Evidence for enhanced persistent emission during sub-Eddington thermonuclear bursts

1.4 MB·English

by  Hauke Worpel

APJ(ACCEPTED)
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
EVIDENCEFORENHANCEDPERSISTENTEMISSIONDURINGSUB-EDDINGTONTHERMONUCLEARBURSTS
HAUKEWORPEL1,2,DUNCANK.GALLOWAY1,DANIELJ.PRICE1
(Dated:January12,2015)
ApJ(accepted)
ABSTRACT
In a recent paper, we found evidence for an increase in the accretion rate during photospheric radius ex-
5 pansionbursts,quantifiedbyavariablenormalizationfactor fa onthepre-burstpersistentemission. Herewe
1 followthisresultuponamuchlargersampleof1759typeIX-rayburstsfrom56sources. Weshowthatthe
0 variablepersistentfluxmethodprovidesimprovementsinthequalityofspectralfitsfortypeIbursts,whetheror
2 nottheyreachtheEddingtonluminosity. ThenewapproachhasanestimatedBayesfactorof64improvement
overthestandardmethod,andwerecommendtheprocedurebeadoptedasstandardforanalysingtypeIbursts.
n
Weshowevidencethattheremainingdiscrepanciestoaformallyconsistentspectralmodelareduetotheburst
a
J componentdeviatingsignificantlyfromablackbody,ratherthanvariationsinthespectralshapeofthepersis-
tent emission component. In bursts that do notshow radiusexpansion, the persistentemission enhancement
9
doesnotexceed37%oftheEddingtonflux. WeusethisobservationtoconstraintheEddingtonfluxofsources

forwhichF hasnotbeendirectlymeasured.
] Edd
E
H
1. INTRODUCTION bysubtractingtheinstrumentalbackgroundonly,butdidnot
.
h TypeIX-raybursts,discoveredinthe1970s(Grindlayetal. find that the spectral fits were improved by doing so. In a
p 1976;Belianetal.1976),arisefromthermonuclearrunaways study of neutronstar radii derivedfrom cooling tail spectra,
- Güveretal. (2012) noted the possibility of variations in the
in accreted H/He material on the surface of a neutron star
o
persistentemissionspectrumandexcludedburstswhosepre-
r (e.g., Woosley&Taam 1976; Strohmayer&Bildsten 2006).
t Gasflowingfromalow-massstellarcompanionaccumulates burstpersistentfluxwasmorethan10%oftheEddingtonflux
s of that source, so thatthe contributionfrom persistentemis-
a on the surface of the neutron star (e.g., Woosley&Taam
sion is always small. in’tZandetal. (2013) studied a PRE
[ 1976; Joss 1977) . There it undergoes hydrostatic heat-
burstfromSAXJ1808.4- 3658usingcombinedChandraand
ing and compression, triggering unstable nuclear burning
1 RXTE data and found that an observed excess of photons at
when the temperature and pressure are high enough (e.g.,
v both low and high energies can be well described by allow-
Fujimotoetal. 1981; Strohmayer&Bildsten 2006). These
0 ing a 20-fold increase of the pre-burst persistent emission.
eventsareobservedasasuddenincreaseintheneutronstar’s
7 Thisapproachwas appliedto 332PRE burstsobservedwith
X-ray luminosity, to many times the persistent level (see re-
0 RXTE by Worpeletal. (2013; hereafterWGP13), where we
views by Lewin&Joss 1981; Lewinetal. 1993). Typical
2 foundthatallowingthepersistentemissiontovaryinintensity
bursts exhibit rise times of 1–10 s, durations of a few tens
0
duringa burst improvesthe spectral fits, and that the persis-
. ofsecondstoafewminutes(e.g.,Gallowayetal.2008),and
1 emitatotalenergyof1039–1040erg. tent emission usually increases temporarily to several times
0 itspre-burstlevel.
Type I bursts provide a probe into the conditions on the
5 Since the intensity of the persistent emission is expected
surface of the neutron star and yield insights into its inter-
1 toincreasewithincreasingaccretionrate,WGP13interpreted
nal structure (Lattimer&Prakash 2007). Performing such
: thiseffectasatemporaryaccretionenhancement,possiblythe
v measurementsrequiresan accuratedeterminationof the flux
resultofthedisklosingangularmomentumviaradiationdrag.
i throughouttheburst. Thisinturnnecessitatesagoodunder-
X Other interpretationsare possible; in’tZandetal. (2013) ar-
standing of the X-ray spectra since bolometric flux cannot
gue for reprocessing of the burst spectrum in the accretion
r be measured directly from photon count (Blissett&Cruise
a disc.
1979),andwemustalsoknowhowtoseparatethefluxfrom
The"variablepersistentflux" approachhassince beenap-
the expandingatmosphere from that arising from other sites
pliedsuccessfullybyotherstudies(e.g.,in’tZandetal.2013;
in the neutron star system. One such contribution is the ac-
Keeketal.2014;Peilleetal.2014),anditisbecomingclearer
cretiondiscitself. ItemitsX-raysthroughthe conversionof
thatburstsaffecttheaccretiondiscandcanbeusedtoprobe
gravitational potential energy of the inspiralling gas. This
accretionphysics. Inaninvestigationofalongdurationburst
emission is present before the burst, and has traditionally
from4U1636- 536,Keeketal. (2014) foundthatthe persis-
beenassumedtoremainconstant(bothinspectralshapeand
tent emission was enhanced by a factor of 2 and also in-
inintensity)throughouttheburst(e.g.,vanParadijs&Lewin ≈
ferred a significant modification of the inner accretion disc.
1986;Lewinetal.1993;Kuulkersetal.2003;Gallowayetal.
Adepletionoftheaccretiondisc throughradiationdragdur-
2008).
ing a burst was predicted by Walker (1992), who found in
Munoetal. (2000) and Strohmayer&Brown (2002) al-
numerical simulations that the accretion rate after the burst
lowed for the persistent emission to be suppressed entirely,
candeclinetemporarilytohalfthepre-burstlevel.Peilleetal.
