provides a valuable method for distance
estimation, applicable to clusters considerably more distant than
those where spectral types of the contained stars can be ascertained.
When the distribution of the clusters in space is discussed, it is
found that they are grouped round a centre situated near the Sun
and show no clear relation to any structural features of the Galaxy.
Out to about 6500 light years distance the distribution is more or
less uniform, but beyond that distance they appear to thin out
quickly, and the limit of distance so far reached is not more than
16,000 light years. Trumpler has shown that this very probably
only demonstrates the inadequacy of our data. He gives the
effect of the absorbing layer in the vicinity of the galactic plane
as the most serious obstacle in the search for more distant galactic
clusters, another being the heavy effect of the obscuring Milky Way
dark clouds. In addition, however, he has shown that there would
be great difficulty in distinguishing any clusters at remote distances,
owing to the greatly increased number of faint background stars
then photographed, or seen, along with the cluster stars, in greater
relative numbers. In fact, he demonstrates that, for example, the
Pleiades and Praesepe (each distant about 500 light years) would
not be detectable as clusters beyond about 16,000 light years, owing
to the effect of background stars, on photographs taken with or-
dinary plates. On photographs using light of longer wave lengths
which is less absorbed by interstellar dust, greater distances could
be investigated with the help of instruments of large aperture and
wide field. This would help to bring out some structural galactic
features so far not detectable by study of galactic clusters.
Another useful application of photography on red-sensitive
plates may 'be found in the added ability to study galactic clusters
which may be behind obscuring dust clouds or nebulae. For
example, photographs of the kind, taken with Mt. Wilson 100-
inch have revealed that the well-known trapezium of stars in the
Orion nebula (M 42) is at about the centre of a cluster of 130 fainter
stars 5' in diameter. The four trapezium stars are supergiants of
early spectrum, the others are dwarfs of later types. It seems
probable that this group is part of a normal galactic cluster blotted
out by the nebular obscuration except close to the trapezium.
The distribution in galactic longitude of 334 of these objects
is as follows in percentages :
Longitude Longitude Longitude Longitude
90-180 180-270 270-360 0-90
26 29 31 14
114 Stellar Astronomy
The small number in the 0-90 quadrant is undoubtedly due to
the obscuration by the dust clouds of the Milky Way from Aquila
to Cygnus (part of the great Rift).
As regards distribution on the sky in galactic latitudes, very few
(9 per cent.) are outside 10 north or south ; in fact, there are only
four listed clusters in higher latitudes than 30 north or south. The
concentration to the galactic plane is therefore very pronounced,
practically all being inside a layer less than 4000 light years thick.
Distances and dimensions of a selection are :
Table 23
GALACTIC CLUSTERS.
Cluster. Distance Diameter
(light years) (light years)
NGC 752 1300 17
Perseus double cluster ... 4300 40
M34 1450 13
Pleiades 500 20
M38 2800 15
M36 3200 15
M37 2700 19
M35 2700 23
M41 1300 12
M50 2700 13
M46 2100 16
Praesepe 500 13
M67 2400 13
Group 6 Carinae 800 18
M6 1700 13
M7 800 12
M23 2100 16
M25 3200 33
M 11 4400 16
M71 4000 10
M39 1100 11
M52 4500 17
The diameters above are from "estimated" angular diameters
and are of the more central parts of the clusters ; "limiting" or
overall dimensions based on counts of the cluster stars with allowance
for the normal stellar background, would be generally 2 to 3 times
as large. There appears to be a systematic connection of diameters
The Galactic System 115
with stellar concentration, and also with poorness or richness ;
the diameters are less with greater concentration but increase
with richness. Nearly half are from ten to fifteen light years
in diameter, and three-fourths from about seven to twenty light
years ("estimated" dimensions) ; the overall figures are about
fifteen to sixty light years, for all physical types of cluster, the
majority being between thirty and fifty light years.
Is THERE A "LOCAL" SYSTEM?
The late Dr. B. A. Gould was of the opinion that a belt or stream
of bright stars girdles the sky nearly in a great circle forming an angle
with the Milky Way, the northern point of the intersection being
in Cassiopeia and the Southern near the Southern Cross. Sir John
Herschel had previously thought he recognised the southern part
of such a stream and believed that the appearance of the bright stars
gave reason "to suspect that our nearest neighbours in the sidereal
system form part of a subordinate sheet or stratum deviating ....
from parallelism to the general mass which forms the Milky Way."
By means of studies of distribution of the B type stars brighter
than 7 m -0, Shapley showed that their mean line of position seemed
to be inclined at about 12 or 14 to the galaxy and that it coincided
approximately with Gould's belt of stars, although the fainter and
more distant stars are more closely confined to the galactic plane
itself. From the relatively uniform absolute magnitudes of B stars
it was possible to ascertain their distribution in space and find that
they appeared to form a flattened cluster with its equatorial plane
inclined to the plane of the Milky Way. The work of Charlier was
considered to confirm the existence of the cluster, the dimensions of
which were about 3000 light years diameter by about 800 light years
thickness, the centre lying in the direction of the constellation Argo
(galactic longitude 240) at 300 light years distance from the Sun.
Another type of stars found to be concentrated towards this part
of the sky are M stars brighter than 8 m -0 (see Table 12). A consider-
able fraction of the brighter A stars appears to belong to this 'local
system," and it has been thought that the galactic bright and dark
nebulae are concentrated in it and in the much farther off Milky
Way star clouds, the regions between being apparently practically
devoid of such objects.
Recent work has, however, produced results which do not all
favour the actual existence of this Local Cluster. This work is based
on counts of stars with different assumed values for space light
absorption. Bok (using an absorption of 04 magnitude per 3260
light years, or 1000 parsecs) found a result in favour and others have
116 Stellar Astronomy
obtained similar results. But Oort, using different methods, in
which counts of numbers of the nebulae outside of the galactic
system visible at different galactic latitudes were employed as a
means of estimating the loss of light of the stars due to absorption,
arrived at the view that the Sun's neighbourhood is one of low, and
not high, density of stellar population, suggesting that we are
situated in a "local void" in the Milky Way system, perhaps between
arms of a galactic spiral nebula.* Some astronomers consider,
therefore, that the conception of a clearly marked Local Cluster
will have to be abandoned ; but it is difficult to see how the distri-
bution in galactic longitude and in distance outwards of such objects
as the bright B and M type stars, can otherwise be explained. It
may be noted that the different speeds of rotation of the stars round
the centre of the galaxy, decreasing from that centre, would seem
to entail that the existence of such a Cluster could only be temporary.
On the other hand, there are condensations on the arms of spiral
nebulae which may be such local clusters in the systems concerned.
THE GLOBULAR CLUSTERS.
Of these beautiful objects about 90 are listed, ranging from that
known as 47 Toucani, which is nearly 1 in diameter as measured
by densitometer on photographs and visible to the naked eye as a
hazy fifth magnitude star, down to NGC 2419, about 5' diameter
and eleventh magnitude. M 13 in Hercules, diameter about 18'
and just about visible to the naked eye as a sixth magnitude star,
is the finest globular cluster seen from northern latitudes, co Centauri
is comparable with 47 Toucani in size and brightness.
Globular clusters are strongly concentrated towards the centre,
but by counts of stars an elliptical plane of symmetry is shown
towards which the variables and bluer stars seem concentrated,
suggesting that fundamentally the structure is really somewhat
oblate. Although there is similarity of size, form and total lumin-
osity, deviations from the average have been frequently noted.
Some, such as Messier 19 and w Centauri, are elongated in shape,
Messier 62 is strikingly non-symmetrical, NGC 4147 has very few
giant stars, while nearly a third of these objects are very loose in
structure, requiring special examination to show their globular type.
Detailed study shows that many intermediate forms exist between
the loosest and the most concentrated clusters, and twelve sub-
* A later investigation by Bok and MacRae, however, suggests location of the
Sun in a cluster of elongated shape which may lie along a spiral arm of our Galaxy.
This is an interpretation of an apparent decrease in star density in the direction
away from the galactic centre, with increase and then decrease towards it, and little
change in the directions at right angles.
The Galactic System 117
divisions have been decided upon by Shapley as a classification based
on concentration towards the centre, Class I being those most
marked and Class XII those least marked in this way. The cluster
a) Centauri is remarkable for the uniformity in the magnitudes of
its brightest stars, a peculiarity shared by N G C 5272, 5927, 6273
and 6656. These clusters are all moderately concentrated (Classes
VI to VIII) and two of them, CD Centauri and Messier 3, are the
richest of all in variable stars. The various classes are widely
spread in apparent brightness and diameter and are not related to
the .integrated stellar magnitudes except that there is a slight
tendency for the less concentrated ones to be faint. This classifi-
cation by concentration perhaps gives an indication of developmental
age and if so should prove useful in studies of the problems of the
origin and life-history of stellar clusters.
The numbers of stars contained are of the order of scores of
thousands or perhaps even hundreds of thousands. Shapley
estimated that the average globular cluster contains more than
20,000 stars brighter than the Sun. On this basis there will be over
a quarter million stars, if the proportion of main sequence stars
fainter than the Sun is the same as in our vicinity. All spectral
types appear to be represented, the colour indices observed ranging
from about -0-5 to +2-0. The integrated spectra of the clusters
range from A to M, about nine-tenths being, however, in the F5 to
KO classes.
The methods employed for finding distances of the globular
clusters have been various. In order of approximate importance
they are : the period-luminosity relationship of Cepheid variables ;
the magnitudes of the 25th brightest stars of a cluster, which range
from about 1-3 to 0-9 magnitudes brighter than the short period
Cepheids (absolute magnitude zero) this difference decreasing with
degree of stellar concentration of the cluster concerned ; angular
'diameters of the clusters' main bodies ; and integrated stellar
magnitudes. These methods are linked up with each other. The
first two are the most reliable ; the other two are used to strengthen
the determination made from them, and together with the second
method, for those clusters where Cepheid variables have not been
found or had their periods firmly established.
Table 24 gives data for twelve selected objects ; all are situated
in galactic latitudes away from the Milky Way zone, for which
distances can be more accurately obtained than for those in lower
latitudes where the amount of light absorption is difficult to assess.
The classification on Shapley's scheme, which is based on concen-
tration to the centre, is given in the last column.
118 Stellar Astronomy
Table 24
GLOBULAR CLUSTERS.
Distance (light years). Class (Shapley)
47 Toucani 25,000 III.
M13 31,000 V.
M 5 33,000 V.
M 15 37,500 IV.
M 3 39,000 VI.
M 2 45,000 II.
M 72 54,000 IX.
M 53 66,000 V.
NGC 6229 98,000 VII.
NGC 5634 104,000 IV.
M 75 137,000 I.
NGC 2419 183,000 VII.
The actual dimensions are much greater than for galactic clusters ;
the denser parts are of the order of 30 to 100 light years diameter,
but the overall dimensions are three or four times as great when
measured by densitometer on small-scale photographs. This means
that a star as bright as the Sun, situated at the outskirts of an
average cluster, would be reduced to fainter than 7th magnitude
and be invisible without optical assistance from the centre of the
cluster.
The density of stellar distribution is high, perhaps more than a
thousand times that in the Sun's vicinity in the central cluster
regions ; but, nevertheless, the distance of the stars there from then-
nearest neighbours would with that density average about three-
fourths of a light year.* To an observer near the centre the sky
would have many stars brighter than Venus appears to us, and in
some cases (as there are a few supergiants present more than 1000
times as luminous as the Sun) the sky might have stars giving as
much light as a bright Moon does to us.
The stars so far studied in globular clusters are mostly giant or
bright main sequence branch stars, the brightest being late type
supergiants. Long exposure photographs with the larger telescopes
of the future will be able to settle whether there are the usual giant
and main sequence branches, as found in galactic clusters and in
the stars of our system generally.
* Shapley gives even a much smaller separation. He states that "in the centre
of a globular cluster like Ml 3 the separation of one star from another must be less
than one hundredth of our distance of 4'3 light years from a Centauri, our nearest
known neighbour." (Harvard Reprint, No. 272, p. 516). This means a stellar
population several million times as dense as in the vicinity of the Sun 1
The Galactic System 119
The integrated absolute magnitudes are found to range from
about -6 to -9 (photographic) with an average value of -7-5,
corresponding to about -8-0 (visual) allowing for colour index.
This is equivalent to nearly 160,000 Suns, which suggests a mass
for the average cluster of the same order. Recently, however, a
much higher value, of the order of a thousand times as much, has
been suggested as the result of a mathematical investigation by
Finlay-Freundlich, a conclusion rather difficult to accept in view
of the total luminosity.
The distribution of globular clusters is very striking. A definite
relation to the plane of the Galaxy is shown, and it appears certain
that this plane, defined by the faint stars and by the Milky Way
Clouds, is also a symmetrical and fundamental place for the globular
clusters. They are about equally distributed on each side of this
plane and form a large flattened ellipsoidal group 150,000 light years
in diameter by about 120,000 in thickness. The centre is in the
direction of Sagittarius (galactic longitude 330) at a distance of
about 30,000 light years from us.
The percentages in quadrants of galactic longitude are :
Longitude Longitude Longitude Longitude
90-180 180-270 270-360 0-90
1 15 70 14
*
The sun is situated towards the edge of the aggregation and this
explains the great concentration in the quadrant 270-360. Few,
if any, globular clusters are to be found within 5000 light years
from each side of the plane of the Galaxy, but it seems that this
scarcity is due to the effect of obscuring clouds and not to any real
absence.
SIR WILLIAM HERSCHEL'S MILKY WAY STUDIES.
In two historic papers, "Account of some Observations tending
to investigate the Construction of the Heavens' ' and "On the
Construction of the Heavens/' Herschel gave an account of the
problem of the structure of our stellar universe, together with the
results of about 3300 counts or "gages" of the numbers of stars
in fields 15' diameter, made with his 18-7-inch metallic twenty-foot
reflector. It will be interesting to consider briefly, in the light of
modern knowledge, what may be inferred from Herschel's pioneer
work. He assumed that the extension of our system in any given
direction is proportional to the cube root of the number of stars
counted in the field of his telescope, which is. a perfectly sound
conclusion provided there is an average uniformity of size and
120 Stellar Astronomy
scattering of the stars and that there is no light obscuration in space.
