Oscillations During Thermonuclear X-ray Bursts: A New Probe of Neutron Stars

Tod E. Strohmayer

NASA's Goddard Space Flight Center, Greenbelt, MD 20771

"I- of — e, (.so caUe, Type I, X-ray ^"^ ^"a^
mass X-ray binaries (LMXB) with the Rossi ^.^^^ - 600 H, rangl
amplitude, high coherence X-ray *^~^££ZIZn of the X-ra y burst flux
Substantial spectral and timing evdence pomt to rotat.onal mo de9 of neutron

. the cause of these oscillations, and it is l.ely that %^£^ SL** of these

as well as the physics of thermonuclear burning on accret.ng neutron stars.
KEYWORDS: stars: neutron - stars: rotation - X-rays: bursts - equation of state

1. INTRODUCTION

During the past 25 years X-ray astronomers ^^^^£^t

in an attempt to identify the spin frequencies £ ^^^^ ly pr L P ted

example Wood et al. 1991; Vaughan et al. 199 4) J^*™^^ t L millisecond

by the discovery in the radio ^^^^^^S'^ suggesting

radio pulsars see Backer et al. 1984), and suDseque

their origin lie in an accretion-induced spin-up phase of LMXB £ee the e J

Bhattacharya 1995 and references *^>\*^ r ^£ ,',»" „g neutron stars

little or no direct evidence to support the existence rf ap«Uy sp,nn g

in LMXa This -«^t££r££^.£?tL. ° f te '— h

s^srsssi- * *•* ™ z -

" It'^ent these osciiiations have ^^<Z£^^Z

induced S pi„- up (WetSXapo n H^S^^r^ ? """^
review our observational understanding of th« n ' contribution I will

they can be understood in th^ ^context nf °T *' ^ empha * is ° n how

I will discuss how detailed model! nf of tnT ^nl^ ° f *" X " ray burSt flux "
structure can be used to nWpt § ♦ osclIlat ion amplitudes and harmonic

neutron stars and her Le the I S "* fT^T m ^ maSSeS and radii *
Inferences which caTbe dTa wn 1. H ., T* ° f SU P ranuclear density matter,
also be discussed Twn ctndude w[th? ^J f thermonuclear burning will
—ties and where ^^^^ ^^l^^^- **
2- OBSERVATIONAL PROPERTIES OF BURST OSCILLATIONS
4 B U r i72°8 SC i la h i0 S 1 th " freqUenCy ° f 363 Hz were first d ^overed from the LMXB

served frequencies are g^inS?"^ ^ ?u S0UrCeS and their ob -

important obwvationS^t^oJ;? «*«"nder ° f thiS SeCti ° n I review ^
evidence supporting^' S^^^™ "* «*«* * * «* the

2.1. Oscillations at burst onset

Many bursts show detectable oscillations durine the « 1 - 2 , ri«,r * ■ ,
thermonuclear bursts Forexamnlp ^™h g ™ G ~ 1 ~ 2 s ™etimes typical of

some bursts from 4U 1728-34^^ os 2 ^ . I & SwMk (1 " 7) Sh ° Wed that
s of the observed onse of the burst T p f T^/T " ,MBBM 43 % within 0" 1
decreased monotonica l v ^ !h P h ^ Sh ° Wed that the Oscillation amplitude
the burst l^^^^^TtSTh ^ ^L" 5 the fiSing P° rtio ^the
burst had Jo.dll-^^tSj^S^SJ^^ J U 1 f«S-™-
of radius expansion beginning „.«!. * v. ~ u ' then showed an e P is °de

(see Strohmayer et ffi^ wh ? th « °f cillation »**ame ""dectable
flux approaching 100 % right at *t%^£ m .° dulatl0 f * the thermal burst
the burst there exists a IoSIpH h ? L I ""^ Mth the idea that ea ^ in

the neutron star T htstet io th T f^,^" modula ^ d by the spin of
when the spot is sma lest 2th Tsno ' , m ° dulation amplitudes are produced
surface, ^ ^^Z^r^^^^Z^ of the neutron star

MteXZX™^^ sugg r ts that f emission is iocai - d

and temporal resolution to sLl , J E , few / nstr ^ents had the collecting area
thermonuclear *JT£t&^^^"» ** *■ times of

- — evolution -ft2£«^^

1 20

1 OO

SO

60

40

r

20

-

1 _, —

- 1.5x10

FIGURE 1. The amplitude of oscillations at 580 ~g J^risi ng ph-o^a
burst from 4U 1636-53. The amplitude is greatest near the onset 01
decreases as the burst flux increases.