(2014)performedastudyofquasi-periodicoscillationsfrom
1SchoolofPhysicsandAstronomy,MonashUniversity,Clayton,Vic- 4U1636- 536and4U 1608- 522,andfoundthattheseoscil-
toria3800,Australia lations were suppressed for severaltens of secondsafter the
2Leibniz-InstitutfürAstrophysikPotsdam(AIP),AnderSternwarte16,
burst.Theyattributethisphenomenontoadepletionofthein-
14482Potsdam,Germany
2
neraccretiondisc,thoughitsfastrecovery(5-10timesfaster BAR)4.
than the viscous time) remains a mystery. Clearly a greater We classified type I bursts as either belongingto the pho-
observationalandtheoreticalunderstandingofthe behaviour tosphericradius expansion(PRE) class of bursts, or not, ac-
ofaccretionontotypeIburstersisrequired. cordingtothecriteriaforradiusexpansiondescribedin§2.3
Disentangling the burst component of the spectrum from of G08. In brief, these criteria define radius expansion as
the persistent component is difficult, as the various compo- an increase of the surface area of the photosphere together
nents are usually spectrally degenerate. Furthermore, we withadecreaseinitstemperature. Asmallnumberofbursts
do not have spatial resolution and therefore cannot attribute fulfil some, but not all, of the criteria and are classified as
different spectral components to different sites in the neu- "marginal"PREbursts.
tron star system. This problem will be further compli- Ourdatareductionproceduresarethe same asthosein §2
cated if, as we expect, both the persistent and burst com- of WGP13, unless otherwise stated, and we refer the reader
ponents can vary in spectral shape during a burst. In- to that work for further details. To estimate and removethe
deed, it has long been known that the spectral shape of instrumental background we used the full-mission, “bright”
the persistent emission, as well as its intensity, is a func- source(>40countss- 1)modelsreleased2006August6with
tionofaccretionrate(Hasinger&vanderKlis1989;seealso the pcabackest tool. Table 1 lists interstellar absorption
Lyuetal. 2014). There are, however, suggestions that be- columndensitiesforallburstsourcesandthereferencesfrom
tweenburststheaccretionspectrumremainsconstantinshape which these were drawn; the table includes several sources
on timescales longer than those of a burst, though its in- that were not investigated in WGP13 because they have no
tensity may vary (e.g., Thompsonetal. 2005; Bagnolietal. PREburstsintheMINBARcatalog.
2013; Linaresetal. 2014). During a burst it is, of course,
much more difficult to detect changes in the accretion spec- 2.1. Burstselection
tral shape. A sudden loss of high energy (&30 keV) pho-
WerestrictoursampleoftypeIburststoexcludeeventsthat
tons has been detected from several sources, but this effect
areunsuitableforanalysis. Wediscarded57burstsforwhich
has been attributed to rapid coolingof the coronaand is not
noStandard-2datawasavailable,preventingestimationofthe
related to accretion rate (Maccarone&Coppi 2003; Jietal.
instrumentalbackground. Someburstsourceslieincrowded
2013; Chenetal. 2013). Changesin the shape and intensity fieldscontainingotherLMXBswithinthe 1◦RXTEfieldof
ofthepersistentemission duringa verylong(20,000s)burst ∼
view. Ifthe othersource(s)wereactiveat thetime ofobser-
from 4U 1636- 536were reportedby Keeketal. (2014), but
vation,thentheirpersistentemissionwouldbeconfusedwith
variations on these timescales can happen in the absence of
thatoftheburstsourceanditwouldbeimpossibletoseparate
bursts,andtheburstsweconsiderinthispaperareverymuch
the persistent emission of the burst source from that of the
shorter.
othersource(s).Suchburstsneedtobeexcludedfromconsid-
PRE burstschangethestructureof theneutronstarphoto-
eration. Ourprocedurefor removingsource-confusedbursts
sphere,andthisislikelyto causethespectrumofthephoto-
is the same as WGP13 §4.1. A total of 168 bursts were ex-
sphereto deviatefromits usualnear-blackbodyshape. Such
cludedasbeingsourceconfused.Ourcatalogalsocontains16
changesare unrelatedto the accretionspectrum. As pointed
typeIburstsfromtheRapidBurstertakenduringoffsetpoint-
outbyWGP13,thesewillconfoundspectralanalysesofper- ingstoavoidconfusionwiththenearby4U1728- 34.Wealso
sistentemissionduringaburst.Suchcomplicationscanbere-
excluded35burstswhoseradiusexpansionstatuswasunclas-
movedbyconsideringnon-PREbursts,butcaremustbetaken
sifiableduetodatagapsorverylowflux,and58burstsclas-
toaccountforlowersensitivityduetotheirintrinsicallylower
sified as "marginal"(i.e. satisfying onlysome of the criteria
flux.
of§2.3inG08).
Inthispaperweinvestigatetherelationshipbetweenaccre-
tionandtypeIbursts.WeapplythefittingmethodofWGP13
2.2. Characterizingthepersistentemission
to every type I burst detected by RXTE. In addition, we in-
As in the previous studies G08 and WGP13 we adopted
vestigatethevariabilityofthe accretionspectraimmediately
the integrated X-ray flux for a 16-second interval prior to
beforeandafterbursts,todeterminewhetherourspectralfit-
the start of each burst as the persistent emission. This spec-
tingprocedurecanbeconfoundedbyrapidchangesintheac-
trum includes a time-dependentcontribution estimated as in
cretionspectrum. In§5wedevelopamethodforobtaininga
WGP13. Subsequentmodelfitstoeachpersistent(andburst)
lowerboundonthe Eddingtonfluxforsourcesthathavenot
spectrum used the corresponding model spectrum estimated
yetbeenobservedtoundergoPREbursts.
forthatburstasbackground.
For each burst we fit the persistent emission with a set
2. DATAANALYSIS
of nine alternative models in turn. These are summarized
We used observational data from the Rossi X-Ray Tim- in Table 2, and are the same six persistent models as in
ing Explorer (RXTE), publicly available through the High- WGP13,withtheadditionofwabs*disko,wabs*diskm,
Energy Astrophysics Science Archive Research Centre and wabs*(CompTT+gaussian). The first two of these
(HEASARC)3. The observations date from shortly after the includeaccretionrateexplicitlyasavariableparameter,mak-
satellite’s launch on December 30, 1995 to the end of the ingitpossibletoinvestigatetherelationshipbetweenthenor-
RXTEmissiononJanuary3,2012.OursampleoftypeIbursts ˙
malizationfactor f andM.ThelatterwasusedbyPeilleetal.