Many writers, such as F. G. W. Struve, Proctor, Gore and Miss
Clerke, considered that the disc theory of the shape of our galactic
system, thus derived by Herschel, was entirely abandoned by him
in his later writings. It is true that a uniform distribution of stars
as at first postulated was afterwards admitted to be far from correct,
but it would appear better to describe the later opinion of Herschel
rather as an admission of great lack of uniformity and that there
are many aggregations of stars throughout the system, than as
complete abandonment of the idea of a stratum or disc formation.*
Serious objections to the shape and size of the section revealed
by his counts besides want of uniformity in the spacing of the stars
are to be found. In the first place, it was evident from subsequent
photographic results (as well as from his later surveys with his
four-foot reflector) that the limiting magnitude of the 18-7 inch
reflector (about 14 m -5) was not nearly faint enough for the investi-
gation. Secondly, the "cloven-disc" form given by him as the
shape of our system is certainly not a physical reality, the'bifurcation
of the Milky Way on which it is based being an effect of obscuring
cosmic clouds. Thirdly, it is possible that there is considerable
irregularity in the distribution of the stars throughout the system,
the apparent general form of which was described by A. R. Hinks
as "no single mass of stars .... but an assemblage of more or
less distinct clouds of stars tumbled roughly into one plane." The
effect of these factors is to render worthless any conclusions as to
details of the shape of the Galactic system. Their effect on an
estimate of size, based simply, as Herschel's was ,on a unit which
is the spacing of the stars in the Sun's vicinity, was to give too small
a dimension, particularly in the direction of the system's greatest
extension. Accordingly, with the average distance apart of the
stars in the solar neighbourhood, about seven light years (see
Appendix F), the dimensions of Herschel's section (which is one at
right angles to the galactic plane through Aquila to Canis Major),
850 units by 155 units, or 5950 light years by 1085 light years, are
evidently much too small.
At the same time, however, study of Herschel's later papers
shows that these dimensions were not finally considered to be
adequate, particularly for extension in the galactic plane. As
one writer (Macpherson, "Modern Cosmologies/' page 36) puts it :
"at the close of his career he viewed the galactic zone as in the main
* Herschel's view of the disposition of stars in the Galactic stratum could be
taken as similar to that of Wright of Durham (the first to suggest a disc theory).
In his "Original Theory of the Universe" (1780) he wrote : "Let us imagine all the
stars scattered promiscuously, but at such an adjusted distance from one another,
as to fill up the whole medium with a kind of regular Irregularity of objects."
The Galactic System 121
an optical effect and the stellar system as a disc vastly more extended
than that of 1785." The great pioneer value of Herschel's work is
undeniable, and we have in effect stood on his shoulders in order
to look further into the depths of space.
THE MAIN GALACTIC STRUCTURE.
We are now in a position to review the state of knowledge re-
garding the probable shape and scale of our Milky Way system.
Shapley's studies of globular clusters and of the galactic star clouds
led him to conclusions involving "enormous dimensions of the
super-system of globular clusters and of the Galaxy. Once the
positions in space are determined, it becomes clear that globular
clusters are a part of the Milky Way system. They are associated
physically with the system of stars, gaseous nebulae, and galactic
clusters which is more or less symmetrically arranged with respect
to the equatorial plane of the Galaxy. In measuring the distances
of the remotest globular clusters, therefore, we are but measuring
the depth of our own galactic system. The one-sided distribution
of globular clusters is recognised as an indication of the Sun's very
eccentric position in the galactic system. In this same southern
part of the sky we find the densest galactic star clouds and the
greatest frequency of faint Novae and of other types of distance
objects [see Table 12], which is but further evidence of the greater
depth of the galactic system in the direction of Sagittarius. Also,
in that general direction are some obstructing dark nebulae, which
may be wholly responsible for the seeming absence of globular
clusters from regions close to the galactic plane. If the obstructing
material were removed, we might see clouds of faint Milky Way
stars .... and globular clusters still more distant than those
now known."
Shapley's idea of the dimensions of the Galactic system at the
time of his first studies may be described as that of a flattened disc
about 300,000 light years in diameter and perhaps 10,000 light
years thickness with its centre (that of the system of globular
clusters) at 65,000 light years distance from the Sun towards the
star clouds of Sagittarius, surrounded by a less flattened roughly
ellipsoidal group of globular clusters, nine-tenths of which are
contained in a thickness of 100,000 light years ; the stratum 10,000
light years thick being made up of clouds of stars and bright and
dark nebulosities.
These conclusions were based chiefly on photometric studies
of the magnitudes of various types of stars. The form and size
of the Galaxy had been investigated also by statistical methods
using star counts, parallaxes and proper motions (for the nearer
I
122 Stellar Astronomy
stars) and radial velocities. The most comprehensive of these
statistical investigations was that by Kapteyn (1923) and his results
were very different from those of Shapley. He found that the
Galaxy appeared to be a vast cluster of stars and involved nebulae
of lenticular shape, about 60,000 light years diameter and 12,000
light years thickness, containing about 47,000,000,000 stars, with the
Sun near its centre. These figures were only intended by him to
be a preliminary outline giving a generalised view. They took no
account of the probable clustered nature of the Galaxy nor of irre-
gularities in its general shape. The final results would require to
take such factors into account ; and it was realised that the photo-
metric study of faint Cepheid variables and other types of stars
would considerably modify the conclusions provisionally arrived
at by the statistical methods.
The later discovery of an appreciable amount of interstellar
light absorption, which was not thought to be of a sensible quantity
at the time, showed that this Kapteyn generalised scheme is far
from a reality. It also showed that the dimensions of the Shapley
system, now considered to be substantially a correct one in its
outlines, were considerably too large, a further exaggeration being
due to assumption of somewhat too bright absolute magnitudes
for the Cepheids used in the measurement of distances of the globular
clusters and the dimensions of the system outlined by them.
The most likely value for the overall diameter of the Milky Way
system is now thought to be from 100,000 to 120,000 light years,
with the Sun's distance to the centre about 30,000 light years and its
speed of rotation round that centre approximately 150 miles per
second, giving a period of revolution for the Sun of the order of
200 million years the "cosmic year."
Estimates of the total mass of our Galaxy range from 10 11 to
2 x 10 11 times the Sun's. About half of this is thought to be stellar
masses ; the other half is dust and gas with perhaps nine-tenths of
this half of gaseous constitution.
Recent investigations have shown that the cluster type variables
(Cepheid with periods up to 1 day) are found, in considerable num-
bers, at distances above and below the main Galactic plane, of as
great as 30,000 to 40,000 light years. These constitute what
Shapley has termed the "haze" or "corona" of our stellar system,
and lead to a dimension of perhaps as much as 100,000 light years
at right angles to the main stratum of the Galaxy, which includes
the globular cluster system also. Density distributions perpen-
dicular to the central plane have been found for stars of absolute
magnitudes -2 to +8. These show that giants are more concen-
trated to the middle stratum than dwarfs. For the giants of -2
absolute magnitude the density at 5000 light years distance is only
The Galactic System 123
about I/ 1000th of that near the region of the Sun, while for the + 8
dwarfs the density at about the same distances vertically above
and below is as high as l/20th of that near the Sun.
Co-operative methods of research are now under way which,
it is hoped, will lead towards correct ideas of the shape, structure
and size of the Galaxy. Two of these may be mentioned as of
first-class importance. The first is that due to the selection for
the purpose by Kapteyn of 206 special regions evenly distributed
over the sky, in which determination of magnitudes, spectra, proper
motions, etc., are still being made at several of the world's largest
Observatories. The other is a count of stars by magnitudes down
to the fifteenth in Milky Way regions ; the galactic zone of the sky
is divided into a number of sections, each of which is having the
attention of a separate Observatory or institution, the scheme being
arranged and the results dealt with by Harvard College Observatory.
It is perhaps correct to say that the trend of recent ideas of the
structure of the body of the Galaxy can be summarised as follows :
The notion of a main Galactic system essentially composed of
separate stellar agglomerations may have to be abandoned as being
chiefly the effect of obscuring matter in the galactic stratum itself.
Extragalactic systems, which are presumably all systems of the
same sort as our own, do not certainly resemble an accumulation of
separate stellar clouds. There are apparently no dynamical effects
of a "Local Cloud" or "System" clearly evident in stellar move-
ments, which seem to be governed so far as investigations can
as yet say, by the general rotation round the centre in Sagittarius.
Owing to the shearing effect of the rotation of the Galaxy at de-
creasing speeds from the centre, such sub-systems should presum-
ably dissipate in a time much shorter than what is considered to be a
permissible period of existence for the Milky Way system, and they
would not re-form. In view of these and other difficulties, it may
be natural to suppose that the less luminous regions between the
apparent star clouds are largely due to obscuring matter, the general
cloud-like appearance of the Milky Way being therefore to a con-
siderable extent an illusion. It seems preferable to think of our
Galaxy as a flattened system, in all probability with a spiral arm
structure, but with the star density varying as a more or less con-
tinuous function of the distance from the Sagittarius centre. Fairly
:onsiderable local aggregation may exist, which must be regarded
>nly as transitory eddies in a sort of whirlpool, which form and
lissipate, and the smaller galactic clusters, of more permanent
type, may be gravitationally possible. Absorbing matter which
argely produces the appearance of many Milky Way star clouds
[and it may be the "Local System") is superposed.
124 Stellar Astronomy
In the foregoing account only a main outline of the chief features
of the Galactic structure is attempted. In the opinion of one of
our greatest authorities, B. J. Bok of Harvard, the dimensions and
total mass are probably fairly well determined. He considers,
nevertheless, that there is as yet very little definitely decided re-
garding details of the system, and that the "big problem on the
post-war agenda will be to find out if our Milky Way system is really
the huge spiral nebula many astronomers suppose it to be."
As an addendum to this section, reference may be made to recent
results of a novel method of research which may assist in investiga-
tions of Galactic structure. By means of a large concave metal
mirror of more than 30 feet diameter "short wave" (1-87 metre)
radiations from Milky Way regions have been studied by Reber of
Illinois, U.S.A., who has found that these radiations are strongest
from the Galactic centre in Sagittarius with other concentration
in the brighter parts and a minimum in Perseus. Since the wave
length is relatively great, there is very little absorption due to cosmic
dust, and it is suggested that the intensity roughly indicates the
amount of material between us and the far edge of the Galaxy. The
freedom from absorption should perhaps lead to a better idea of the
structure of the Galaxy than can be got by other methods, and these
preliminary results may mean that we have here an astronomical
tool of some value in the making.
The Galactic System
125
REFERENCES PART III CHAPTER I
Author.
W. Herschel,
Shapley,
Shapley,
Shapley,
Shapley,
Kapteyn,
Hubble,
Trumpler,
Trumpler,
Trumpler,
Bok,
Goldberg and
Aller.
Cuffey,
Subject.
Milky Way gaugings.
Publications.
Phil. Trans. Roy. Soc.,
1784-5.
Nature, Oct. 21 and 28, The Galactic system.
1922.
Mt. Wilson Contributions Globular clusters and
(during years 1915 to Galactic system.
1921).
"Star Clusters" Globular and
Galactic clusters.
"Galaxies" Galactic structure.
Mt. Wilson Contributions, Scale and structure
No. 230. of universe.
Mt. Wilson Contributions, Galactic nebulae.
Nos. 241 and 250.
Pub. A st. Soc. Pacific, Galactic clusters.
37, 307.
Lick Observatory Bulletin, Galactic clusters.
14, 154.
Astrophysical Journal,
91, 186.
"The Milky Way"
"Atoms, Stars and
Nebulae."
Pub. A st. Soc. Pac.,
52, 193.
Galactic clusters.
Galactic structure.
Planetary nebulae.
Colour Indices and
distances of clusters.
CHAPTER II
EXTERNAL SYSTEMS THE UNIVERSE.
ON photographs taken with large star cameras and with the
big reflectors, hundreds of thousands of nebular images
are found, the positions of which show a marked avoidance of
low Galactic latitudes. This "zone of avoidance" as it has been
termed, is due to the obscuration of dust clouds ; it varies in width
from about 10 to 40. The widest part is at Galactic longitude
330 in the direction of the centre of our system, which suggests
that there is probably a bulge in the lenticular shape of the main
body of our Galaxy, such as is seen on some photographs of edge-on
spirals (see Plate 9), the visible Milky Way being at its widest
there also.
The research of the past twenty years has definitely established
that these nebular images represent stellar systems external to our
own Galaxy and situated at distances which ratige up to many
millions of light years. The steps in the ascertainment of this
fundamental fact in the constitution of the Universe are outlined
in the chapter which follows.
Many lists of these objects have been compiled for different
research purposes ; but so far only one covering the whole sky.
This was made with similar instruments for the north and south
skies, and is known as the Harvard survey of nebulae brighter than
13th stellar magnitude. It contains 1249 objects and involved
two years' work by numbers of the Harvard Observatory staff. Its
penetration into space is to something like 10,000,000 light years.
There has been in progress a deeper Harvard survey with 18th
magnitude as the limit, intended to ascertain the details of dis-
tribution of these external systems through a very large volume of
space and to help in the solution of various related problems. This
survey was being carried out with two powerful refractor star
cameras, a 24-inch in South Africa and an 18-inch in the States ;
md it is expected that the total number of galaxies photographed
will be not less than about a million, which will extend to more than
100,000,000 light years in depth. It is anticipated that very soon
similar and even deeper soundings of space will be possible with the
lew Schmidt-type reflectors which have the large field of the re-
Fractor cameras combined with the speed of the large reflectors.
Five other surveys, not of the whole sky, but of selected areas,
lave been made to limiting magnitudes 18-5, 19-0, 19-4, 20-0 and
128 Stellar Astronomy
21-5. All but that to 19^0 were made at Mount Wilson Observa-
tory with the 60 and 100 inch reflectors ; the exception was the
work of the 36-inch reflector at Lick Observatory. The data
secured by these surveys provided the material for counts of nebulae
in 900 fields well distributed over the surface of the whole of the
northern galactic area, and over rather more than half of the
corresponding southern area. The counts, reduced to standard
conditions for definition, atmospheric extinction at different sky
altitudes, and for galactic obscuration, concerned more than 100,000
nebulae and were transformed to numbers per square degree for
comparison of the results got by the different telescopes.