TABLE 1. Burst oscillation sources and frequencies

Object
4U 1728-34
4U 1636-53
4U 1702-429
KS 1731-26

Aql X-l
Gal. Center

Frequency (Hz)
363
580 (290)
330
526
549
589

intervals during several bursts and plotted ^ the flux £ , J^^feS
black body emission from a spherical surfac * this ratio * aeon P P

to {m * t where d and H ^^^^Z^^S, line connects
2 shows such a plot for a burst from 4U 728 J^ In th p ^ ^ ^^

successive time intervals, with the burst beginning evolution indicates

diagonally to the upper right and then acrc*s t , tte ML rh» evolu ^

that the X-ray emitting area is not constant, but ^™ Taam

burst rise. The spectra of type I bursts are not _true , Mack bod«s <
& Howard 1986; Ebisuzaki 1987; Lewin, van ^"fj^X™/'^ spec trum.
argument here concerns the energetics ^^f^^^ expansion
Since the effect is seen in burst s tha do no t ^ P h p ^

the neutron star.

2.2. Expectations from the theory of thermonuclear burning

S^^!^^.**r an x - ray burst burns * a *" -

> 103 difference etwel the a cult L ^ "^ ^ « ewraI hou "" This
unlikely that the condition ; reo . Z u "^ tim6SCaleS means that * is

taneously over ttetSSl'T ^instability will be achieved simul-
(1978), led to the studv of ! , realization, first emphasized by Joss

surface (^1^^^^^° T* IT** 0Ver the neUt ™ Star
sten 1995). The subsecond ril ' ft *' ^^ & ^J™ * 1984 ' and Bild-
convection play ZZ P Zt^l2l t ^^ ?""* ^^ SUgS6StS that
especially in the low aTret ion rat re ^ ^ bUming fr0nt P^P^tion,

Bildsten ( 1998) tet^^S?*™ f ^J"* t0 ^ ^ ition col "™s (see
(1995) has shown tha nZ hi 7 ^ bU ™ ng °" neUtron stars )- BUdien
mhomogeneousXlavC ran f H?"* *" u^™ *" SUrfaces is in general
rate, wifh low S^S^ 1 ? ^ ^ the ,OCaI a - retion
and standard type I bursts w MeS ^T * fustible accretion columns
Propagation wh'ch may b man esS tnZ "7 '*? ^u ^ n0nco ™ctive
that the physics of thermit, T " g flar6S - TheSe studies emphasize

lem and SJt /^SStt^ 8 " .T^ * mU,ti - dim ™^ prob-
The properties of oSSf-lh f P ', ^^ * the ° nSet of bursts -

Picture ■ J the rr^tZ^^ZZSJ:^ *°» " *" *"> «*

- SSt Sotrmt^r g*s 5 ? E H T bb r onic

and that the strong signal a?™ H ft" ' he 5p ' n { "">"""y * 290 Hz,

correct this resuUhL Mer.„L ?■ " ""'f by nearly uti Hal hot spots. If
particular, hoT L Cn ^caS ^Z ** *" I* 8 '" ? ""*" """'"^ '"
-s „ f seconds, and JJ.'T.^'X^tS^

2.3. The coherence of burst oscillations

in the cooling tauT^S 1 t™, ' " "*t " """^ "* * > ~3 Hz

cooling tail of a bursffrorT/u S 53 Te °° "° J**"* "' "*" "° m '" "*
of the six burst oscillation «L™ 5' fVe<!ue ° c >' evol »"°" has been seen in live

.be ph^ics °n^2™oZ%7:z ,» ?,r monly rr ied - ith

0.0070 r

0.0060

0.0050 r

0.0040 r

O.0O30

1 .0x1

' 8 3.0X10 -8 4.0X10"
F BO , (ergs cm" 2 s'')

5.0x1 O

FIGURE 2. Bolometric flux F bol versus F^/kTss^ *^£^£££
The burst evolves from lower left to upper right and then to the left This beh av ,or
J strong evidence for an increasing X-ray emission area during the burst rise.