a
isbasedontheburstcatalogueof(Gallowayetal.2008;here-
(2014)andweincludeitforcompleteness. Wethenselected
after G08), with the addition of 880 type I bursts detected thefitthatgavethebest(i.e. lowest)χ2 torepresenttheper-
ν
afterthepublicationofthatpaper.TheentireRXTEburstcat-
sistent spectrum for that burst. As shown in Figure 1, this
alogformspartoftheMulti-INstrumentBurstArchive(MIN-
suite of models provide statistically adequate fits so we re-
3Seehttp://heasarc.gsfc.nasa.gov 4 seehttp://burst.sci.monash.edu/minbar
3
TABLE1
NH VALUESANDEDDINGTONFLUXES
Source Non-PREBursts PREbursts SWFCa SBCb NH Reference FEdd
1022cm- 2 10- 9ergs- 1cm- 2
4U1746-37 22 3 0 2 0.3 1 5.8±1.4
MXB1659-298 11 12 0 0 0.2 2 17.0±4.0
AqlX-1 52 12 0 0 0.4 3 99.6±21.3
SAXJ1810.8-2609 4 1 1 0 0.3 4 111.2±2.5
IGRJ17480-2446 277 0 0 0 0.5 1 ··· c
CygX-2 34 7 0 0 0.1 5 13.1±2.1
GS1826-24 67 0 0 0 0.4 6 ···
XTEJ1709-267 2 0 0 0 0.4 7 ···
4U1820-30 0 16 34 7 0.2 1 57.1±7.7
SAX1808.4-3658 1 8 2 0 0.1 8 230.1±13.2
GX17+2 5 2 0 4 1.9 9 13.3±2.5
RapidBurster 19 0 0 0 1.7 10 ···
IGRJ17473-2721 2 0 0 0 3.8 11 113.5±12.1
CirX-1 13 0 0 0 0.7 12 ···
HETEJ1900.1-2455 0 7 0 0 0.2 13 123.9±10.6
4U2129+12 5 1 1 1 0.0 1 40.8±1.6
1M0836-425 17 0 0 0 2.2 14 ···
4U1735-444 7 10 0 0 0.1 15 34.2±5.6
1A1744-361 3 0 0 0 4.5 16 ···
4U1722-30 0 3 23 1 0.8 1 61.7±12.4
GX3+1 1 2 0 1 1.6 17 59.9±0.9
EXO1745-248 15 2 0 0 3.8 1 69.0±0.2
XTEJ1739-285 6 0 0 0 2.0 18 ···
2S0918-549 1 2 3 0 0.3 19 119.2±12.4
SerX-1 11 6 0 0 0.4 5 29.4±7.1
GRS1741.9-2853 1 4 1 0 11.3 20 35.3±10.9
2E1742.9-2929 65 1 0 0 1.2 18 37.8±1.4
4U1728-34 30 64 0 0 2.6 21 95.0±8.4
XB1832-330 0 1 0 0 0.1 1 33.7±4.4
IGRJ17511-3057 7 0 0 0 0.6 22 ···
4U1608-522 28 18 5 0 0.9 23 167.2±26.0
GRS1747-312 1 1 0 0 1.4 1 13.4±4.4
XTE1814-338 27 0 0 0 0.2 18 ···
XTEJ1723-376 2 0 0 0 7.9 18 ···
4U1254-69 3 0 0 0 0.3 24 ···
4U1702-429 43 5 3 0 1.9 18 87.7±4.5
SAXJ1750.8-2900 3 2 1 0 0.9 18 54.1±2.1
XTEJ1701-462 1 2 0 0 2.0 25 43.4±1.4
XTEJ1810-189 3 1 0 0 4.2 26 54.2±1.8
EXO0748-676 143 5 0 0 0.8 27 46.5±4.6
4U1916-053 1 12 0 0 0.3 28 30.6±3.6
XTE2123-058 3 0 0 0 0.1 29 ···
XTE1759-220 5 3 0 0 2.8 18 15.7±0.8
4U1636-536 269 76 2 0 0.2 5 72.6±9.1
IGR17191-2821 5 0 0 0 0.3 30 ···
SLX1744-300 10 0 3 0 4.5 31 13.9±3.1
SAXJ1748.9-2021 16 11 0 0 0.5 1 38.0±6.0
4U1323-62 35 0 0 0 2.4 32 ···
KS1731-260 21 4 3 0 1.3 33 48.6±5.6
XTEJ1710-281 37 3 0 0 0.4 34 7.1±1.5
IGRJ17498-2921 0 1 0 0 1.2 18 51.6±1.6
SAXJ1747.0-2853 6 10 2 0 8.8 35 52.5±7.1
SLX1735-269 1 0 0 3 0.1 36 49.4±3.9
4U1705-44 77 4 0 0 1.9 37 41.0±3.8
4U0513-40 11 4 3 0 0.0 1 14.5±3.5
SAXJ1806.5-2215 4 0 0 0 1.0 18 ···
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Asaietal.(2000); 6. in’tZandetal.(1999); 7. Jonkeretal.(2003); 8. Wangetal.(2001); 9. Farinellietal.(2007); 10. Frogeletal.
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Gavriiletal.(2012);17. Oosterbroeketal.(2001a);18. J.in’tZand2014,privatecommunication;19. Juettetal.(2001);20. Sakanoetal.
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Pirainoetal.(2007)
aBeppoSAXWide-FieldCamera
bSupplementalBurstCatalog(seetable3)
cNoPREbursthasbeenobservedfromthissource
4
temperatureT andnormalizationK ,andb istheinstru-
bb bb inst
mentalbackground. Pisamodelforthepre-burstpersistent
180
emissionthatalso includesabsorption,thoughforsomeper-
Theoretical
160 sistentmodelswedonotretainthesamenH–thisisameans
ra Measured to adjust the low energy end of the accretion spectrum and
ect140 should not be interpreted as saying anything physical about
p
s thehydrogencolumndensity. The accretionenhancementis
nt 120 quantifiedwiththe f normalizationfactor.Wehavefitatotal
e a
st100 of160,017spectra.
si
r
e
p 80
of 3. RESULTS
er 60 Profilesoffitparameters,usingbothmethods,forthreeex-
mb ampleburstsareshowninFigure2. Wehaveselectedbursts
u 40 from three different sources to illustrate the results. These
N
20 plotsclearlyshowthat faisenhancedtoseveraltimesthepre-
burstlevel, asfoundforradiusexpansionburstsby WGP13.
0 This result is typical for all the bursts in our analysis. The
0.0 0.5 1.0 1.5 2.0 2.5 3.0
χν2 fa forspectraprecedingtheburstappeartobeslightlylower
thanunity,butthisisanartefactoffittingthesespectrawitha
FIG.1.—Distributionofχ2ν forthespectralfitstothepersistentemission modelthatincludesaburstcomponentwhichinrealityisab-
(histogram)comparedtoatheoreticaldistributionofχ2ν foracollection of sentbeforetheonsetofnuclearburning.Thiscausessomeof
spectrawiththesamenumberofdegreesoffreedom(curve).AKolmogorov- thepersistentfluxto be misidentifiedasburstemission. Fit-
Smirnovtestgavea97%probability(D=0.11)thatthetwocurvesarecon- ting the pre-burst spectra with just a normalization-variable
sistent withhaving been drawnfromthe samedistribution, indicating that
persistentmodelgivesresultsconsistentwithunity.
oursuiteofmodelsforthepersistentemissionspectraisadequateforusein
subsequentwork. InFigure3weshowthedistributionsofχ2ν forthevariable
persistent normalization fits and the standard approach fits,
gardthesepersistentmodelsacceptableintheanalysisofthe compared with a theoretical distribution of χ2 for a model
ν
burststhemselves.