The average number of galaxies per square degree photographed
at the zenith with an hour's exposure of the 60-inch reflector in the
best conditions, for the sky north or south of 40 galactic latitude,
clear of the main effects of galactic light absorption, was found to
be 109. For the 100-inch similarly the number was 237, the
limiting brightness for this instrument with these conditions being
19 m -8.
It should be remarked that the investigations of Shapley and
others have shown that there is no appreciable intergalactic absorp-
tion of light. Shapley has measured the angular diameters and
stellar magnitudes of several thousand galaxies situated many
millions of light years away, and has shown that the diminution of
brightness with diameter is closely in accord with what is to be
expected if intergalactic space is practically transparent. He has
also found that selective absorption must be inappreciable. There
is added confirmation by the absence of reddening with distance
in globular clusters, and by the fact that these objects do not appear
fainter in proportion to their diameters or larger in proportion to
the brightness of the contained stars than the nearer ones, as should
be the case if light were absorbed. Both these investigations make
the reasonable assumption that the averages of absolute sizes of the
galaxies, and of the globular clusters, are the same in the volumes of
space concerned.
The distribution of the nebulae from the small-scale aspect as
derived by these researches is markedly non-uniform. They are
seen singly and in groups of increasing numbers up to great clusters
of thousands of members. But when samples of very large numbers
are considered, and in terms of very great volumes of space, the
clustering tendency gets smoothed out and the distribution ap-
proaches a large-scale uniformity, although down to faint magnitudes
there are still evidences of some enormous groupings. Down to
moderately bright magnitude it is found that the stars greatly
outnumber the nebulae ; but at the faintest limits the number of
nebulae per square degree gets comparable with the number of stars
External Systems The Universe 129
photographed. For instance, photographs taken with the 100-inch
at the galactic pole, where galactic obscuration is least, show about
2400 nebulae per square degree, a higher number than the stars
on the plates ; and it is considered by Hubble that there are probably
100 million nebulae in the entire volume of space out to the limit of
distance concerned.
There is much diversity in size and brightness, and they range
from a few very bright ones, such as the Andromeda nebula, M 31,
which is about 3 in diameter over its brighter parts and visible
as a hazy spot to the naked eye, down to multitudes of tiny specks
on long exposure photographs with the large reflectors.
It was only by photography that details of the structure of the
larger specimens could be ascertained for purposes of any classifica-
tion that might be possible. Several schemes have been published of
which the one due to Hubble may be briefly described. His scheme
involves a series in three broad types, elliptical (or spheroidal as
Shapley prefers to call this type), spiral, and spiral with a luminous
bar crossing the nucleus and the surrounding disc of nebulous light.
The three types may be represented by a Y-shaped diagram.
The stem is the elliptical or spheroidal series, starting at the foot
with specimens of circular outline and progressing to more elliptical
forms. One of the arms is the spirals ; it begins with those which
have the arms closely disposed passing to others with the arms more
openly spread and more distinct ; and the other arm is the so-called
" barred spirals" of types which correspond to the graduations of
openness in the normal spiral branch. The first of the three types
are designated EO to E7 as oblateness increases ; the second Sa,
Sb and Sc ; and the third SBa, SBb and SBc. In the E type or
class it may be taken that they are all ellipsoidal or spheroidal of
various degrees of oblateness and not in any case a torpedo-shaped
body, which would not be gravitationally stable. In the spiral
types the arms are found on close examination to be enhancements
on the background of light surrounding the nucleus ; and it has
also been shown that the light from the arms does not constitute
as large a fraction of the light from outside the nucleus as was first
thought. Observation has not yet certainly shown what is the
direction of rotation of the spiral arms ; i.e., whether this occurs
with the convex side forward or the reverse, and it is not known
whether the points of junction of the arms with the nucleus advance,
are stationary or regress in space. Such evidence as is available,
however, strongly suggests that the convex sides of the arms are in
the front of a rotational movement.
There is also a relatively infrequent Irregular type, the Magellanic
Clouds being the brightest examples. A peripheral band of ob-
scuring matter (presumably dust or gas or both) is often found in
130 Stellar Astronomy
the Sa and Sb types, most clearly indicated when they are edge-on
or nearly so (see Plate 9).
On photographs of bright spirals and Irregulars taken with the
largest reflectors under the best conditions, star images are numerous;
but until lately the ellipsoidal E-types and the central regions of
spirals had not been resolved into stars. Any stars shown were
O or B type giants and supergiants, about 1000 to 40,000 times as
luminous as the Sun, and they are brightest in the Sc or Sb classes of
nebulae ; no stars had been found in the Sa class. It was none
the less considered that all classes are probably composed largely of
stars, and that these stars are not bright enough to be distinguishable
except in the cases mentioned. This idea has received strong
support from recent photographs taken with the 100-inch reflector,
using red-sensitive plates, of the central regions of M31, and of
its two companions M 32 and NGC 205, which have been thus
partly resolved so as to show masses of reddish stars (similar to
K-type giants), estimated to be about 500 times as luminous (photo-
graphically) as the Sun. It should be noted, however, that the
integrated spectrum of M 32 is of a type resembling a G 3 type
dwarf-star, according to Sinclair Smith, who had previously studied
this smaller galaxy on plates of the ordinary kind taken with the
100-inch reflector, and had concluded that there are perhaps
20,000,000 stars in it, the bulk of which are of a somewhat hotter
type of spectrum than the reddish giants, that have so far shown
on red-sensitive plates.
Two other objects that are nearby galaxies, NGC 147 and
NGC 185, have also been partially resolved similarly and there
seems strong hopes that with the aid of the Palomar 200-inch
reflector and the new technique all the nearer galaxies will be at
least partly resolved.
The order of appearance of stars in photographs of galactic
systems may be described as follows : Supergiants and giants are
found in the outer regions of spiral systems ; main sequence, and
perhaps giants also, in their nuclear regions ; and in the ellipsoidal
type the stellar composition seems to be similar to that of the nuclear
regions of the spirals. Among galaxies in general the relative
distribution changes systematically through the sequence of struc-
tural forms, the brighter supergiants being found closer towards
the centre as the degree of openness of the spiral arms becomes
greater. It may thus be said that if the order of stellar evolution
is from supergiants and giants towards and through the main se-
quence, the evolution of the galaxies themselves is not necessarily
from ellipsoidals to spirals of increasing openness, but conceivably
the reverse of this. The practicability of a general classification
of galaxies into ellipsoidal and spiral types cannot, of course, be
External Systems The Universe 131
taken to prove that one type developes into a succeeding type of the
series, in an evolutionary sequence. The giant and main sequence
stellar distribution among the various types as mentioned, and the
fact that the spiral arms appear as enhancements which may have
as it were grown out of the material of the nebulous background,
suggest at least a possibility that the evolutionary order might turn
out to be from Irregular through spirals to the ellipsoidal kind.
Globular clusters have been found (as was suggested should be
the case in an earlier edition of this book) in several of the brightest
galaxies such a M 31, M 33, M 101, NGC 6822, the Magellanic
Clouds, and others. They are generally not so large or luminous
as those of our own Galaxy, their absolute magnitudes ranging from
- 4 to - 7 as against the Galactic range of - 6 to - 9. In general,
the spectra of the galaxies are similar to that of the Sun ; the H and
K lines of calcium, the G-band of iron and some hydrogen lines
can be distinguished. The spectra of the E class are generally of
G type, and those of the spirals from G 3 to F 9, the earlier types
on the average with the more open galaxies. Many of the spirals,
but very few of the ellipsoidal, show bright lines due, no doubt, to the
presence or absence of gaseous nebulae and of the high temperature
stars which cause the emission.
The colours of all types, except the Irregulars, afe rather redder
than would be expected from the spectral type, i.e., the colour
indices are greater than the normal for the spectrum and the colour
classes correspond to somewhat redder and cooler types of stellar
spectra. But there is no satisfactory explanation of this ; there
is no intergalactic selective absorption to account for it, although
local absorption in their own structures might perhaps be responsible.
As regards details of the colours inside a particular galaxy, a
striking difference is found between the nucleus and the arms in
spirals. For M 51 (NGC 5194, see Plate 10), an Sc spiral, Car-
penter found a strong increase towards the blue end of the spectrum
between the nucleus and the arms, the colour index varying from
-f O m -6 near the nucleus to -O m -3 about one revolution of the
spiral arms from it. This is what would be expected if the hotter
type stars were in the arms and the cooler ones nearer the centra:!
regions. In the case of M 82, an I or irregular type, there was no
essential difference found between the inner and outer parts.
On classifying 600 of the brightest specimens, Hubble found
that about a sixth are ellipsoidal ; the remainder are all spirals,
with the exception of 2J per cent, of the total classed as Irregulars.
These proportions are about the same as are shown by the thousand
brightest of the 13th magnitude Survey by Shapley and Miss Ames.
In the clusters of hundreds of nebulae, twenty-five of which are
known, all types of galaxies are present ; but the ellipsoidal kind
132 Stellar Astronomy
seem usually to predominate. One of the richest, that in Coma,
has about 2000 members. A hundred or so groups composed of
fewer members have also been noted ; one of these contains our
Galaxy and at least twelve other systems.
DETERMINATION OF DISTANCES AND DIMENSIONS.
The first effective steps in this were due to the discovery of
Novae in a few of these nebulae less than 30 years ago ; this in-
dicated that distances were probably of the order of several hundred
times that of the average galactic Nova, itself a distant object.
This was followed by identification of stars, of a type known to be
highly luminous, in the larger spirals ; and in 1922-3 by the detection
of Cepheid variables in M 33, NGC 6822, and M 31. The distances
being derivable from the Cepheid period-luminosity relationship, a
search for these variables in other large spirals soon led to a know-
ledge by this period-luminosity relationship of the distances and
dimensions of the nearer and brighter objects. The stages in the
determination of distances and dimensions of these nebulae were
as follows : The brightest stars in the nearby galaxies, in about
10 of which (all within a million light years from us) they could be
closely studied, were found to be generally of a fairly uniform
luminosity roughly 48,000 times that of the Sun (or -7 absolute
magnitude). This criterion was applied to the members of clusters
of nebulae, as in some of these individual stars could be detected
even although it was not possible to define their types. Thereby
distances up to several million light years could be ascertained ;
the Virgo cluster of several hundred was thus found to be 7,000,000
light years away. Measurements of the luminosities of the indi-
vidual brighter nebulae in all such clusters also showed an approxi-
mate uniformity from one cluster to another, of 100,000,000 times
the Sun (or - 15 absolute magnitude) ; this provided a method for
finding distances of faint nebulae where, owing to great remoteness,
separate stars could not be seen. Distances of clusters of nebulae
as far away as a hundred million or more light years could be de-
tected in this way ; the faintest nebulae photographed by the Mount
Wilson 100-inch are thus known to be something like 500 million
light years from us. (See Appendix J).
The distance of any very remote faint galaxy, too far away to
show Novae, non-variable stars of high luminosity, or Cepheid
variables, cannot be individually determined, however, with any
reasonable degree of accuracy, by these methods. This is owing
to the very considerable range of luminosities of the individual
galaxies, over more than five magnitudes, although the great
majority are not far from the average value. A distance based
External Systems The Universe 133
on an assumed absolute magnitude for an individual galaxy (say
an average absolute magnitude of - 15) would, therefore, be subject
to large unavoidable possible error, as no means of classifying a faint
specimen as a giant, normal, or dwarf of the species is available.
Hubble has determined the average real dimensions of the main
bodies for the various types. He gives 2000 to 5000 light years
for the EO to E7 classes, 6000 to 10,000 light years in the case of
the spirals, the values increasing with greater openness of structure
(Sa to Sc and SBa to SBc), and about 6000 light years for the I or
irregular class. It should be noted that these dimensions, which
are for the larger axes of form, do not refer to limiting or overall
sizes ; Shapley has found mean diameters of 13,000 and 16,000 light
years for spheroidals and spirals respectively from densitometer
measurements of photographs.
There is a great range in size, although the majority are close
to the median size. For example, M 31 is about 40,000 light years
in length and 9000 in breadth over its brighter parts ; but over all,
including an outlying haze of stars, the dimensions are 60,000 by
54,000 light years, demonstrating that it must be a giant com-
parable in size with our Galaxy, also a giant, if not indeed a super-
giant, system.
INTERNAL MOTIONS AND MASSES.
The determination of the masses of the galaxies is a problem of
the greatest importance in discussing the nature and history of the
stellar universe. Several methods have been employed. One is
based on the total luminosity of a system. Taking an average
absolute magnitude of -15, or equal to 100,000,000 Suns, and
assuming that half of the mass is stars and the other half gas and
dust (Bok's estimate), also that the average unit of stellar mass of
the Galaxy radiates light at the same rate as a similar unit of solar
mass, the total mass of a typical Galaxy would be that of 200,000,000
Suns (2xl0 8 Suns).
Another, and probably more reliable method is based upon
spectrographic measurements of radial velocities at points along
the major axes of some of the brighter objects, that happen to be
placed edge-on, or nearly so, to us. Mass can thus be estimated for
the material between a given point and the centre of a galaxy in
much the same way as the Sun's mass is found from orbital motions
of the planets. But the spectrographic results are difficult to inter-
pret, as we do not yet know how the stars and other material are dis-
tributed in relation to the points for which the velocities have
been measured.
134 Stellar Astronomy
Recent studies of M31, M33 and other spirals have produced
rather uncertain results. For M 31 (undoubtedly a very large
specimen) a mass of about 10 11 times that of the Sun has been
found ; and for M 33 (probably rather larger than the average)
2 x 10 9 the Sun's, or only a fiftieth of M 31, although the ratio of
luminosities is a tenth. The mass for M33 is, however, about
ten times that derived above for the average spiral from luminosity.
There does not appear to be any method open for reconciliation of
this rather great difference, except by the attribution of a very large
fraction of low-luminosity stars of relatively large mass and/or
non-luminous matter such as gas, dust or other dark bodies.