The shell then spins back up as it cools and recouples to the bulk of the neutron
t „ angular momentum ^"^jl^^ ^''.evend hundred Hz spin

oTfinHe Juration equal to the length of the data trains in «^ «u£
areue strongly that the mechanism which produces the modulations is a nigmy
:ZXoL, such as stellar rotation, and that the ^^^
served during bursts represent the spin frequency of the neutron star.

2 4 The long-term stability of burst oscillation frequencies

The accretion-induced rate of change of the neutron *"*&J^%'"£^
is approximately 1.8 x 1CT 6 Hz yr" 1 for typical neutron star and LMXB parameters.

Parameters. Thi,doppli"hif{ e ~, v H„ • , ' g ^"""^ LMXB s y st <™

-d searcXra-StppTer ST*" Pe ' i0d diS,rib ° tta «"»» "»«■

ST 329

328

327

S5H=r^ :r^rf,rs

3. BURST OSCILLATIONS AS PROBES OF NEUTRON STARS

of neutron star* Tn „= ♦ ■ . u f related to the structure and evo ution

probe neutron stars.

3.1. Mass - Radius constraints and the EOS of dense matter
Using the rotating hot spot model it is possible to determine constraints on the
mass and radius of the neutron star from measurements of the maximum observed
modulation amplitudes during X-ray bursts as well as the harmonic content <rf the
pulses The physics that makes such constraints possible is the bending of pho-
ton trajectories in a strong gravitational field. The strength of the deflection is a
function of the stellar compactness, GM/c*R, with more compact stars producing
greater deflections and therefore weaker spin modulations. An upper limit on the
compactness can be set since a star more compact than this limit would not be able
to produce a modulation as large as that observed. Complementary information
comes from the pulse shape, which can be inferred from the strength of harmon-
ics. Information on both the amplitude and harmonic content can thus be used
to bound the compactness. Detailed modelling, during burst rise for example can
then be used to determine a confidence region in the mass - radius plane for neutron
stars Miller k Lamb (1998) have investigated the amplitude of rotational modu-
lation pulsations as well as harmonic content assuming emission from a point-like
hot spot. They also show that knowledge of the angular and spectral dependence of
the emissivity from the neutron star surface can have important consequences for
the derived constraints. More theoretical as well as data modelling ,„ this area are
required.

3 2 Doppler shifts and pulse phase spectroscopy

Stellar rotation will also play a role in the observed properties of spin ^odutation
pulsations. For example, a 10 km radius neutron star spinning at 400 Hz has a
surface velocity of v sjnn /c < 2,u apin R « 0.084 at the rotational equate « This
motion of the hot spot produces a Doppler shift of magnitude ^~J'^'
thus the observed spectrum is a function of pulse phase (see Chen k Shaham 1989) .
Measurement of a pulse phase dependent Doppler shift in the X-ray spectrum wouki
provide additional evidence supporting the spin modulation mode and also yields
a means of constraining the neutron star radius, perhaps one of the few direct
methods to infer this quantity for neutron stars.

The rotationally induced velocity also produces a relativistic aberration which
results in asymmetric pulses, thus the pulse shapes also contain information on the
Tpin velocu/and therefore the stellar radius (Chen k Shaham 1989). The compo-
nent of the spin velocity along the line of site is proportional to cos 9, where * ,s
the latitude of the hotspot measured with respect to the rotat.onal equator. The
modulation amplitude also depends on the latitude of the hotspot, as spots near
the rotational poles produce smaller amplitudes than those at the equator. Thus
a correlation between the observed oscillation amplitude and the size of any pulse
phase dependent Doppler shift is to be expected. Dectection of such a correlation in

hyp a o"hti S 0f bUIStS W ° Uld Pr ° Vide Str ° nS COnfirmation of the "Atonal modulation

Searches for a Doppler shift signature are just beginning to be carried out

d ^ ""t I!" tS haV c Sh ° Wn that SpeCtral Variati0ns with P ul ^ Phase can be
detected (see Strohmayer, Swank, & Zhang 1998). The varations with pulse phase

ttTde a a that a T ^"r ° f ^ ^ ^ ^ ^^ -nsltntlS
InlfT a ^Tr^" 6 gradl6nt is preSent on the stel,ar su ^e, which when
rotated produces the flux modulations. Ford (1999) has analysed data during a
burst from Aql X-l and finds that the softer photons lag higher energy photons in
a manner which is qualitatively similar to that expected from a rotating hot spot
S rohmayer & Markwardt (1999) have shown that signals from multiple burial
be added m phase by modelling the frequency drifts present in individual bums