thatadequatelydescribesthedata. FitsfrombothPREbursts
Thereisnodifferenceinthedistributionsofbest-fittingper-
andnon-PREburstsareshown. We performedKolmogorov-
sistentmodelsbetweenthePREandnon-PREbursts. Weas-
signedeachmodeladistinctnumericallabelandperformeda Smirnovtestsonthemeasureddistributionsofχ2ν againstthe
theoretical. D and p values are listed on Figure 3, with the
Kolmogorov-Smirnovtestontheresultingdistributions,with
variablefitslistedfirst. Theseresultsconfirmwhatisvisually
D=0.03anda95%probabilitythatbothareconsistentwith
evident in the Figure: the variable persistent normalization
havingbeendrawnfromthesamedistribution.
fits significantly improve the quality of the spectral fits for
Agaspressuredominatedaccretiondisc(wabs*diskm)is
bothradiusexpansionand nonradius-expansionbursts. The
notthepreferredmodelforanypersistentemissionspectrum,
spectralfitsforPREburstsaregenerallypoorerthannon-PRE
indicatingthatthisisnotagooddescriptionofaccretiondiscs
burstsforbothfittingmethodsand,althoughthevariableper-
inLMXBsystems. Instead,weexpectthedisctoberadiation
sistentnormalizationmethodimprovesthedistributionofχ2,
dominated,andpossiblyshowinghardemission. ν
thedeviationfromamodelthatisstatisticallyconsistentwith
For6bursts,nopersistentemissionmodelcouldbefitwith
thedataisstillpresent. Itisclearthatradiusexpansionintro-
χ2ν <3.5. Theseburstswereexcludedfromfurtherconsider- ducesasignificantspectraleffectontopofthevariationsin-
ation.
ducedbyenhancedpersistentemission.Thesecondandthird
panelsshowthatcoolingtailspectraofPRE burstsaremore
2.3. Fittingprocedure
poorlyfitthanspectrafromnon-PREbursts. Thismayimply
AsinWGP13wefirstfiteveryburstspectrumwiththestan- thatPREaffectsthediscand/orphotosphereinamannerthat
dardapproach:ablackbodyspectrum,correctedforinterstel- persists for some time after the photosphere has returned to
larabsorptionusingtheappropriatehydrogencolumndensity thesurfaceofthestar.
for the burst source (see Table 1). We use the recordedpre- We assessed the relative improvementof the variable per-
burstemission,includingtheinstrumentalbackground,asthe sistentfluxtreatmentoverthestandardanalysisbyestimating
backgroundfor these initial fits. See G08 for furtherdetails the Bayes factor, as follows. We interpret the probabilities
regardingthisfittingmethod.Thestandardfitsprovideacom- calculatedfromtheK-Sstatisticsasthegloballikelihoodfor
parison model and spectral parameters, as well as sensible each model, i.e. p(DM,I) where D is the set of χ2 values
i
spectral parameters to seed the variable persistent emission correspondingtothem|odelfits,M representseachfittingap-
i
fits. proach (model), and I the priors. Even if this interpretation
We then re-fit all the burst spectra, replacing the back- is not strictly correct, we expect that the K-S probability is
groundwiththeinstrumentalbackground,andaddingavari- proportionaltotheactuallikelihood,sothattheratioofprob-
ablepersistentemissioncomponentappropriateforthatburst abilitiesisagoodestimateoftheratiooflikelihoods.Follow-
(§2.2). Thatis,wemodelledthetotalspectrumas ingGregory(2005),theothercontributiontotheBayesfactor
S(E)=A(E) B(E;T ,K )+f P(E)+b(E) , (1) calculation is the penalty imposed by the additional degree
× bb bb a× inst offreedomintroducedwiththevariablepersistentfluxfactor
whereS(E)isthefittedspectrumasafunctionofenergyE,A f . Sincethestandardapproachisaspecialcase ofthevari-
a
is the absorptioncorrectiondueto interstellar hydrogen(see able persistent flux approach (with f fixed implicitly at 1),
a
n valueslisted inTable 1), B isa blackbodyspectrumwith wecomparetheeffectiveuncertaintyfortheformerapproach
H
5
TABLE2
XSPECMODELSFORFITTINGTHEPERSISTENTEMISSION
XSPECmodel Number Notes
ofspectra
wabs*diskoa 160
wabs*diskma 0
wabs*(bbodyrad+powerlaw) 425 nHfixedtoliteraturevalues
wabs*(bbodyrad+powerlaw+gaussian) 271 nHfixed,Gaussianenergysetto6.4keV
wabs*(compTTb) 39 nHallowedtovary
wabs*(bbodyrad+powerlaw) 46 nHallowedtovary
wabs*(gauss+bremss) 321 allparametersvariablec
wabs*(bbodyrad+diskbbd) 183 allparametersvariablec
wabs*(compTT+gaussian)e 314 nHfixed,Gaussianenergysetto6.4keV
Totalusablespectra 1759
Rejectedduetosourceconfusion 168 Otheractivesourcesinfield
Backgrounddatamissingorunusable 57
Nogoodpersistentmodelfit 6 Minimumχ2ν>3.5
Marginalradiusexpansion 58
Radiusexpansionstatusunclassified 35
aSeeStella&Rosner(1984)
bSeeTitarchuk(1994)
cAllparametersarevariableforthegenerationofpersistentemissionmodels. Theirvaluesaresubsequentlyfrozenforthe
burstspectralfitsin§2.3
d SeeXSPEC manual(http://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/manual.html)andrefer-
encestherein
eSeePeilleetal.(2014)
(arising from the Gaussian statistics on the pre-burst persis- beginning of the burst and the point at which burst flux de-
tent spectra) with the prior for the latter approach, which is clines below 10% of its peak value, and performed Kendall
flat between f =- 100,100. The median total counts in all τ rank correlations on burst flux against f for each burst.
a a
the pre-burst spectra is approximately 9,000 counts, and so Wefoundpositivecorrelationsin1000outof1419non-PRE
weadopt104counts,givingacharacteristicwidthoftheprior bursts,ofwhich919areatgreaterthan3σ significance. Per-
inthestandardapproachofδf /f √104/104=0.01. The formingthesame testonthe coolingtailsofPRE bursts, we
a a
≡ foundpositive correlationsin 299out of 316. Of these, 286
overallestimateoftheBayesfactoristhen
wereatgreaterthan3σ significance. Thesenumbersdemon-
p(DM ,I) δf 5.77 10- 3 0.01 strate that there is a more direct relationship between burst
B | 1 a = × =64 (2)
≈ p(DM2,I)∆fa 4.51 10- 9× 200 fluxand fa fornon-PREburststhanforPREbursts.