Another method has been used involving analysis of the spec-
trographic radial velocities of 32 members of the Virgo cluster. The
recessive radial velocities, which range from about 600 to 900 miles
per second, do not seem to be connected with magnitude or position
in the cluster and this has been taken by Sinclair Smith, the inves-
tigator responsible, to indicate that the cluster is dynamically a
stable system. Assuming the greatest peculiar velocity to be that
of a body describing a circular orbit, or to be the velocity of escape
from the cluster, this gave the total mass of the galaxies in the
cluster and, when divided by the number of galaxies contained, the
average mass per galaxy. The value found, 2 x 10 11 that of the
Sun, is more than 10 times what appears probable from the two
methods already described, and at present there is no obvious means
of reconciling the figures. It is of interest to note that the total
mass of our Galaxy, perhaps a very large Sc type spiral, is considered
to be of the same order, from calculation based on its rotation ;
and that that of M31, a large Sb type, found from the spectro-
graphic method, is similar.
Periods of rotation at different points outwards from the centre
have been found for several galaxies by the aid of spectrographically
measured radial velocities ; for M31, 11 million years for the core
and 92 millions for the outer regions ; and for M 33, 59 millions and
200 millions similarly. These periods, although generally shorter,
are of the same order as that found for the stars in the Sun's vicinity,
round the Galactic centre (200 million years). In both M31 and
M 33, however, there is no evidence of central condensation of mass
provided by the measured rotation periods, and this may throw
some doubt on the generally accepted idea that our Galaxy has
such a concentration. In these two systems the rotational velocities,
except for a short distance near the centre of M 31, increase outwards
from the centre, decrease only showing itself far out from the nucleus,
like the decreasing rotational velocities observed in the neighbour-
hood of the Sun, which is evidently in a position well out from the
centre of our system.
External Systems The Universe 135
CLUSTERS OF GALAXIES.
As already stated, more than 25 of these are now listed, but
Hubble considers that, in surveys down to the 20th magnitude,
probably one for each 50 square degrees of the sky, or perhaps a
total of 600 clusters allowing for the obscured part of the sky, would
be found. Those known are ' composed of hundreds of galaxies
(2000 or more are believed to be in the Coma cluster) with a range
of about a hundredfold in their luminosities (five magnitudes). All
types are represented, usually with the ellipsoidal class the most
frequent, and more concentrated towards the centre of the clusters
than the other types. The distances of a selected number of
clusters are as below :
Table 25
Cluster. Distance (light years).
Virgo - 7,000,000
Pegasus, - 24,000,000
Hydra, - 24,000,000
Cancer, - 29,000,000
Perseus, - - - - 34,000,000
Coma, - 45,000,000
Ursa Major, - - - 85,000,000
Leo, - . . _ 117,000,000
Corona Borealis, - - 130,000,000
Bootes, - 240,000,000
An idea of the size and contents of one of these clusters has been
published by Zwicky. He remarks that the cluster in Coma has
2000 or more members ; 650 of these, all 100,000,000 times the
Sun's luminosity, have been photographed with an 18-inch Schmidt
reflector. The overall diameter for the volume occupied by the
galaxies considered is about 5,000,000 light years, and the distance
to its nearest neighbours of each galaxy in it will average about
300,000 light years or six times as close as for the "unclustered"
galaxies of space. (See Appendix L). However, Zwicky has
suggested that practically all the galaxies may be contained in more
or less regular clusters. He remarks that about twenty clusters
are known within 40 million light years distance, and that if these
clusters are really large enough to fill the volume, each has a diameter
of about 25 million light years and contains from 2000 to 4000
individual members. If this idea is correct there should be about
30,000 such clusters accessible to the 100-inch reflector.
According to Shapley, however, the dimensions of the nearest,
and one of the best explored, of these clusters (that in Virgo) are
136 Stellar Astronomy
much less only about 1J million light years in diameter; it con-
tains about 250 galaxies according to the same authority. But it
seems possible that these figures might be augmented by means of
photographs taken with Schmidt cameras.
THE LOCAL GROUP.
As has been remarked earlier, about 100 groups, each composed
of a few galaxies, have so far been noted. The most important of
these to us is the one to which our Galaxy belongs. The limits
of this group are taken to be roughly a million light years from our
system ; and the nearest of the galaxies outside of the group is about
2 J million light years away. In this connection it may be remarked
that Zwicky has stated that the group may be actually part of the
nearest cluster that in Virgo presumably situated well out from
its centre.
The volume in space occupied by the group is approximately
ellipsoidal in form, with M 31 near one end of the major axis and
our Galaxy near the other end.
Table 26 gives particulars of the members so far discovered.
Table 26
MEMBERS OF THE LOCAL GROUP OF GALAXIES.
Object. Type. Distance. Absolute Diameter
(light years) . Magnitude, (light years] .
Our Galaxy Sb or Sc ? ( -20 ?) 100,000
M31 Sb 750,000 -17-9 40,000
Magellanic Cloud I 72,000 -15-9 15,000
M33 Sc 780,000 -14-9 14,000
Magellanic Cloud I 82,000 -14-5 12,000
M32 E2 750,000 -12-9 3,000
Fornax System E 470,000 -11-9 6,500
NGC205 E5 750,000 -11-5 3,500
NGC6822 I 525,000 -10'8 3,000
1C 1613 I 730,000 -10-8 3,500
Sculptor System E 225,000 -10-6 3,000
NGC185 E 670,000 -10-6 2,800
NGC147 E 670,000 -10-3 2,700
The average absolute magnitude of the members of the group is
-13-3, or more than a magnitude fainter than what is assumed
as the average for all galaxies. This is because of the presence of
so many faint members ; but it is rather difficult to believe that
there may not be many more of the abnormally faint type in space
Mount Wilson Observatory.
PLATE 9 NEBULA, NGC 891.
An edgewise spiral galaxy in Andromeda ; distance about 8,000,000 light years
(Lundmark).
Mount Wilson Observatory.
PLATE 10- NEBULA, CANES VENATICI
NGC 5194-5.
A spiral galaxy seen at right angles to its plane ; distance about 2,000,000 light
years.
External Systems The Universe 137
than have been so far found, and that - 15 or - 14 absolute magni-
tude, generally used as the average, may not be somewhat high.
Another apparent inconsistency is found in the very different pro-
portions of numbers of galaxies of the different types shown in
Table 26 as compared with the general field. In the latter, the
proportion is for spirals, ellipsoidals and irregulars, nearly five-
sixths, about one-sixth and one-fortieth respectively (see page 131).
In the local Group, the proportions are very different from this.
For the same types they are less than a quarter, nearly a half, and
nearly a third. Of course, the number of objects in the Local Group
is a small total, but nevertheless the two discrepancies of magnitude
and type are there. On the other hand, Hubble states that a
"careful re-examination of the surveys demonstrates that such
nebulae [the fainter type] would be detected if they existed in con-
siderable numbers. . . . The presence in the Local Group appears
to be a unique feature, and they detract from its significance as a
fair sample of nebulae in general." Nevertheless "the fact that the
Galactic system is a member of a group is a very fortunate accident,"
leading to the possibility of closer study of the different types.
A short account of the chief characteristics of these nearby
galaxies follows, in order of distance.
THE MAGELLANIC CLOUDS OR NUBECULAE. These objects,
resembling to the naked eye two detached portions of the
Milky Way (there is, however, no visible connection) are
situated in R.A. 5 h 18 m , Dec. -68-7 (Nubecula Major) and R.A.
O h 50 m , Dec. -73-5 (Nubecula Minor). The galactic co-ordinates
corresponding are, respectively, 247 long., -33 lat., and 268 long,
and -44 lat. Known to the ancients, the greater Cloud is referred
to by Al-Sufi (tenth century) as the "White Ox" (el-baker}. It is
considerably the brighter to the naked eye, Sir John Herschel
finding that "strong moonlight . . . totally obliterates the lesser,
but not quite the greater." They are both round or oval to un-
assisted vision, although the Nubecula Major presents "the appear-
ance of an axis of light, very ill-defined, and by no means strongly
distinguished from the general mass, which seems to open out
at its extremities into somewhat oval sweeps, constituting the pre-
ceding and following portions of the circumference." (Outlines of
Astronomy, page 655). Miss Clerke describes this appearance
similarly : "To the naked eye it shows vaguely a brighter axis,
spreading at the ends so as to produce a resemblance to the Dumb-
Bell nebula." (System of the Stars, page 51). The nebula 30
Doradus is visible as a small bright patch in the following part.
According to Sir J. Herschel, the areas occupied are 42 square degrees
(Nubecula Major) and 10 square degrees (Nubecula Minor), but
138 Stellar Astronomy
recent long-exposure small-scale photographs show very much
greater areas.
The dominating feature in both is an elongated patch of densely
crowded stars. Star clusters of the globular and open types, and
considerable numbers of gaseous nebulae have been observed in
both systems. Thirty-two O-type stars, ranging from 9 m -9 to
14 m -0 (photographic) are contained in the Nubecula Major and nine
stars of the P Cygni type (a class of star with bright line spectrum
resembling that of a Nova), from 9 m -5 to 13 m *0 (photographic) ;
while the Nubecula Minor is known to contain at least one O-type
star. A plot of these 41 stars in the Nubecula Major covers an
elliptic area 6 by 4-3 ; the major axis is in position angle 130,
not very different from the angle 120 found for the brightest
elongated part of the Cloud.
Estimates of distances are given in Table 26. They correspond
to distances of 41,000 and 57,000 light years to the south of the
galactic plane. Their true space separation is about 30,000 light
years, centre to centre.
There are many very remarkable objects in the Clouds. For
example, the nebula 30 Doradus in the Nubecula Major seems to be
the largest known gaseous nebula, being much larger absolutely
and brighter than the great nebula in Orion, which it outshines
9000 times. According to Shapley, if it were placed in the con-
stellation of Orion more than all of which it would cover, it would
give as much light as 200 stars like Sirius and cast perceptible
shadows on the Earth.
Then the eclipsing binary star S. Doradus is 300,000 times (the
two components together) as luminous as the Sun, i.e., the com-
ponents radiate at a rate entailing loss of mass of over a million
million tons per second ! In the larger Cloud there are more than
20 stars each at least 150,000 times as luminous as the Sun ; while
others K and M variables in the two Clouds are of such brightness
and colour as to suggest that they are larger than Betelgeuse, which
is 360 million miles in diameter.
More than 30 globular clusters have been found in the large
Cloud and a few in the other. The radial velocities of the Clouds,
determined spectrographically from bright lines in gaseous nebulae
in the two systems, show when analysed that the Clouds move in
space at right angles to the direction of the Sun's galactic rotation
with a speed of 300 miles per second, this being parallel to a tangent
to the edge of our Galaxy assumed to be circular in shape.
THE GALAXIES IN SCULPTOR AND FORNAX. These were dis-
covered in 1938 by Harvard astronomers. They are both composed
of swarm' 5 of stars, slightly concentrated towards their centres,
External Systems The Universe 139
That in Sculptor has 10,000 stars in it brighter than 19 m *5 ; very
few are brighter than 18 m -0, so that there are no supergiant stars.
Some Cepheids are present, giving the distances shown in Table 26.
There is no structural detail discernible beyond the concentration
referred to. The Fornax galaxy has several globular clusters in it.
After the discovery of these two galaxies a search with a special
camera was made to ascertain if more of such systems were to be
found. None was discovered, but it would be very difficult to
identify objects of the class if more than several million light years
away, owing to their loose and inconspicuous aspect.
NGC 6822. This is an object very similar to the Magellanic
Clouds, discovered originally by Barnard visually, at R.A. 19 41 m
Dec. - 15, 20 from the centre line of the Milky Way. By the bold
assumption of an analogy between this object and the Magellanic
Clouds, Shapley at first estimated a distance "of the order of a
million light years/' this estimate being based on its angular dimen-
sions, size and luminosity of its involved nebulae, and magnitudes
of its brightest stars. Hubble has made an elaborate study from
photographs taken with the 100-inch Mt. Wilson reflector. He
finds total apparent angular dimensions of 20' x 10', with a brighter
core, 8' x 3', similar to this feature in the Nubeculae. Many general
structural similarities with the Magellanic Clouds are noted, and
from eleven Cepheids, ranging in period from 64 to 12 days, and in
magnitudes at maximum from 17 m -45 to 19 m -05, the distance in the
Table has been estimated. In this galaxy several patches of
gaseous nebulosity with emission lines have been noted ; one is
over 100 light years in diameter.
NGC 147 and NGC 185. Recently these have been found to be
dwarf galaxies, by means of photographs taken with the 100-inch
reflector on red-sensitive plates. The first-named is a large star
cloud with little condensation ; the other is an ellipsoidal galaxy,
flow partly resolved into stars for the first time.
NGC 1613. This is another dwarf, resembling NGC 6822, with
many Cepheids and other variables, but with the patches of nebu-
losity less conspicuous.
M31, M32 and NGC 205. M 31 is a giant Sb spiral; the
outer parts are resolved into dense swarms of stars on photographs
taken by the 100-inch on ordinary plates. All of these stars are
giants or supergiants ; the least bright has two or three hundred
times the luminosity of the Sun. Many Cepheids and Novae and
one Supernova (1885) have been observed in M31. M32 and
NGC 205 are ellipsoidal galaxies, E2 and E5 respectively. They
have been partially resolved on red-sensitive plates ij>to reddish
140 Stellar Astronomy
giant stars, no doubt only the brightest of their stellar populations.
The three galaxies are relatively close together in space, but only
the minimum distances apart as projected on the sky can be de-
finitely known. This minimum is 5000 light years between the
centres of M 31 and M 32 ; the figure for NGC 205 is 8000 light years.
If they all lie in the plane of M 31 (which is inclined about 15 from the
line of sight) the separating distances are 13,000 and 32,000 light
years respectively. More than 200 globular clusters in M31 are
known ; the absolute magnitudes range from - 4 to - 7 with
diameters of 12 to 50 light years, comparable with the figures for the
globular clusters of the Magellanic Clouds but systematically less
bright and smaller than those in our Galaxy. Two maxima are
found at - 5 and - 6-2, and the range of - 4 to - 7 and that for our
galactic system ( -6 to -9) overlap to some extent, suggesting the
possibility of the existence of sub-classes of globular clusters whose
relative richness varies from system to system, with more of the
brighter type attached to our Galaxy than to M31 or to the Magel-
lanic Clouds. Their distribution follows that of the luminosity
of the spiral, unlike the roughly spherical one of the globulars round
our system. There are also a few open clusters, one 50 light years
in diameter.
MESSIER 33. Photographs with the 100-inch Mt. Wilson re-
flector resolve this Sc class spiral in many places into stellar images
in no way different from those of ordinary faint galactic stars.