^ ls ZTtz^ tTonger 1 s ? 1 with whkh to test f ° r D ° p p ier ^ ^^- so

t ernT Z T" "^ ^ 4U ™- m have been added in P^e in an
attempt to identify a rotational Doppler shift. A difficulty in analysing the phase

resolved spectra from bursts is the systematic change in the black body temperature

thanthe bt k H^H T C °° 1S ' A "^ "^ ° f the SpeCtral h ^™> ^
than the black body temperature, is the mean energy channel of the spectrum

LraWP™ * d f nbut,on ° f mean «*anneb in the RXTE proportional counter

4U ™ 490 V Tu PU u Se Ph3Se USiDg SpeCtra fr0m 4 dlfferent «"»* from
channel { J 8 "" tT thG reSUltS ' A Str ° n S modulation of the mean PCA
channel ,s clearly seen. There is a hint of an asymmetry in that the leading edge
of the pulse appears harder (as expected for a rotational Doppler shift) thfn the
traihng edge, but the difference does not have a high statistical signified e More
data will be required to decide the rotational Doppler shift issue.

3.3. Physics of thermonuclear burning

The properties of burst oscillations can tell us a great deal about the processes of
nuclear burning on neutron stars. The amplitude evolution during the risLgTh Le
of bursts contains information on how rapidly the flame front is propagating uZ
amtpodal spot hypothesis to explain the presence of a subharmonic in 4U teS^l

om one S" ♦ T"^ impHcations for the Propagation of the instability

from one pole to another m « 0.2 s (see Miller 1999). In addition, a two pole
flux amstropy suggests that the nuclear fuel is likely pooled by some mechanism
perhaps associated with the magnetic field of star. Further detections and study of
the subharmonic m 4U 1636-53 could shed more light on these issues

Until recently, much of the work concerning burst oscillations has concentrated

the' ati: rf "I PU ; Sati0nSth — 1- a « d »* relation to individual bursL W h
the samples of bursts growing ,t is now possible to concieve of more global studies
which correlate the properties of oscillations with other measures of fhese sourc s
for example, their spectral state and mass accretion rate. This will allow researchers
to investigate the system parameters which determine the likelihood of producing
bursts which show oscillations. Such investigations will provide ins lg ht into how he

2.0

FIGURE 4 Pulse phase spectral variations in bursts from 4U 1702-429. The top
panel shows the mean PCA energy channel as a function of pulse pha* = for 4 bursts
wWch were co-added in phase. The bottom panel shows the pulse profile m the 2 -
24 keV band.

properties of thermonuclear burning (as evidenced in the presence or absence of

o Sons) are influenced by other properties of the system. Furthermore, we can

"s iftheo et"a predictions of how the burning should behave are consul tent with

the hypothesis that the oscillations result from rotational modulation of nonum-

ormXes produced by thermonuclear burning. Initial work m this regard sugg ts

haT burst's which ocL at higher mass accretion rates show '^^"^

tions more often (see Franco et al. 1999). Although preliminary his result appears

rough* consistent with theoretical descriptions of the thermonuclear burning whu*

ndicates an evolution from vigorous, rapid (thus uniform) burning at lower man

'accretn Les (lower persistent count rates) to ^^ b £^J m

non-uniform) at higher mass accretion rates (see Bildsten 1995, for example).

4 REMAINING PUZZLES AND THE FUTURE

Although much of the burst oscillation phenomenology is well described by the
i in moduM on hypothesis several important hypotheses need to be confronted
with more derailed theoretical investigations. Perhaps the most interesting is he
Si which causes the observed frequency drifts. Expressed as a phas 1 p
the frequency drifts seen during the longest pulse trains correspond to about 5 1U
eve S around the star. Whether or not a shear layer can persist that long needs
o be tr"her investigated. The recent observation of a, so far unique spin down in
the Lea in tail of a burst from 4U 1636-53 (see Strohmayer 1999), which might

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