| × WGP13 found that, in PRE bursts, the variations in mea-
Thus,eventakingintoaccounttheadditionaldegreeoffree- sured f cannot be attributed to counting statistics. We re-
a
dom introducedby allowing the normalisationof the persis- peated this test for all non-PRE bursts in our catalog. For
tentfluxtovary,weconcludethatthevariablepersistentflux allspectraobtainedduringnon-PREburstswegenerated100
improvesonthestandardapproachwithaBayesfactorof64. simulatedspectrausingthestandardapproachspectralparam-
Theadditionofathirdvariableparametertothemodelcan eters, and incorporatingcountingstatistics typicalof the de-
haveanadverseeffectontheuncertaintiesin thefitparame- tector. We then fit these simulated spectra with the variable
ters. InFigure4wecomparetheuncertaintiesinfitparame- persistentnormalizationmethod,obtainingastandarddevia-
tersbetweenthetwoapproaches.Itisclearthatintroducing fa tionof fameasurementsarisingfromcountingstatisticsinthe
hasaslightadverseeffectontheuncertaintyintheblackbody absenceofanyvariationofpersistentflux. We foundreal f
a
temperature. Theuncertaintiesinblackbodytemperatureare, measurementsgreaterthanunityto5σsignificancein214of
onaverage,25%largerforthevariablepersistentfluxmethod. 62783.Intheabsenceofarealeffectwewouldexpectatmost
Theuncertaintyintheblackbodynormalizationonaveragein- onesuchcasearisingbychance. Thisexperimentshowsthat
creasesby49%,toabout18%ofthemeasuredvalue.Theun- enhancedpersistentemissionispresentinnon-PREburstsas
certaintyin fa isonaverage27%ofthemeasuredvalue. The well.
poorconstraintson faandblackbodynormalizationarelikely Since PRE bursts are by nature brighter than non-PRE
duetothespectralsimilarityofthetwocomponents.Recently bursts, it is possible that the difference in χ2 between the
ν
Barrièreetal. (2014) showed a severe exampleof this prob-
two classes is simply due to superior signal-to-noise in the
leminusingthevariablepersistentfluxmethodinaNuSTAR
brighterbursts. Toinvestigatethiswetookasubsetofspectra
observationofGRS1741.9- 2853,inwhichthe f factorwas
a from both PRE and non-PRE bursts, with bolometric fluxes
notconstrainedatall. Astheypointout,theproblemoccurs between4.0 10- 8and5.0 10- 8ergs- 1cm- 2andblackbody
when the pre-burst persistent emission is faint, and when it × ×
temperaturesbetween2.0and2.5keV,thesequantitiesbeing
closelyresemblestheburstcomponentinspectralshape.
measuredwiththestandardapproach.Therewere331spectra
WGP13found,forPREbursts,onlyaweakcorrelationbe-
fromPREburstsand655spectrafromnon-PREburstsinthis
tween f andburstflux.Theyfoundthat,althoughmostofthe
high f avalues occurred during radius expansion, there was segmentoftheparameterspace. Thesehadmeanχ2ν of1.17
a and1.35fornon-PREandPREburstsrespectively,andaK-S
antoivneeltyhecloenssstgarneta.tWvaerihaabvielitryepineaftaedwthheinstahnealbyusrisstfflourxnowna-sPrRelE- test indicated a probability of 1.79×10- 6 that these χ2ν are
drawnfromthesamedistribution. Thisshowsthatthepoorer
bursts. We havetakenall spectraforeach burstbetweenthe
6
x)80 Standard fit x) Standard fit x)40 Standard fit
Flu1s− Variable fa fit Flu1s−10 Variable fa fit Flu1s− Variable fa fit
tric 2m −60 4U 1608-522 tric 2m − 8 EXO 0748-676 tric 2m −30 4U 1728-34
e 2002-09-12 07:50:51.5 e 2004-09-25 07:35:16 e 2006-09-08 03:38:13.5
mg c40 mg c 6 mg c20
or or or
ole ole 4 ole
B9 −20 B9 − B9 −10
0 0 2 0
1 1 1
( ( (

0 0 0
-10 0 10 20 30 40 50 60 70 80 -10 0 10 20 30 40 50 60 70 80 -10 0 10 20 30 40 50 60 70 80
time (s) time (s) time (s)
6 6 6
5 Median error bar 5 Median error bar 5 Median error bar
4 4 4
a a a
f 3 f 3 f 3
2 2 2
1 1 1
0 0 0
-10 0 10 20 30 40 50 60 70 80 -10 0 10 20 30 40 50 60 70 80 -10 0 10 20 30 40 50 60 70 80
time (s) time (s) time (s)
3.5 Standard fit 3.5 Standard fit 3.5 Standard fit
3 Variable fa fit 3 Variable fa fit 3 Variable fa fit
2.5 2.5 2.5
2χν 2 2χν 2 2χν 2
1.5 1.5 1.5
1 1 1
0.5 0.5 0.5
-10 0 10 20 30 40 50 60 70 80 -10 0 10 20 30 40 50 60 70 80 -10 0 10 20 30 40 50 60 70 80
time (s) time (s) time (s)
FIG.2.— Comparisonoffittingavariablepersistentemissionfactor, fa,tothestandardapproachfitsfornon-PREburstsfromthreedifferentneutronstars.
Wehaveselectedatypicalhydrogenaccretor(4U1608- 52),adippingsource(EXO0748- 676),andaHe-accretorandlikelyultracompactbinary(4U1728- 34).
Thevariablefitapproachyieldsconsistentlylowerunabsorbedburstcomponentfluxes(toppanels). Thecontributiontothefluxfromthevariablepersistent
emissionincreasestoseveraltimesthepre-burstlevel(middlepanels)duringtheriseoftheburst. Allowingthepersistentemissiontovaryimprovestheχ2ν
(lowerpanels).
spectralfits generally observedin PRE bursts are notdue to shape of the persistent emission. Dipping systems, such as
bettersignal-to-noiseinthebrightbursts. EXO0748- 676andX1658- 298,showsomewhatmorevari-
ability(Sidolietal.2005;Oosterbroeketal.2001b)on 1m
4. ISTHEPERSISTENTEMISSIONSPECTRALSHAPECONSTANT? timescales,andthespectrumbecomesharderduringdi∼ps, as
Our approach of treating the persistent emission as a indicated by hardness ratios. However, the dips are due to
contribution of fixed shape depends upon the assumption obscurationinthesehigh-inclinationsystems. Outsideofdip-
that its shape does not change, at least not on timescales pingintervals,thehardnessratiosareeffectivelyconstant.Itis
of the order of the burst duration, or to a degree suffi- thereforelikelythatnochangeintheshapeorintensityofthe
cient to affect our spectral fits. WGP13 did not investi- persistent emission is to be expectedin the absence of burst
gate this matter directly, but their finding that f generally luminosityonminutetohourtimescales.