Forty-five variables have been found ; 35 are Cepheids of periods
of 13 to 70 days and photographic magnitudes at maximum of from
IS 01 -! to 18 m -0. Of the remaining 10 variables, 4 are irregular, and
one is probably eclipsing. Two Novae of maximum photographic
magnitude 17 m -25 and 17 m -9 respectively have also been observed.
Patches of diffuse nebulosity with white or bluish stars, apparently
of or B type, are situated in the spiral arms. The angular extent
of these patches and the apparent magnitudes of the involved stars
are related as in the case of galactic nebulae (see page 107). Com-
parison of photovisual with photographic magnitudes shows the
colours of the brightest stars in this galaxy to be white or bluish,
unlike those in the galactic globular clusters which are yellow or red.
Star counts down to 19 m -2 (photographic) indicate that stars are
first observable at 15 m -5, and that the relative frequency of stajrs of
different grades of luminosity is similar to that found for supergiants
*Baade, to whom these results are due, divides stellar populations into two types.
One of them contains high temperature supergiants (absolute magnitudes as high as
5 or 6), and a higher proportion of binaries, but less novae and supernovae than
the other, in which the most luminous stars are giants (absolute magnitude 2)
of low temperature. The former type is observed in the arms of spiral galaxies but
not in their central regions ; the latter in the central regions of spirals, in ellipsoidal
galaxies, between the arms in spirals, and in globular clusters.
External Systems The Universe 141
and giants in the solar vicinity. The linear (projected) separation
of M33 and M31 is about 20,000 light years ; they would each be a
fine object as seen from the situation of the other.
A DIP INTO SPACE.
To show how specimens of some of the objects dealt with in the
preceding pages are to be found in an apparently rather uninteresting
small part of the sky, visible on every clear night in northern lati-
tudes, the Bowl of the Dipper, i.e., the quadrilateral formed by
a, j8, y and S Ursa Majoris, may be examined. The area is roughly
45 square degrees or rather more than a thousandth of the entire
sky. The stars at three of the corners of this window into space,
j8, y and S, are all A-type main sequence from 55 to 20 times the
Sun's luminosity, at about 80 light years distance and members of
the Ursa Major moving cluster. The other star, a, is a close binary
pair, consisting of a primary giant K-type, with a companion re-
volving round it in about 40 years, which is visible only with large
telescopes. There is an eighth magnitude star about 6 minutes
of arc to the south-west ; this is, however, probably not physically
connected.
If we assume the quadrilateral a, /?, y, S to be a frame 80 light
years distant, the longest side is a to 8 and the shortest 8 to y;
the former is approximately 13 light years wide and the other about
6 light years. So much for the frame round the area and for the
nearest objects concerned.
Closer scrutiny reveals to good eyesight about a dozen faint stars ;
at a fifteenth of the limit of naked eye vision (9th magnitude) a
hundred or so stars are visible ; while at a thousandth (13th magni-
tude) there are something like 3000 stars to be seen ; and at a
millionth (21st magnitude the limit of the 100-inch photographi-
cally) about 150,000 are to be found. Less than a degree south of
the centre of the quadrilateral, there is a double star Struve (2)
1553, composed of 7 m -3 and 7 m -8 stars separated by about 5 seconds
of arc. Slightly outside the area about 2 south following is the
planetary nebula Messier 97, of circular shape, 3J minutes of arc
in diameter, named the Owl nebula owing to two darker spots in it
resembling eye-sockets ; its distance is not known. Inside the
area there are twelve nebulae, brighter than 13th integrated magni-
tude, probably all external galaxies relatively near to us on the
larger cosmic scale, and one small faint but well defined planetary
nebula, all objects visible with telescopes of moderate optical power ;
and there is one considerable Sb type, patchy spiral nebula, just
n the southern border about 1 south following /?, between that
star and the Owl nebula, NGC 3556, 8' long by !' broad. Assuming
142 Stellar Astronomy
it to be of average luminosity and dimensions it must be at a distance
of several millions of light years.
The distances of the stars other than the four bright enclosing
ones are to be expressed in terms of hundreds or of thousands of
light years ; and there are about a hundred small hazy luminous
patches, galaxies far beyond the limits of our own Galaxy. Many
of these can be detected only on photographs taken with the largest
telescopes. Not far from the centre of the bowl there is a con-
centrated cloud of faint galaxies at a distance, according to Baade,
of 150 million light years.
We thus look out through this frame and find inside it, or very
close thereto, a binary pair, and two planetary nebulae ; and many
external galaxies ranging in distance from several million to 150
million light years. No doubt other interesting objects can be
found, while intensive search with photographs made by the 100-
inch, would show even more distant galaxies such as have been
found in other directions.
RED-SHIFTS AND THEIR MEANING.
The first critical measurements of the positions of lines in the
spectrum of an external galaxy were obtained by Slipher in 1912,
using the 24-inch refractor of the Lowell Observatory. He con-
tinued the work, and by 1925 had measured displacements of the
lines for forty-one objects, two others having been by then measured
elsewhere. The values turned out to be generally larger than that
for any star, and all except 10 per cent.* were towards the red end
of the spectrum, i.e., they were generally shifts which might be taken
to indicate movement away from us. The distances of these
galaxies had been estimated (as described in an earlier section), and
Hubble was able to derive a relationship between these shifts and
distances which, treating the shifts as measurements of velocity,
showed an increase of 100 miles per second for each million light
years of distance. It was then seen that, if this 'Velocity-distance"
relation continued for objects still further away than the most
remote of the objects so far measured (the Virgo cluster), these
shifts could be used as distance criteria, or as checks on distances
otherwise derived. By the year 1936 more than 200 values of
red-shift for galaxies had been secured ; the greatest corresponded
to a speed of 26,000 miles per second for a member of a cluster of
galaxies believed to be about 240,000,000 light years away.
Up to the present the only known cause for the red-shift is
* These referred to objects all in one region of the sky with an apparent velocity
of approach, later practically accounted for by the rotational velocity of the Sun
round the centre of the Galaxy.
External Systems The Universe 143
motion away from us ; and many authorities consider that the
explanation is really such a motion, indicating an expansion of the
universe whereby every galaxy, wherever it is, is receding from all
the others. But some do not favour this as the explanation,*
although everyone is aware that if it is not correct, some entirely
new physical process may need to be discovered to account for the
phenomena.
Red-shifts mean a loss of energy in the light before it reaches
the observer for two reasons if the galaxies are receding ; firstly,
a reduction of energy in each quantum of radiation because of
increase in wave length, and secondly, owing to recessive movement
and the receipt by the observer of a smaller number of quanta per
second. But if the galaxies are stationary, only the first of these
will apply. The cause of what is observed may be either at the
galaxy itself, or act during the transit of the radiation through space.
If the latter is the case, then the galaxies are stationary in space,
apart from any smaller individual motions, and the radiation loses
energy by some undiscovered process in proportion to the length of its
journey. The problem reduces itself in one aspect to the deter-
mination of whether or not the galaxies are actually all moving away
from each other. In principle a solution of this is possible, since a
receding galaxy, having its spectrum shifted to the red, must photo-
graph fainter than one which has no movement (the part of red-shift
due to motion being then not present) at the same momentary
distance. The reduction in brightness would be negligibly small
for low speeds, but would increase with velocity and become of a
nearly measurable amount at the limit of distance to which the
100-inch reflector can reach.
To be able to calculate definitely what would be the stellar
magnitude of a galaxy, if stationary or if receding, it would be
necessary to know its actual distance. This is unfortunately not
possible, as the only method of estimation of great distances is by
means of the observed magnitudes themselves. Bubble's summary
of the position as it appears to him is clear and concise. He says :
"Nevertheless we can approach the question indirectly. From the
measured apparent faintness, we derive two scales of distances
corresponding to the alternative interpretations of red-shifts. We
may, of course, use either scale and accept the small differences as
uncertainties in the investigations. Again, we may explore the
observable region determine the distribution and the law of red-
shifts as accurately as possible using, first, the scale of distance
* For instance, Zwicky has suggested a "gravitational drag of light" (as light
has mass) when it passes the matter throughout space ; and MacMillan, loss of energy
of light photons either because of inherent instability or through collisions with
other photons. These suggestions are all equivalent to a decline *
i.e., reddening, during transit.
144 Stellar Astronomy
for stationary nebulae, in the hope that the wrong scale may lead to
inconsistencies that can be recognised or suspected.
'The programme has been carried out, but the results are not
definite. Using the stationary scale, the distribution is uniform
and the law of red-shifts is linear. Thus we reach a consistent
picture of the observable region as thoroughly homogeneous the
sample, although to us it seems vast, is too small to indicate the
nature of the universe itself. The conclusion seems reasonable,
and even familiar, but in such a universe we do not know how red-
shifts are produced. On the other hand, if we assume that the
nebulae are receding, the apparent distribution is no longer uniform
(the density increases outwards), and the law of red-shifts is no
longer linear (red-shifts increase with distance at an accelerated
rate). These complications suggest an expanding universe that is
curiously young and small.
"Thus, these results, at the moment, seem to favour the concep-
tion of a stationary universe, but they do not definitely rule out the
possibilities of an expanding universe. Judgment is properly
reserved until further information becomes available. The 200-inch
reflector, destined for Mount Palomar, should furnish the necessary
data. It will penetrate so far into the universe around us, and
red-shifts will reach such dimensions, that the dimming factors of
recession, if they are present, should be unmistakable/'
It may be remarked that in these investigations the observed
stellar magnitudes of the galaxies are appropriately corrected for
the effect on them of the shifts. Also the necessary adjustments are
made for reduction to a simultaneous epoch ; the light received from
the galaxies is of varying ages up to hundreds of millions of years
during which, if red-shifts are velocity shifts, the galaxies would
have receded to appreciably greater and greater distances than those
estimated from their apparant faintness.
Some investigators do not agree with Hubble's results. Eddiug-
ton, for instance, by a different statistical treatment of the counts of
galaxies, found that these actually confirm the interpretation of the
shifts as an effect of recession. And Shapley does not consider that
the evidence for increase in density of distribution outwards, found
by Hubble on the hypothesis that the galaxies are receding, is very
strong. It is pointed out that if the Mt. Wilson surveys, on which
the deduction is based, are employed separately for the two galactic
hemispheres, the increase in density in the northern hemisphere
is not appreciable ; also that other gradients of changing density
of distribution of distant galaxies have been found across the sky
considerable greater than the radial outwards gradient suggested
by Hubble.
External Systems The Universe 145
It appears sometimes to be assumed that an expanding universe
is a necessary consequence of the general theory of relativity. %he
hypothesis of expansion has certainly got the sanction of that
theory ; but this is not by itself a sufficient support as a non-
expanding universe can also be fitted into it.
AGE OF THE UNIVERSE.
If the galaxies are really receding, then it follows that the radius
of the universe doubles every 1,300,000,000 years assuming acceler-
ated velocities, or every 2,000,000,000 years if the velocities are
constant. This would mean that about 2000 million years ago
all galaxies in the universe were close together and seems to suggest
a date for origin of all its stellar and other contents. This extent
of time might therefore give an idea of the age of the stars and other
celestial objects, while it may be noted that it agrees with the order
of magnitude of estimates of the age of the earth and solar system.
Two scales of age for the universe are at present discussed by
astronomers a few thousands of millions, and millions of millions
(billions) of years anything between having little if any evidence
to support it. In favour of the shorter scale, which is now tending
to take the place of the other, there is the effect of the supposed
expansion of the universe already mentioned, and calculations of
the probable duration of life of star clusters and of binary stars
also appear to favour it.
The duration of life of a cluster of stars as a structure depends
on three factors which vary in importance according to the density
of the cluster and its position with respect to the centre of the
Galaxy. These factors are : gravitational interaction between the
constituent stars ; gravitational disturbances by "field" stars
passing through or near to the cluster ; and a "tidal" shearing force
due to the tendency towards different (and therefore dispersive)
velocities, in their galactic orbits, of cluster stars situated at varying
distances from the galactic centre, this shearing force being greater
for a cluster of a given diameter and constitution the nearer it is to
that centre. For loose galactic clusters, like the Hyades or Ursa
Major clusters, the first of these factors is not important ; in denser
galactic clusters, like the Pleiades or Praesepe, all three are effective ;
while for the globular clusters, generally well away from the galectic
plane and much more massive, only the first of the three is appre-
ciably important.
The duration of life of the galactic clusters is considered to be
of the order of 10 9 to 10 10 years ; and the simultaneous existence
of several hundred of these, estimated to be on their way to what,
on the longer cosmic time scale, would be relatively ea^ly disinte-
146 Stellar Astronomy
gration, looks more consistent with the shorter time scale than with
one which is more than a hundred times as long as their own life
times. This assumes that there is no means whereby new clusters
are formed which continuously replace those dispersed, an assump-
tion based on the very great improbability of the creation of new
clusters by chance encounters between unattached stars, or in any
other conceivable way.
For globular clusters, however, the life times are calculated to
be much longer about 10 12 years. With them the factor of
importance, as stated above, is interaction between the constituent
stars, which produces "velocities of escape" whereby the stars
gradually leave the cluster. It would appear that either the short
scale (10* to 10 10 years) or the long one (10 12 to 10 18 years) would
suit.
As regards binary systems of the wide visual type, their rate of
dissolution, and the maximum ages attainable, depend on the nasses
and separations of the component stars and also on the star density
in their vicinity. For separations of from 1000 to 10,000 times the
Earth's distance from the Sun, the maximum ages should range
from about 10 10 to 10 9 years. And statistical enquiry does not
show the relatively large number of wider pairs which would result
during the much greater periods of time possible with the longer
scale.
Further support for the shorter scale may be provided as the
result of recent calculations by H. N. Russell, based on the current
hypotheses of stellar evolution and the generation of energy by the
carbon cycle process, and assuming a composition, for a star in the
solar stage, of 51 per cent hydrogen, 42 per cent helium and the
remainder the other elements. He gives the times which would be
taken, if the universe and its stars existed for so long (a total of
about l-6x!0 n years), to pass through the main sequence from
K8 through G to B9 spectral types, and shows that because of high
absolute magnitudes in the post-Solar stage there would be found,
in all surveys down to a given apparent magnitude, at least ten
times as many stars in the post-Solar stage as in the Solar and
pre-Solar stage, which is of course not the case. Having
regard to the fact that the carbon cycle causes a change in mass
of only at most 0-7 per cent (see page 81), it may be said that the
observed absence of stars of nearly Solar mass but of hotter spectral
types and greater luminosities appears to be evidence against the long
time scale.