a
returns to its pre-burst level, with good χ2, suggests that On shorter timescales, the pre-burstlightcurve is remark-
ν
this assumption is not unreasonable. Similarly, Keeketal. ablyflatprecedingburstsfor4U1636- 536(Nathetal.2002),
(2014) and Peilleetal. (2014) also report that the persistent the Rapid Burster (Bagnolietal. 2013), and 4U 1608- 52
emission returns to its original level soon after the burst. (Peilleetal. 2014), and is also flat over a large range of ac-
Thompsonetal.(2005)andBagnolietal.(2013)havefound cretionratesinIGRJ17480- 2446(Mottaetal.2011). These
that the persistent emissions of 4U 1826- 24 and the Rapid works suggest that short-term intensity variations are not
Burster respectively are remarkably stable over kilosecond prevalentinthepersistentemissionprecedingbursts. Togain
timescales between bursts. Linaresetal. (2014) found vari- furtherconfidencethatthe persistent emission shape and in-
ability over 10 minute periods in the intensity of the per- tensityarenotsignificantlyvariableonshortertimescalesthan
sistentemiss∼ionofIGRJ18245- 2452,withnochangeinthe minutes or hours, in the absence of a burst, we took every
7
Radius expansion bursts (Eddington limited) Radius expansion bursts (Cooling tail)
180 140
a a
r Theoretical (variable fa) r Theoretical (variable fa)
t160 t
ec Variable fa ec120 Variable fa
p140 Standard fit p Standard fit
s s100
t 120 Variable persistent flux t Variable persistent flux
burs100 pD == 10..5236×10−3 burs 80 pD == 70..9357×10−7
f 80 Constant persistent flux f 60 Constant persistent flux
er o 60 pD == 20..651×10−12 er o 40 pD == 30..9438×10−11
b b
m 40 m
u 20 u 20
N N
0 0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
χ2 χ2
ν ν
Non-radius expansion bursts
1600
a
r Theoretical (variable fa)
ect1400 Variable fa
p1200 Standard fit
s
t Variable persistent flux
s1000 D = 0.23
ur p = 5.77×10−3
b 800
f Constant persistent flux
o D = 0.43
er 600 p = 4.51×10−9
b 400
m
u 200
N
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
χ2
ν
FIG.3.— Histogramsoftheχ2ν forthevariablepersistentnormalizationandstandardapproachspectralfits(redandblackhistogramsrespectively),andthe
theoreticalχ2ν distributionsforamodelthatadequatelydescribesthedata(redandblackcurvesrespectively). ThefirstpanelshowsspectrafromEddington-
limitedPREbursts,thesecondpanelshowscoolingtailspectrafromPREbursts,andthethirdpanelshowsspectrafromnon-PREbursts. Itisobviousthatthe
variablepersistentnormalizationapproachgivesbetterfitsoverallthanthestandardapproach. Itcanalsobeseenthatablackbodyburstspectrumisfarfrom
acceptableinPREbursts,eveninthecoolingtailwhentheatmospherehasreturnedtothesurfaceofthestar. Thevariablepersistentnormalizationapproach
correctsformuchofthiseffect. Non-PREspectraarebetterdescribedbyablackbodyandconstantpersistentmodel,buteventhesearesignificantlyimproved
with the variable persistent normalization approach. Results of Kolmogorov-Smirnov tests are also shown; we list the K-S statistic D and null hypothesis
probabilitypforthevariablepersistentnormalizationandstandardfitsrespectively.
700
3500 4000
Standard Standard
3000 Variable fa 3500 Variable fa 600
mber of spectra221055000000 mber of spectra2231050500000000 mber of spectra435000000
Nu1000 Nu1000 Nu200
500 500 100
00.00 0.02 0.04 0.06 0.08 0.10 00.0 0.1 0.2 0.3 0.4 0.5 00.0 0.1 0.2 0.3 0.4 0.5
∆kT/kT ∆K /K ∆f /f
bb bb a a
FIG.4.—Histogramsoftherelativeuncertaintiesinthespectralparametersusingbothapproaches. Theadditionofthe faparametercausesthetemperature
andnormalizationoftheblackbodycomponenttobelesstightlyconstrainedthaninthestandardapproach.Thepersistentfluxfactor faitselfisoftenverypoorly
constrained.
8
9000 500
χ2
8000 Theoretical ν
a
ctr7000 χν2 a400
e tr
p6000 c
e
of s5000 f sp300
o
er4000 er
b b200
m3000 m
u2000 Nu
N
100
1000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
χ2 00 1 2 3 4 5
ν χ2
ν
14000
700
pre-Burst f f
a a
a12000
r 600
t
c
e10000 a
p tr500
c
s e
f 8000 p
o s400
f
ber 6000 er o300
m b
4000 m
Nu Nu200
2000
100
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
f
a 0
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
f
a
FIG.5.—Measureddistributionof fa (redhistogram),andmeasuredand
theoreticalχ2ν (thickandthinbluecurves)forpre-burstemissionintheab- FIG.6.—Measureddistributionof fa (redhistogram),andmeasuredand
senceofanynuclearburning.The favaluesareverystronglypeakedaround theoreticalχ2ν (thickandthinbluecurves)forStandard-2datacoveringthe
1,andthemeasuredχ2ν arelow,indicatingthatthepre-burstemissiondoes observationsofeighteenselectedbursts. The favaluesaretightlyclustered
notchangeintensityorspectralshapetoanydetectabledegree. aroundunity,andtheχ2ν aremarginallyhigherthanthetheoreticaldistribu-
tionassumingawell-fittingmodel.Thissuggeststhatthepersistentemission
doesnotchangeshapeorintensitytoanydetectabledegreeontimescalesof
0.25spre-burstspectrumfromeveryburstandfititwithjust
anhourbeforeandafteratypeIburst.
f timesthepersistentmodelforthatburst,i.e.,nothermonu-
a
clearburstemission.Thedistributionsof f andχ2 areshown fewminutestoanhourbeforeandaftertheburst.Wealsoex-
a ν
inFigure5. Thisdatatypicallycoversafewtensofseconds cludedaneclipseofEXO0748- 676beginningat2004-09-25
prior to every burst. It is plain to see that f is distributed 07:20:29,15minutesbeforetheburst, whennofluxwasob-
a
tightly around unity, indicating that the persistent emission servedfromtheneutronstar(seealsoHomanetal.2003),and
generally does not vary greatly in intensity on timescales of spectra occurringafter a data gap towards the end of an ob-
1sorless. Theχ2 distributionalsoimpliesthattheshapeof servationof4U1636- 536thatbeganat2001-09-0504:56:51.