But there is as yet no general agreement. Recent work by
Zwicky, for example, on the distribution of the contents and con-
stitution of the clusters of galaxies is taken by him to show that
these clusters could not have been formed in the short time of the
External Systems The Universe 147
smaller scale, and to suggest that the universe is*stationary and not
expanding at all, and that the red-shift is not produced by motions
of recession.
The reader will have noted the uncertainty in such matters as,
for example, the source of stellar energy, the origin and evolution
of the stars, and in the fundamental question of the red-shifts and
their meaning. Much light will be thrown on these by investigations
now in progress ; in the last-mentioned particularly by the results
to be obtained in the next decade or so from the use of the 200-inch
telescope at Mt. Palomar. Meantime the aphorism of Lord Bacon
(Advancement of Learning, v. 8) will be a sound guMe for speculation :
"If a man will begin with certainties, he shall end in doubts ; but
if he will be content to begin with doubts, he shall end in cer-
tainties."
REFERENCES PART III CHAPTER II
Author. Publication. Subject.
E. Hubble, 'The Realm of the Galaxies and the
Nebulae. ' ' Universe.
E. Hubble, 'The Observational Ditto.
Approach to Cosmogony."
H. Shapley, "Galaxies," Ditto.
H. Shapley, Harvard College Obser- Transparency of
vatory Bulletin, No. 864. Space.
A. S. Eddington, Observatory, 58, 108. Discussion on Age
J. Jeans, E. A. Milne. of Universe.
B. J. Bok, Observatory, 59, 77. "Galactic Dynamics
and the Cosmic
Time-scale."
F. Zwicky, Pub. Ast. Soc. Pac., "Clusters of
54, 185. Nebulae."
B. J. Bok, Monthly Notices Royal 'The Time-Scale of
Astronomical Society, the Universe/'
106, 61.
APPENDIX A.
EXPLANATION AND DERIVATION OF SOME ASTROPHYSICAL TERMS.
Absolute Magnitude The formula for this is
M=w+5+51og7T
where M is absolute magnitude, m stellar magnitude (visual, photographic
or bolometric) and TC parallax in seconds of arc. This expression is
derived as follows : The ratio of apparent brightness at distances
corresponding to a parallax jcand to one of 0"-100 is 2-512 m ~ M This
/ 0-100 \ 2
ratio is also 1 ) since light received varies inversely as the square
\ TU /
of the distance or directly as the square of the parallax. Hence
2-512 m - M - ( ) from which
\ TC I
(m M) log 2-512 - 2-0 2 log TT
M = m + 5 4- 5 log TC, since log 2-512 = 0-400,
Or M m + 55 log r (r in parsees) ; M = m + 7-56 5 log d
(d in light years).
Bolometric Magnitude, Effective Temperature and Surface Brightness
Total radiation varies as surface area and also as the fourth power of
effective temperature (Stephan's Law). It consequently is =Z) 2 jT 4 x a
constant. In order to define bolometric stellar magnitude it is necessary
-, - , , . . ^ , . luminosity
to adopt some standard and this is done by assuming ~~ -
total radiation
= 1 in the case of a star of effective temperature about 6000K. As
the Sun has almost this temperature (5800K.), we may use its absolute
magnitude to derive an approximate formula for bolometric absolute
magnitude as follows :
ur Aa 2l 8 D 4 log (775800)
M bo , - 4-9 - ^ 2 5][2 - ^ 2 gi2
= 4-9-5 log D - 10 log (r/5800) (1)
Similarly total luminosity, or visible radiation, is = D*j x a constant,
when j is the surface brightness per unit of area of a star compared with
the Sun. Visual absolute magnitude is then
M vis = 4>9 - 5 log D + J (2)
/ being the difference between the star's and the Sun's surface brightness
in stellar magnitudes. The correction to visual absolute magnitude
(or to visual apparent stellar magnitude) in order to obtain bolometric
magnitude is, by subtraction of (1) from (2) :
M^ - M bol = 10 log (r/5800) + /.
Appendices
149
The values of T have been found for ditterent types by several inde-
pendent methods, while J has been ascertained from studies of eclipsing
binaries, differences of colour index, and interferometer measurements of
stellar diameter. In the Table, approximate figures for various classes
of stars are given for T, J and (M^
GIANTS.
SPECTRUM.
Mvi Mboi
T
J
(*Wvis fbol)
BO
20,000K
-3-2
+ 2-2
AO
10,500
-2-3
+ 0-3
FO
7,400
-1-0
+ 0-1
GO
5,200
+ 0-3
+ 0-1
KO
4,000
+ 2-3
+ 0-7
M
3,100
+ 4-5
+ 1-8
MAIN SEQUENCE.
SPECTRUM.
M vi s M boi
T
J
(Wvis Wbol)
BO
20,000K
-3-2
+ 2-2
AO
10,500
-2-3
+ 0-3
FO
7,400
- 1-0
+ 0-1
GO
5,800
0-0
0-0
KO
4,700
+ 1-2
+ 0-4
M
3,300
+ 3-8
+ 1-6
Colour Index (photographic mag. minus visual mag.) This has been
determined by Seares for different types, as follows :
Spectrum.
Giants.
Dwarfs.
BO
AO
FO
GO
KO
M
-0-32
0-0
+ 0-38
+ 0-86
+ 1-48
+ 1-88
-0-32
0-0
+ 0-38
+ 0-72
+ 0-99
+ 1-76
7
150 Stellar Astronomy
According to this table, the dwarf stars of G, K and M type are not so
"red" as the giants of the same spectral type, i.e., they have a higher
effective temperature, which is also shown in the preceding table of
temperatures, etc.
Colour index was at first obtained exclusively by comparison between
photographic and visual, or photo-visual, magnitudes. It is now more
usually determined by the photo-electric cell from measurement of
galvanometer or electro-meter deflections when the star's light is passed
through colour filters. This method is susceptible of considerably greater
accuracy, giving results believed to be within one per cent of the correct
value.
Space Reddening. Distant stars are often noted to be redder, i.e.,
have a greater colour index than what is appropriate to their spectral
type. The difference between the observed colour index and the normal
value is termed the colour excess. It has been found to be greatest in
directions towards the galactic centre and low galactic latitudes. Several
investigators have measured it to average about a tenth of a magnitude
per 1000 light years distance. But it may be noted that abnormal
reddening will not be always entirely due to interstellar matter, some
effect of the kind being observed in the case of stars with emission lines
in their spectra.
APPENDIX B.
SPECTRAL CHARACTERISTICS.
Type There are two groups : one shows bright bands due to
hydrogen, helium and some other elements, and the other shows absorp-
tion lines of the same substances. The first group are the "Wolf-Rayet"
type, the second are the "absorption O" type (Examples y Velorum,
i Orionis)."
B Type Absorption lines of helium and hydrogen most prominent
(8 Orionis).
A Type Hydrogen lines most prominent (Sirius).
F Type Calcium H and K lines most prominent with hydrogen lines
next (S Aquilae).
G Type H and K lines ; but hydrogen lines no longer prominent ;
many metallic lines (Sun).
K Type Calcium still strong ; numerous metallic lines and con-
tinuous spectrum decreasing rapidly towards violet (Arcturus).
M Type Calcium still prominent, with bands in green, and blue and
violet end very weak (Betelgeuse). M a , M b , M c are now referred to as
MO, M3, M8 respectively.
R and N Types seem to constitute a sort of side chain branching off
at G or K ; R and N taking the place of K and M in the order, while
Appendices 151
5 type represents a similar third branch. S is characterised by absorption
bands of zirconium oxide ; R and N by bands due to carbon compounds.
The spectra of the bright-line gaseous nebulae are classified as P ;
temporary stars as Q, The letter g and d prefixed to the type letter
signify giant or dwarf respectively ; e attached indicate the presence of
bright lines, p that the spectrum is peculiar.
APPENDIX C.
STELLAR TEMPERATURE AND DISTRIBUTION OF ENERGY IN SPECTRA.
The total radiation from a perfect radiator follows Stephan's Law,
which states that the total energy in all wave lengths radiated per second
from each square centimetre of a hot black surface is
E - aT*
a is a constant determined experimentally as 5-72 x 10'* and T is absolute
temperature in degrees centigrade. The value of E for the Sun is
6-25 x 10 10 ergs per second per square centimetre as determined experi-
mentally by Abbott and others (10,000,000 ergs per second is a watt or
T^ of one horse-power). From the formula T is found to be 5750K.
The temperature can also be found from Wien's Law, which states that
the maximum intensity of radiation in a perfect radiator is
0-289
A m centimeters.
By studies of the Sun's spectrum with a bolometer A m is found to be
4'70xlO~ 6 centimetres, giving r = 6150K. Stellar temperatures can
be similarly ascertained.
For the hotter stars (20,000K), A m = 145 x 1Q- 5 cms. ; for the coolest
(2000K) it is 145 x 10"* cms. This means that to obtain an adequate
knowledge of stellar spectra a considerable range of wavelength has to be
photographed. Assuming that all points in the spectra where the energy
exceeds 10 per cent, of that at maximum must be covered to achieve
this, the range to be photographed is from 6 x 10' 8 to 5 x 10~ 4 cms., which
becomes in effect 2-9 x 10~ 5 at the shorter end owing to absorption by
ozone in the* earth's upper atmosphere.
APPENDIX D.
MODERN INDIRECT METHODS OF PARALLAX ESTIMATION.
Some of the principal indirect methods are described briefly below :
Spectroscopic Parallaxes These are due to the discovery by W. H.
Adams and Kohlschutter that the intensity of certain lines in stellar spectra
152 Stellar Astronomy
varies with the luminosity of the star. For example, in the two K type
stars, Aldebaran (giant) and 61 Cygni (dwarf), the lines at A 4077 and
A 4215 (both due to strontium) are strong in Aldebaran and weak in
61 Cygni, the reverse being the case for the calcium line A 4227. By
Calibration of such relationships in stars for which parallax and absolute
magnitudes have been directly obtained, it is found possible to determine
a definite numerical relationship between absolute magnitude and in-
tensity of lines. Thousands of parallaxes of stars down to 8th magnitude
and fainter have been thus obtained. Theory shows that these varia-
tions of line intensity are due to the state of "ionisation" of atoms in a
stellar atmosphere, and are connected with the gravity potential at the
star's surface. Spectroscopic parallaxes are therefore correct only for
stars of mass equal to the average of their type corresponding to those
used in making the calibration curves, and seem to require some mass-
factor correction, stars of large mass giving too large spectroscopic
parallaxes and vice versa*
Spectral Parallax is obtained by assuming the absolute magnitude
to be equal to the mean for the spectral type. For example, Vega is
an AO star of 0*1 apparent visual magnitude. Assuming that it is a
"main sequence" star of average luminosity, the absolute magnitude
is + 0-6 (see Table 3). From the formula M=w +5 + Slog TU (Appendix
A) we get 5 log TC = M m 5, whence spectral parallax of Vega is
0"-126, which is very nearly the same as the best trigonometrical values.
Usually it is not possible to say whether a star is a giant or a dwarf
without careful examination of the spectrum. Proper motion is a fairly
good criterion, a large value usually indicating a dwarf star. In the case
of double stars, the relationship of spectra (see page 46) gives a good
indication, and spectral parallaxes for double stars are of some value.
In clusters of physically connected stars the magnitudes and spectra when
plotted often show a configuration resembling that of Fig. 1. The
absolute magnitudes of the stars can thus be derived and an approximate
parallax for the cluster obtained.
Variable Star Parallaxes One of the most powerful aids to the
estimation of great distances has been provided by the Cepheid period -
luminosity relationship (see Table 16). An example will illustrate. A
faint variable star with a light curve showing Cepheid characteristics, a
period of 20 days and median photographic magnitude 19-0, is found on
photos of a spiral nebula taken with a powerful reflector : what is the
distance ? The absolute magnitude (Table 16) is 2-6 ; from the
* Despite the rather despondent outlook of R. A. Proctor, referred to on page 1,
he made a very interesting speculation a few years later (Mysteries of Time and
Space, p. 410, 1883). This was to the effect that the various degrees of strength
of the lines in stellar spectra might provide evidence as to the size of a star, and
that "if so, se shall have a new means of dealing with the architecture of the heavens ;
for, knowing something of the real size of a star in this way, we may infer its distance
from its apparent size, and thus place it correctly in position in space, instead of
knowing only the direction in which it lies." (By "size" Proctor, of course, here
means brightness). A similar suggestion, made later by Schwarzschild, was re-
collected by Kohlschutter and acted upon by him and Adams in 1914.
Appendices 153
formula 5 log TT = Af-w-5 we get a parallax of about 0*-0000048,
corresponding to a distance of about 700,000 light years. This illustrates
the method, but a number of Cepheids in such an object would be thought
necessary for a reliable determination. The Long Period variable stars
may also be used to find distances approximately, using an absolute
magnitude according to period. (See p. 52).
Dynamical Parallaxes of Double Stars By adopting a total mass for
a binary system for which the orbital elements are known, it is possible
to derive a parallax from a formula based on Kepler's Laws,
parallax = -
(fWj H- #^2) 3 it
where a is the semi-axis major of the orbit in seconds of arc, m + m 2 the
combined mass (usually assumed to be about twice that of the Sun) and P
the period in years. Rather accurate approximations to parallax can
be obtained by using in conjunction with this formula the empirical mass-
luminosity formula (page 11). For example, taking the binary 2^3121,
magnitudes 7-3, 7-6, P=34 years, a 6"-8, and assuming m l +m 2 =Q-5,
1-0, 2-0 and 3-0, we get :
Assumed Wi+Wa, 0-5 1-0 2-0 3-0
Parallax (from formula
above) 0"-081 0"-064 0"-051 0"-045
Corresponding abs. mags. 6-8, 7-1 6-3, 6-6 5-8, 6-1 5-6, 5-9
Combined masses by mass-
luminosity formula, 1-3 145 1-6 1-7
On plotting the mass values of the first and fourth lines against the
parallaxes of the second line, two curves are obtained which intersect
at a parallax of 0"-056, identical with the best trigonometrical result.