ν
thepersistentemissionisnotchangingappreciably,although Weanalyzedthedistributionof fa andχ2ν. Theseareplotted
ofcoursetheshortexposuretimesandassociatedlowphoton in Figure 6, showing that almost all of fa values measured
countsmakedetectingsuchchangesdifficult. thiswayareclusteredtightlyaround fa=0.95- 1.0. Thereis
Totestformoresubtlespectralshapechanges,weincreased asmallerpeakataround fa 0.85,dominatedbytwobursts,
≈
the exposure time to obtain better signal-to-noise. For the butvisualinspectionoftheir facurvesshowtheir favaluesto
threeburstsstudiedinFigure2,andthefifteenburstsinvesti- stayapproximatelyconstantthroughouttheobservation.
gatedbyPeilleetal.(2014)(seetheirTable1),weinspected Thesteadinessofboth faandχ2ν overtimesuggeststhatthe
the RXTE Standard-2 data covering the entire observation. persistentemissiondoesnotchangegreatlyineithershapeor
These are spectra binned into 16s intervals. We fit each of intensityontimescalesuptoanhourbeforeandafteratype
thesespectrawiththepersistentmodelforthatburst,withall Iburst.
parametersfrozen,and f normalizationallowedtovary. We Finally, we investigated the extent to which we can de-
a
consideredonlyspectrarecordedwithinanhourbeforeoraf- tectchangesintheaccretionspectralshapeif theyreallyare
ter the burst but excluding those during the burst, to avoid present, assuming that a change in the intensity of the per-
contamination by the burst emission. That is, we excluded sistent emission reflects a change in the accretionrate. This
spectra recorded between the beginning of the burst (burst is particularly necessary near the burst peak, since this is
flux has reached 1/4 of the peak burst flux) and the end of where the persistent emission spectral shape is most uncer-
thePCAdataoftheG08catalog.Thisdatatypicallycoversa tain;wehavealreadyfoundthatitreturnstoitsoriginalshape
9
deep in the cooling tail. We selected a non-PRE burst from properties: theprolificbursterGS1826-24exhibitsveryreg-
4U 1636- 536 that uses the disko model (Stella&Rosner ularburststhatareincloseagreementwithnumericalmodels
1984), recorded 2005 Apr 4, 10:48:43. For this burst PCUs of X-ray bursts (e.g., Hegeretal. 2007; Galloway&Lampe
0and2onRXTE wereactive. ThismodelcontainsM˙/M˙ 2012). The11HzpulsarIGR17480- 2446isthemostslowly
Edd
explicitlyasavariableparameterandincorporatesphysically- rotating source that shows burst oscillations (Cavecchietal.
motivated changes in the spectral shape. This model is as- 2011), makingthat sourcean importanttest of burstoscilla-
sumed to be in equilibrium for this burst and does not take tionmodels. NeithersourcehasasinglereportedPREburst.
intoaccountchangesinitsstructureinducedbyaburst;there The Rapid Burster (MXB 1730-335)is our major source of
areasyetnotheoreticalspectraofadiskmodifiedinthisway, knowledge about type II bursts, and has one reported PRE
andwe expectthattheassociatedspectralshapewilldeviate burst(Salaetal.2012). Thisevent,however,wasdetectedby
froma blackbodyto a similar degree, thoughnotperhapsin theSwiftX-rayinstrumentandthemeasurementwasnotsen-
thesamemanner. sitive enough to constrain the Eddington flux to better than
Thebestfitaccretionratewas 0.205M˙/M˙ andthepeak about50%(seetheirFig. 2).
Edd
f was 3.3. The normalization of this persistent model was AninterestingobservationisthatalltheresultsofWGP13
a
2cosi/d2=1.648,whereiistheinclinationandd isthedis- fallbelowtheline faγ=1,whereγ isthepre-burstaccretion
tance in units of 10 kpc. At an assumed distance of 6 kpc flux as a fraction of the Eddingtonflux, consistentwith pre-
(Gallowayetal. 2006), this gives an inclination of 72◦, in dictionsofBurger&Katz(1983)andMiller&Lamb(1996);
agreementwithPandeletal.(2008)andCasaresetal.(2006), bothworkssuggestthattheEddingtonaccretionrateisanat-
˙
who also infer a high inclination (greater than 64◦, and uralupperlimitto M. Thisobservationraisesthepossibility
36◦- 74◦respectively)forthissystem.Thenormalizationwas ofobtainingalowerboundontheEddingtonfluxforagiven
kept frozen in the subsequent analysis. We generated 2,000 source, that is, FEdd > faFpers, where FPers is the bolometric
simulated spectra, folded througha PCA response appropri- fluxofthepre-burstpersistentemission.
atetotheobservedburst,ofthewabs*diskomodelwithM˙ InFigure8weshowpeak faagainstγforeverytypeIburst
takingrandomvaluesbetween0.067M˙ and0.667M˙ .We detectedbyRXTE.For0.01<γ<0.4thenon-PREburstsap-
Edd Edd
thenfitted those simulatedspectra with fa times the original peartobeboundedaboveby faγ .(faγ)max,where(faγ)max
persistentmodel. The measured f and χ2 are givenin Fig- appearstobesomewhatlessthan0.5.Thiswouldgivealower
a ν
limiton the Eddingtonflux roughlytwice as constrainingas
ure7,lefttwopanels.Intheabsenceofburstemissionwecan
wclietahrliyncdreetaescitnagcMh˙aansgweeinllsapseacntrainlcsrheaapseeviniaththeeinintecnresaitsyeoinftχh2νe γtheremquoisretscoknnsoewrvinagtivFeEdeds;toimuratmeeftahFopderfso<rdFeEtedrdm. iDnientgertmheinEindg-
dingtonfluxesforPREburstersisgivenintheAppendix.
persistent emission. We then repeated the process, this time
Wenowdescribeamethodbywhichweestimatetheupper
includingablackbodywithtemperature2.0keVandnormal-
boundof f γ thatisreproducibleandmoreobjectivethanes-
izationrepresentingaspherewithradius10kmatadistance a
timatingby eye. We treatthe measuredx =(f γ) valuesas
of6kpc(i.e.,thesurfaceof4U1636- 536). Thiswefitwith i a i
normal distributions centered around their measured values,
theusualvariablepersistentfluxapproach(righttwopanels).
withstandarddeviationsσ equaltotheuncertaintyinthe f ,
Itisevidentthat,althoughwecanstilldetectenhancedpersis- i a
timesγ. Thisnormaldistributionisgivenby
tentemissionthroughanincreased f ,wehavelosttheability
a
todetectachangeinitsspectralshape.Thisexperimentgives 1 (x- x)2
usconfidencethatourapproachofsimplyvaryingthenormal- G(x,σi,xi)= exp - i . (3)
izationofthepersistentemissionwillintroducenodetectable √2πσi (cid:20) 2σi (cid:21)
systematiceffects. Thefractionofthisdistributionlyingabovex =(f γ)
max a max
This analysis is not sensitive to changes in the persistent is
∞
spectrumoutsidethe2.5-20keVenergyrangeweconsiderin
A(σ,x) = G(x,σ,x)dx
thispaper. in’tZandetal.(2013)combineddatafromChan- i i i i
Z
dra, which is sensitive at energies below 2keV, with RXTE 1xmax x - x (4)
data for a radius expansion burst from SAX J1808.43658. = 1+erf i max ,
2(cid:20) (cid:18) √2σ (cid:19)(cid:21)
They obtainedsimilar f values as WGP13 did studying the i
a
same burst with only RXTE data, suggesting thatchangesin andsothetotaloveralldatapointsis
thepersistentspectrumbelow2.5keVarenegligible. Athigh
energies,thereisevidencethatthehardX-ray(>30keV)flux 1 n x - x
A = 1+erf i max , (5)
decreasesduringa burst, in apparentconflictwith our result T
2 (cid:20) √2σ (cid:21)
(Chenetal.2013;Jietal.2013,2014a,b). However,thisphe- Xi=1 i
nomenon is attributed to the rapid cooling of the accretion wherenisthenumberofdatapoints.
disc corona, which contributesthe majority of the very hard Thequestionishowtofindx . Firstwemakeaguessζas
max
X-rays. Anincreasein2.5-20keVfluxattributedtoaccretion tothevalueofx andcalculateanA fromthisandthedata
max T
ratechangedoesnotconflictwith a simultaneousquenching pointsx. Thenwetakeasetofndatapointsxˆ withrandom
i i
ofhighenergyphotonsthroughthecoolingofthecorona. valuesbetween0 andζ. We assigntoeachxˆ anuncertainty
i
ofσ,thatis,arandompointisgivenameasureduncertainty.
i
5. EDDINGTONFLUXESFROMNON-PREBURSTS Thisassumestherealdata pointsareevenlydistributedwith
For neutron stars for which no radius expansion bursts uncertainties independent of their values, but the procedure
have been observed, the only lower bound on their Edding- canbemodifiedtosuitotherassumptions. Fromthisrandom
ton fluxes are the peak fluxes of their brightest bursts. A setxˆ wecalculateanexpectedtotalarea(A (rand))thatcan
i T
better knowledge of their Eddington fluxes would be of ob- becomparedtotherealone(A (observed)). If,forinstance,
T
servationalutility,asmanyofthesesourcesshowinteresting A (rand)<A (observed)thenourguessforζ wastoohigh
T T
10
5 5
a) c)
4 4
No burst flux With burst flux
3 3
a a
f f
2 2
1 1
0 0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
M˙ M˙
5 5
b) d)
4 4
3 3
2χν 2χν
2 2
1 1
0 0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
M˙ M˙
˙
FIG.7.— ResultsoffitstosimulateddiskospectrawithMallowedtovary,bothwith(panelsa.andb.)andwithout(panelsc.andd.)aburstcomponent.In
bothcasesanincreasein faisdetected. Whenthereisnoburstcomponent,andonlyachangeintheintensityofthepersistentemissionisbeingtestedfor,the
increasingχ2ν withincreasingM˙ indicatesthatchangesinthespectralshapearedetectable. Inthepresenceofburstemission,itisnolongerpossibletodiscern
thespectralshapechangesinthepersistentemission. Wecanthereforesimplyvarythenormalizationofthepersistentemissionwithoutintroducingsystematic
effects.
and we try again with a lower ζ. Once the ζs converge, we 18.1 5.5 10- 9 and 42.0 10.5 10- 9 erg s- 1 cm- 2 re-
take this value to be x . Making many realizations of the spect±ively.×IGR 17480- 24±46 is ×located in the globular
max
randomset, we cangetanexpectedx . However,toavoid cluster Terzan 5, with a known distance of about 5.5 kpc
max
the analysis assigning too much weight to outliers, we take (e.g.,Papittoetal. 2011), and a hydrogen accreting neutron
many bootstrap subsamples of the original data set and take star with 1.4M would have an Eddingtonflux of 57 10- 9
⊙
theoverallxmax tobetheaverageofthosefromthebootstrap ergs- 1 cm- 2. Cir X- 1is believedto be 7.8-10.5kpcd×istant
samples;italsogivesusuncertaintiesonxmax. (Jonker&Nelemans2004).Ourresultsuggestsitisprobably
Applyingthisprocedure,wegetxmax=0.84 0.34forthe at the nearer end of that range, since the more distant value
±
PRE bursts and xmax =0.37 0.089 for the non-PRE bursts. wouldgiveanEddingtonfluxof16 10- 9ergs- 1 cm- 2 fora
±
We notethatthe faγ relationisaphenomenologicaloneand canonicalneutronstar,slightlyhighe×rthanourestimate. We
does not depend on any physical interpretation, though it is
also get a marginally more constraining Eddington flux for
consistent with the requirement that the accretion luminos- 1M0836- 425of23.1 6.5 10- 9ergs- 1 cm- 2.
ity not exceed Eddington. To test whether our new method ± ×
givesa morestringentlower boundthan the peakburstflux, 6. CONCLUSION
wecomparedthetwomethodsforeverysourceforwhichten
Wehaveextendedthevariablepersistentfluxmethoddevel-
or more non-PRE bursts have been observed, but excluding
therapidaccretorsCygX- 2andGX+17- 2. Wealsoexclude opedbyWorpeletal.(2013)andin’tZandetal.(2013)toall
SLX1744- 300,asthatsourceisdifficulttodistinguishfrom type I bursts observed by RXTE. Our method gives superior
the nearby (∆θ 3′) SLX 1744- 299 (Skinneretal. 1990). spectral fits to type I burst spectra, whether these are radius
≈ expansionburstsornot. Ourdetailedconclusionsareasfol-
WefirstapplythemethodtosourcesforwhichtheEddington
lows:
flux is known, to make sure the new method never overesti-
i) The variable persistent normalization approach devel-
matestheEddingtonflux.In2of16sources,thenewmethod
opedinWGP13appliesaswelltonon-PREburstsasitdoes
gaveagreaterlowerboundthanthebrightestnon-PREburst,
to radius expansion bursts. The quality of spectral fits gen-
andinnocasedidthenewmethodoverestimatetheEdding-
erally improves, and the intensity of the persistent emission
tonfluxbeyondobservationaluncertainties.Theseresultsare
usuallyincreasesduringaburst,typicallybyafactorof3-4.
showninFigure9.
ii)Theadditionofathirdvariableparameterincreasesthe
Applying the new method (with x = (f F ) since γ
i a Pers i uncertainties in the fit parameters. In particular there is a
is unknown) to sources with unknown Eddington flux, we
degeneracybetween f andblackbodyburstcomponentnor-
get a better bound than the non-PRE bursts for the sources a
Cir X- 1 and IGR 17480- 2446, with F greater than malization,likelyduetotheindistinctnessofthetwospectral
Edd components.