The value of this method may be considerable in the case of remote pairs,
where the errors of observation are of the same order as the parallaxes
themselves (see Observatory, April, 1925, p. 113).
In the case of slow-moving pairs, for which the elements of an orbit
are not known, an approximation of some value for parallax can be
obtained. Taking the simplest case of a pair with a circular orbit, the
plane being at right angles to the line of sight, we get P =6-28 a/v, where
tv28 is the ratio of circumference to radius of a circle, and v the rate of
relative motion of the components. Substituting for P in the formula,
a 3
m i + m * = . we g et
I a t; 2
' * m+m
39-7 (
This formula can be adjusted by the theory of probability for ellipticity
and foreshortening of orbit, and then becomes for the average case
(using 2-0 for m 1 +w 2 )
TC = 0-33 V sw*
where s is the apparent angular separation and w the apparent mean
154 Stellar Astronomy
annual relative motion, both in seconds of arc. Appropriate values for
m l +w 2 can be adopted to suit the particular case. There are also other
similar formulae of some utility, particularly in statistical work. One
of these is
TT = 0-022 s 0}
where s is the mean angular separation and 9 the mean annual change
in position angle of the components.
Eclipsing Binaries By the study of the light curve and radial
velocity curve, the absolute sizes of eclipsing pairs can be ascertained.
The spectral type being known, the absolute magnitude can be calculated
from the surface brightness. For example, on page 44, it is explained
how the diameter of the brighter star in the Algol system, spectrum B8,
has been found to be 3*1 (Sun = 1). If of GO type the luminosity would
be 3*1 2 or 9'6 times the Sun, or nearly 2*5 magnitudes brighter. The
surface brightness / for a B8 star being -2 '5 (see Table, Appendix A),
it follows that the absolute magnitude of the primary of Algol is
M = 4'9 - 2*5-2-5= -0.1. The apparent magnitude is 2'1 and the
parallax (from 5 log TC = M - m -5) is 0"*036, which is fairly close to the
trigonometrical result (0"'027). Corroboration is afforded by the mass
of the star, 4 '7 times that of the Sun, which corresponds (by the mass-
luminosity formula) to an absolute magnitude of -0*4 and a parallax
of 0"'032. The parallax of Algol is therefore probably very close "to
(T'032, the mean of the three values.
APPENDIX E.
APPARENT ANGULAR DIAMETERS OF THE STARS.
These can be estimated if visual magnitude and spectral type are
known. If j is the surface brightness compared with that of the Sun,
then, taking 1919"-3 as the Sun's mean angular diameter and 26-7
as its apparent stellar magnitude, D" being the angular diameter of the
star, we have
Light from Sun
2 ^ 2*512 W+267
Light from Star
or
and D" = 0-0088 /-* (0-631)*
For example, the calculated angular diameter of Arcturus, w=0-2,
spectrum KO, / = +2-3 (whence j =0-12) is
0-0088 x 2-9 x (0-631) ' 2 0"-023
which is nearly the same as found by interferometer measurement at
Mt Wilsoi? (see Table 1).
Appendices 155
Actual Diameters The luminosity of a star, compared with that of
the Sun, is proportional to the squares of their diameters multiplied by
their surface brightnesses. In terms of stellar magnitude :
/ 2 log D \
M = Sun's abs. mag.- ( ^ ^ j + J
- 4-9 - 5 log D + J
whence
log D = 0-2 (/ + 4-9 - M),
M being absolute magnitude, and D the diameter of the star (Sun = 1).
APPENDIX F.
AVERAGE DISTANCE OF STARS TO NEAREST NEIGHBOURS.
It may be shown (see B. A. A. Journal, 36, 31) that the average distance
from a star to its nearest neighbours is given by the expression
s - 1-61
where s = distance required, r = radius of volume considered and N
number of stars in that volume. The most recent work indicates that
there is about one star per 300 cubic light years in the Sun's vicinity,
which is the same as one star per sphere of 4.15 light year radius, whence
s = 1-61 x 4-15 light years,
or about 7 light years.
APPENDIX G.
DENSITY OF INTERSTELLAR MATTER IN THE GALAXY.
Assuming that the total interstellar mass (gas and dust clouds) is
equal to 10 11 times that of the Sun ; diameter (central lenticular part),
100,000 light years, thickness (maximum), 20,000 light years, we have
Mass of Sun = 1-98 x 10 33 grammes.
Total Mass = 1-98 x 10 38 x 10 n = 1-98 x 10 44 gms.
TT Diameter 3 ,
Total Volume = (TT 3-14 ).
6 5
- 1-05 x 10- 1 (10 6 x9-46xl0 17 ) 3 cm. 8
= 8-6 x 10 68 cm. 8
1-98 x 10 44
" 846 x 10" " 2
156 Stellar Astronomy
That is to say, of the order of 10~ 26 that of water, as against the 10' 22
required in the hypothesis of collection of hydrogen mentioned on page 87.
APPENDIX H.
APPROACHES AND COLLISIONS BETWEEN STARS.
Assuming that the stars are scattered at random, the expression for
the time between approaches of stars in general to a given star is
S
t =
3-14 / 2 v
where t is in years, S is the volume containing one star, / the limiting
distance and v the average relative velocity of the stars.
Let S = 300 cubic light years, I = the radius of Neptune's orbit
(srVff tight year) and v =25 miles per second ( T Vff tight year per year), then
300 x 2150 2 x 7400
t = --------------------------------
3-14
= 3-2 x 10 12 years,
i.e., there would be, on the average, one approach within a distance equal
to the radius of Neptune's orbit every 3 billion years.
It can be shown that for actual collision, allowing for the effect of
mutual gravitational attraction, something like one hundred thousand
billion years (10 17 years) would be necessary, and that with 35 thousand
million stars (the number suggested by Seares and van Rhijn) there would
be a direct collision observed only about once every three million years ;
The number of dark bodies necessary to account for novae on a collision,
or even near approach theory (although near approaches are much more
numerous than collisions) seems too great.
APPENDIX J.
APPARENT MAGNITUDES AND DISTANCES OF GALAXIES.
The formula M=w+5-f51og7r may be written
M = m + 5 5 log r, where r is distance in parsecs.
^ ,., m + 5 M ^ M
From this log r = =0-2 + 1
5 o
Substituting 15 for M, we get
log r = 0-2w + 4-0
or log d = 0-2w -f 5-51
when d is in light years instead of parsecs.
Appendices 157
The value 15 is for an average galaxy. As the limiting magnitude
photographed by the Mt. Wilson, 100-inch is 21, such a galaxy would
be at a distance so that log d = 0-2 x 21 + 4-51 = 8-71, which corres-
ponds to a distance of 500 million light years.
APPENDIX K.
THE CEPHEID PERIOD-LUMINOSITY RELATION.
/
A theoretical period-luminosity relation can be derived which gives
some support to the values of the accepted curve ; or, alternatively,
gives support to the application of the relation to galactic Cepheids where
it has not yet been possible to derive it directly owing to the very small
parallaxes and proper motions involved.
The relation period (P), inversely proportional to the square root of
the density (p), may be written as P 2 proportional to 1 /p. Volume is
proportional to mass/density (fi/p), and the surfaces of the stars are
proportional to the two-thirds power of the volume, or to (/x//o)f . Assuming
the period-luminosity relation to be valid P 2 can be substituted for \jp t
and we have surface proportional to (p P 2 )t. As radiation is proportional
to surface and to the fourth power of the surface temperature (Stephan's
Law) we have
Radiation (R) = k (p P 2 )! T 4 , where k is a constant,
whence k - #///, PI T 4 .
From this formula, absolute bolometric magnitudes may be derived,
estimating masses by a curve based on the formula of page 11, and
assuming 3-2 (the observed value for the 10-day Cepheid).
Period Mean Effective Bolometric Estimated Bolometric
days. Spectrum. Temperature, abs. mag. Mass abs. mag.
(Observed) (Sun = 1 ) (Computed) .
0-5 A 6 8500 -0-4 3-7 -0-5
1-0 F 1 7100 0-9 4-4 0-9
5-0 Gl 5100 -2-5 8-4 -2-3
10-0 G3 4750 -3-2 12-0 (-3-2)
20-0 G6 4400 -4-1 19-5 -4-2
50-0 G9 4100 -5-6 45 -5-7
The agreement between the observed and calculated values of bolo-
metric magnitude provides remarkable support for the relative accuracy
of the period-luminosity curve ; and at the same time for the validity
of the theoretical relation between period and density in Cepheids, the
computed magnitudes being based entirely on observational data,
astronomical or laboratory, plus the assumption of the gravitational
period-density relationship referred to.
158 Stellar Astronomy
It is also worth noting that calculation on the same lines, but adopting
a brighter or fainter absolute magnitude than 32 for the 10-day Cepheid,
shows larger differences for the stars of shorter or longer periods than in
the table above. This is at least a rough confirmation of the order of
luminosities of the accepted period-luminosity curve, the general trend
of which is shown to be very close to what is calculated from the assump-
tions in the table. (See B.A.A. Journal, 38, 255, 1928).
APPENDIX L.
THE MEAN DISTANCE OF A GALAXY TO ITS NEAREST NEIGHBOURS.
From the formula
Log d XB 0-2 w + 4-51,
the distance of an average galaxy, and the effective limit for the 100
million galaxies, which can be photographed with the 100-inch reflector,
is 500 million light years (Appendix J).
By the formula in Appendix F,
r
s = 1-61 (where s is distance apart),
we get as the average distance to its nearest neighbour,
500,000,000
s - 1-61 " l r = 1,730,000 light years.
100,000,000*
APPENDIX M.
HYPOTHESIS OF COSMIC EVOLUTION.
There are so many uncertain factors, such as the question of me
expanding or stationary universe, its size, the density of the matter in it
(masses of galaxies being still uncertain), the real nature of the spiral
arms, etc., that it has been thought advisable to condense the account
of the speculations of Sir James Jeans, given at some length in the first
edition of this book, into this appendix, as an interesting and valuable
hypothesis, but hardly more than that at present.
Jeans draws attention to the great numbers of external nebulae of
regular shapes (elliptical, spiral, etc.), each in mass and size apparently a
star system. Differing in shape and in apparent dimensions and bright-
ness, those of the same type are mostly of the same real size and roughly
the same luminosity. The types can be arranged in a practically con-
tinuous sequence which, he considers, it is reasonable to believe is an
evolutionary one.
Appendices 159
Rotating initial spheres of gaseous matter were formed from the
original chaos ; these can be calculated, on reasonable asumptions of the
density and temperature of the primeval medium, to have had the mass
of an average external galaxy, and also to have had the spacing apart
which is observed. The effect of tidal forces caused on each other, no
matter how small, can be shown to be ejection of matter localized at
two opposite points on the equatorial edge of the flattened rotating
spheroids, taking the form of spiral streams, in which condensations
would form, the mass and spacing of which can again be estimated, on
reasonable assumptions of density and temperature, to be what should
be expected for the stars as we find them.
Thus Jeans considers that at one stroke there is a possible explanation
of the formation of the stellar contents of the universe.
The scheme outlined deals with three generations of astronomical
bodies as follows :
First, a primeval chaos of hundreds of millions of light years diameter
(or less if the universe is expanding) and a total mass of the order of at
least 10 15 times that of the Sun ; second, a series of stellar systems of
the galactic type thousands of light years in diameter and of masses of
the order of 10 9 times the Sun's ; third, stellar bodies of solar mass, each
generation having been derived from the preceding, chiefly through the
agency of "gravitational instability."
It may be observed of this hypothesis that if the spiral arms "trail"
behind the nucleus in its rotation (i.e., move with their convex sides in
front), which appears to be probably the case (see page 129) formation by
ejection as described could not have taken place. It may also be
remarked that the difficulties attending an explanation of the origin of
rotational movement of the condensations are not met.
GLOSSARY
(OF SOME IMPORTANT TERMS)
ANGULAR the angular separation between lines of sight to dia-
DIAMETER, metrically opposite points in the apparent outline or
APPARENT : disc of an object.
ATOM : the smallest amount of an element which can enter into a
chemical reaction ; it consists of a nucleus, in which is
concentrated most of the mass, made up of at least two
kinds of particle, positively charged protons and neutral
neutrons, each with a mass nearly equal to that of a hydro-
gen atom. The number of protons in the nucleus equals
the number of surrounding electrons (each of mass nearly
equal to 1/1840 of a hydrogen atom), the total of the
negative charges on which balance the total positive
charges on the nuclear protons. This number is the
atomic number of the element. The atomic weight is very
nearly equal to the number of protons and neutrons
together. Other particles possibly concerned in atomic
structure are the positron and the neutrino, each with the
same mass as the electron, but with a positive charge and
no charge respectively, and the mesotron with the same
charge as an electron, but about 150 times as great a mass.
BOLOMETER : an instrument for measuring heat radiations, used with
large telescope for the study of the radiation from, and
temperatures of, stars and planets. It consists of two
very thin strips of blackened platinum forming two arms
of an electrical circuit, the increase in resistance due to the
radiation absorbed being measured by a galvanometer.
CATALYST : a substance which, while accelerating (or retarding) the
speed of a chemical reaction, suffers no perceptible change ;
it probably acts by the formation of some reactive inter-
mediate compound.
COSMOGONY : theories on the origin and evolution of celestial bodies.
COSMOLOGY : the science concerning such theories.
DEUTERIUM : "heavy" hydrogen, an isotope (q.v.) of that element of
atomic weight 2*014. DEUTERON : the nucleus of a
deuterium atom, composed of a positron and two neu-
trons, or of a proton and a neutron ; possibly concerned
with production of energy in the interior of a star at an
early evolutionary stage.
Glossary
161
DOPPLER'S alteration in frequency of light vibrations due to motion
PRINCIPLE of a source towards or away from an observer, whereby
a receding body appears redder and lines in its spectrum
are displaced towards the red, or bluer and towards the
blue in the case of an approaching body,
GALAXIES : nebulae observed outside the Galaxy (Milky Way system) ;
gigantic clusters of stars or ''island universes" separated
from one another by enormous distances.
GALAXY, our own stellar system, composed of stars, dust and gas
THE and radiation.
IONISATION : the subtraction from (positive ionisation) or addition to
(negative ionisation) an atom or molecule, of electrons ;
it results in alterations in the lines of the spectrum, atoms
which have lost two, three or more electrons having
spectra built on the same plan as those of elements of an
atomic number less by the number of lost electrons.
ISOTOPES : varieties of an element of the same properties and atomic
number, but different atomic weights, the atomic nuclei
being of different structure and different numbers of con-
tained neutrons.
LIGHT YEAR: the distance travelled by light in one year, 63,290 times
the radius of the Earth's orbit (Astronomical Unit), or
5'88 xlO 12 miles, or 0'307 parsecs (q.v.).
LUMINOSITY : the total actual output of a star, as opposed to its apparent
brightness in the sky or, also, to its surface brightness per
unit of radiating area. It is usually measured with the
Sun's value as the unit.
MAGNITUDE, a star's brightness as compared with an adopted standard
STELLAR : such as the Pole star, or with a sequence of stars based
on the Pole star. It is graded so that a star of a given
magnitude is 2*512 times brighter than one of the next
lower magnitude ; this figure corresponds to an assumed
ratio of 100 for a difference of five magnitudes.
NUCLEAR the net positive electric charge on the nucleus of an atom,
CHARGE : numerically equal to the atomic number, to the number
of protons in the nucleus, and to the number of electrons
outside of the nucleus.
PARALLAX, the angular change in position of a star in the sky caused
STELLAR : by the movement of the earth round the Sun. It is
expressed as the angle subtended by the radius of the
earth's orbit as it would be seen from the star. Trigono-
metric parallax is obtained in modern methods by
photographic measurements of the displacements relative
to fainter background "comparison" stars, corrections
162
Stellar Astronomy
being applied for the estimated smaller parallactic dis-
placements of these stars (i.e., a correction from relative
to absolute parallax).
PARSEC : the distance corresponding to a stellar parallax of one
second of arc, equal to 3*26 light years (q.v.) or to 206,265
astronomical units, or to 19*16 x 10 12 miles.
PHOTON : a quantum (q.v.) of radiant energy, the fundamental unit
of light intensity.
PHOTOSPHERE : the luminous surface of a star, from which much the
greatest part of its radiation proceeds ; situated at about
the level where the atmospheric and ejected parts of the
star's material begin.
PROPER the apparent angular motion (per year or per century) of a
MOTION star or other celestial object outside the solar system, on
the celestial sphere.
QUANTUM : fundamental unit of radiation with which is associated
a definite amount of energy which is dependent only on
the frequency of the radiation.
RADIAL the motion per second in the line of sight of a star or other
VELOCITY : celestial object as ascertained by the application of
Doppler's Principle (q.v.).
RADIATION : the emission of any rays, wave motion or electrically
charged particles, from a source. The term is usually
applied to electromagnetic waves travelling at 186,300
miles per second ; the best known, in order of increasing
wave length, are gamma rays, X-rays, ultra-violet rays,
visible light rays, infra-red (heat) rays, wireless or Hertzian
waves.
RADIATION pressure on a surface due to the momentum which (as
PRESSURE : well as energy) is carried by electromagnetic waves. It is
of importance in its effects on interstellar matter, and in
the interior of a star where it is extremely intense.
TEMPERA- temperature on the absolute or Kelvin scale, zero being
TURE, taken as the temperature at which the molecules of a gas
ABSOLUTE : would have no kinetic energy, i.e., at -273 C. ; absolute
temperature is thus temperature in degrees centigrade,
plus 273.
WAVE- the distance between corresponding phases, e.g., from
LENGTH : crest to crest, of two consecutive waves. It is usually
expressed in Angstrom units of 10~ 8 cm. or 0*39 x 10~ 8
inch, and denoted by the prefix A. Thus A 6000 refers to
a wave-length of 6xlQ- 5 cm. or 1/42,330 inch. The
unit micron (p) is sometimes used ; it is 10,000 Angstroms;
10- 4 cm., or 0*39 x 10-* inch.
INDEX
Absolute magnitude, 2, 148 ; for different spectral types, 10, 13.
Absorption of light in space, galactic, 27, 28 ; Intergalactic, 128.
ADAMS, W. S,, 12, 151.
Age of the Universe, 145.
AITKEN, R. G., 39.
Algol, 44, 47, 48.
Approaches and collisions of stars, frequency of, 156.
Atmosphere, The constitution of a Giant Star's, 69.
Atom, 62, 160.
Atomic number, 63, 160 ; weight, 160 ; structure and spectra, 62-65.
BAADE, W., 140, 142.
BACON, FRANCIS, 147.
BARNARD, E. E., 109, 139.
BERRY, A., 39.
BESSEL, F. W., 16.
Binary stars, ages of, 146 ; eccentricities and periods of orbits, 45 ;
eclipsing, 43, 47 ; frequency of companions, 41 ; origin of, 90-92 ;
spectra of, 40, 46 ; spectroscopic, 42 ; visual, 39.
Black body radiation, 7.
BOK, B. J., 115, 124, 133.
Bolometer, 160.
BRADLEY, J., 16.
BRAKE, TYCHO, 16.
Bright lines in stellar spectra, 68.
Brightness of Milky Way to naked eye, 102.
Brightness, stellar surface, 2, 148.
CAMPBELL, L., 53, 54, 56.
CAMPBELL, W. W., 91.
CARPENTER, E. F., 131.
CASSINI, J. D., 5.
Catalyst, 160.
Cepheid Variable Stars, 49-52, 94-97, 157.
CLERKE, Miss A. M., 137.
Clusters, ages of, 145.
Clusters, galactic, 111-115; globular, 116-119; moving, 20-22.
Collisions between stars, frequency of, 156.
Colour index, 2, 149 ; and apparent stellar magnitude, 31.
Cosmic year, The, 122.
Cosmogony, Jeans's theories of, 158.
c-Stars, 10.
CURTIS, H. D,, 9.
164 Stellar Astronomy
Densities, stellar, 7, 13, 77, 78.
Density of matter in Galaxy, 155.
Deuterium, 160.
Diameters of stars, apparent angular, 8; formula for, 154; on stellar
photographs, 6.
Dimensions, stellar, 5-8, 13.
Dipper, The Bowl of the, 141.
Distance to neighbouring stars, average, 155.
Distribution of stars, 25-27 ; in galactic latitude, 30, 34; in galactic
longitude, 31, 35 ; in space, 34-35.
Doppler's principle, 161.
Double stars, see Binary stars.
EDDINGTON, A. S., 20, 79.
Eclipsing variables, 43-45, 47-49.
Effective temperatures, 2, 148.
Elements in Sun and stars, 65-66.
Energy in spectra, distribution of, 151.
Energy, source of stellar, 79-82.
Evolution of galaxies, 130, 158-159.
Evolution of the stars, 83-90 ; former ideas of, 83-84 ; present ideas of,
85-90.
External galaxies, 127-141.
FLAMSTEED, J., 16.
Galactic latitude, stellar distribution in, 30, 34.
Galactic longitude, distribution of celestial objects in, 35-37, 113, 219.
Galactic nebulae, 103-109.
Galactic rotation, 22-25.
Galactic structure, the main, 121-124.
Galactic system, the, 101-103.
Galaxies, classification of, 129 ; clusters of, 135-136 ; distances and
dimensions of, 132-133 ; distribution of, 128-129 ; evolution of,
130, 158-159; globular clusters in, 131, 140; internal motion?
and masses of, 133-134 ; mean distance to nearest neighbours, 158;
resolution of, 130 ; rotation of, 134 ; spectra of, 131 ; surveys of,
127-128.
Galaxy, density of matter in, 155.
GERASIMOVIC, 52.
GAMOV, G., 36.
Giant and dwarf stars, 7 ; differences in spectra, 67 ; theory of, 84-85.
GORE, J. E., 120.
HALLEY, E., 5, 16.
HERSCHEL, J. F. W., 115, 137.
HERSCHEL, W., 16, 22, 83, 119-121.
HERTZSPRUNG, E., 7, 21, 49, 106.
HEVELIUS, 5.
Index 165
HINKS, A. R., 120.
HlPPARCHUS, 16.
HORROCKS, J., 5.
HOYLE, F., 89.
HOUZEAU, 102.
HUBBLE, E., 59, 106-107, 129, 131, 133, 135, 137, 139, 143-144.
Internal structure of a star, 77-78.
Internal temperatures in a star, 73, 76, 77, 78.
Interior, a star's, 73-78.
Interstellar, light scattering, 29-30.
lonisation, 161.
Isotopes, 161.
JEANS, J. H., 80, 158.
JOY, A., 23, 28, 49, 54.
KANT, I., 22.
KAPTEYN, J. C., 20, 21, 25, 32, 122.
Kinetic energy of stellar motion, 18.
KOHLSCHUTTER, 151.
K-term, the, 17.
KUIPER, G. P., 90.
Lane's Law, 76.
LAPLACE, P. S., 90.
LlNDBLAD, B., 23.
Light in space, absorption of, 27-30, 128.
Light year, 161.
Local System, is there a, 115-116.
Long Period variable stars, 52-55, 97.
Luminosity of a star, 161.
Luminosity Law, the, 32-33.
LUNDMARK, K., 94.
LUYTEN, W. J., 12.
LITTLETON, R. A., 89.
MACPHERSON, H., 120.
MADLER, J., 22.
Magellanic clouds, 137-138.
Magnitude, absolute (bolometric, photographic, photovisual, radiometric,
visual), 2.
Magnitude, stellar, 161.
Main sequence, the, 10.
Mass-luminosity relationship, 11.
Masses of galaxies, 133-134.
Mass, radiation of Sun's, 61.
Masses, stellar, 11-14; empirical formula for, 11.
Matter in galaxy, density of, 155.
166 tr Astronomy
MERRILL, P., 52.
MCLAUGHLIN, D. B., 58, 99.
Mesotron, 160.
MESSIER, C., 3.
MICHELL, The Rev. JOHN, 6, 101.
Milky Way, brightness of, 102 ; concentration of stars to, 30-31 ; poles of,
120 ; Sir W. Herschel's studies of, 119-121 ; star clouds of the, 10
MILNE, E. A., 92.
"Molecular" weight in star's interior, mean, 73.
MOORE, J. H., 12.
Motion of solar system, 16.
Motions of stars, proper, 15-16.
Moving clusters, the, 20-22.
Multiple stars, 41.
Nebulae, classification of, 103; dark, 109-111; designations of, 3;
densities of, 105, 108; diffuse, 105-107; dimensions of, 104,107;
masses of, 104; planetary, 103-105; spectra of, 108-109; source of
luminosity of, 106-107; temperature of, 104,109; variable, 108-109.
Neutrino, 160.
Neutron, 160.
NEWTON, I., 6, 28.
Novae, 56-60; recurrent, 99 ; theories of, 98-100.
Numbers of stars, 25-27.
Obscuring clouds, Milky Way, 109-111.
OORT, J. H., 24, 30, 116.
Origin of stars, 85-86.
0-type stars, 13.
Parallax estimation, modern indirect methods of, 151-154.
Parallaxes from proper motions, 18-19.
Parallax, stellar, 161 ; trigonometric, 161.
Parsec, 162.
Period-Luminosity relationship, Cepheid, 51, 157-158.
Photographic magnitude, 2.
Photosphere, 162.
Photovisual magnitude, 2.
Planetary nebulae, 103-105.
PLASKETT, J. S., 23.
Positron, 160.
Pressures in stellar atmospheres, 66-67.
PROCTOR, R. A,, 1, 20, 152.
Proper motions of stars, 15-16, 162.
Ptolemy, 94.
Pulsation theory of variability, 95-97.
Radial velocities, of diffuse nebulae, 109; of stars, 17, 162.
Radiatior, 162.
Index 167
Radiation pressure, 75-76, 162.
Radiation, rate of stellar, 78.
Radiator, perfect, 7.
RASMUSON, N., 20, 21.
Reddening, space, 29.
Red-shifts and their meaning, 142-145.
.Relationship, Period-Luminosity, 51, 157-158.
Relativity shift, in spectrum of Sirius B, 12 ; in spectrum of O-type
stars, 13.
ROSSITER, R. A., 43.
Rotation, of Galaxy, 22-25 ; of galaxies, 134 ; of stars, 69.
"Rotation effect" in eclipsing binaries, 43-44.
RUSSELL, H. N., 7, 41, 46, 93, 146.
SEARES, F. H., 19, 26, 31, 32.
SHAPLEY, H., 34, 51, 118, 121, 128, 129, 131, 133, 135, 138, 139, 144.
SHAPLEY, Mrs. H., 93.
SIMPSON, G. C., 94.
Sky, Star-occupied, 27.
SLIPHER, V. M., 106, 142.
SMITH, SINCLAIR, 130, 134.
Space, a dip into, 141-142.
Space reddening, 29.
Spectra, of galactic nebulae, 108-109 ; of non-galactic nebulae (galaxies),
131.
Spectral characteristics, 150-151.
Spectral sequence, significance of, 65.
Spectral type, and absolute magnitude, 13 ; and apparent magnitude,
33-34 ; and distance, 34-35 ; and motions, 17.
Stellar energy, source of, 79-82.
StoY, R. H., 103, 105.
Streaming, star, 25.
STRUVE, F. G. W., 39.
Supernovae, 59-60, 100.
Surface and surroundings, a star's, 61-70.
Surface brightness, stellar, 2, 148.
Temperature, absolute, 162 ; effective, 2, 148.
Temperature of space, 109.
Temperatures in a star, internal, 73, 76, 77, 78.
Temporary stars (Novae), 56-60, 98-100.
TRUMPLER, R. J., 13, 28, 107, 112, 113.
Universe, age of the, 145-147.
Unobscured regions, comparatively, 111.
VAN RHIJN, 25, 27, 28, 32.
168 Stellar Astronomy
Variable stars, classification of, 47 ; Cepheid, 49-52 ; eclipsing, 44-45,
47-49 ; Long Period, 52-55 ; irregular, 55-56.
Variability, the cause of stellar, 93-100 ; pulsation theory of, 95-97 ;
secular stellar, 94.
Velocity, stars of great, 24.
Visual magnitude, 2.
Wave-length, 162.
White dwarfs, the, 11-12, 87.
Widening of spectral lines, 69.
WILSON, R. E., 52.
ZWICKY, R, 59, 100, 143, 146.
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