A Global Study of the Behaviour of Black Hole X-ray Binary Discs
Robert Dunn, Rob Fender, Elmar Koerding, Tomaso Belloni, Andrea Merloni
aa r X i v : . [ a s t r o - ph . H E ] S e p Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 5 November 2018 (MN L A TEX style file v2.2)
A Global Study of the Behaviour of Black Hole X-ray Binary Discs
R. J. H. Dunn ⋆ † , R. P. Fender , E. G. K ¨ording , T. Belloni and A.Merloni , Excellence Cluster Universe, Technische Universit¨at M¨unchen, Garching, 85748, Germany School of Physics and Astronomy, Southampton, University of Southampton, SO17 1BJ, UK, AIM - Unit´e Mixte de Recherche CEA - CNRS - Universit´e Paris VII - UMR 7158, CEA-Saclay, Service d’Astrophysique, F-91191Gif-sur-Yvette Cedex, France INAF-Osservatorio Astronomico di Brera, Via E. Bianchi 46, I-23807 Merate (LC), Italy Max Planck Institut f¨ur Extraterrestrische Physik, Giessenbachstraße, 85471 Garching, Germany5 November 2018
ABSTRACT
We investigate the behaviour of the accretion discs in the outbursts of the low-mass black-hole X-ray binaries (BHXRB), an overview of which we have presented previously. Almostall of the systems in which there are sufficient observations in the most disc dominated statesshow a variation of the disc luminosity with temperature close to L ˜ ∝ T . This in turn impliesthat in these states, the disc radius, R in , and the colour correction factor, f col , are almostconstant. Deviations away from the T law are observed at the beginning and end of the mostdisc dominated states, during the intermediate states. Although these could be explained byan inward motion of the accretion disc, they are more likely to be the result of an increasein the value of f col as the disc fraction decreases. By comparing the expected and observeddisc luminosities, we place approximate limits on the allowed distances and masses of theBHXRB system. In a number of cases, the measured distances and masses of the BHXRBsystem indicate that it is possible that the black hole may be spinning. Key words: accretion, accretion discs - binaries: general - ISM: jets and outflows - X-rays:binaries
The outbursts of black hole X-ray binaries (BHXRBs) are dra-matic and intriguing events. They have the potential for allow-ing the study of the physical and emission processes close to theevent horizon. The accretion process and associated intermittentjet-production results in emission across the electromagnetic spec-trum. In the study presented here, we focus on the X-rays, as thesearise from the inner parts of the accretion disc and flow. At the otherend of the spectrum, the radio emission is thought to arise from asynchrotron emitting jet. Therefore the radio emission is a goodtracer of whether a jet is active or not, and the X-rays are good atdetermining the state of the accretion flow.In the now commonly-accepted picture of the changes that oc-cur in the BHXRB system, the BHXRB spends most of its timein a quiescent state. There the total luminosity of the BHXRB isvery low, in all bands. As the outburst starts, the X-rays are char-acterised by a hard emission spectrum with a powerlaw slope of Γ ∼ . - the “hard state”. As the X-ray luminosity rises, the ra-dio luminosity rises in step (Corbel et al. 2000, 2003). The radiospectrum also indicates the presence of a steady jet emitting syn- ⋆ E-mail: [email protected] † Alexander von Humboldt Fellow chrotron radiation. As the outburst progresses, the disc spectrumbecomes increasingly dominant, eventually softening the entire X-ray spectrum as the BHXRB enters the “soft-state”. This transi-tion is very fast compared to the speed at which the luminosityrose. Over the course of weeks or even months, the disc luminosityand temperature decay (Gierli´nski & Done 2004), as the disc dom-inance decreases (Dunn et al. 2010). Eventually the source returnsto the “hard-state” and the luminosity continues to fade. For furtherdetails on this picture of the progression of BHXRB outbursts seeFender et al. (2004); Done & Gierli´nski (2003); Homan & Belloni(2005); Remillard & McClintock (2006); Done et al. (2007);Belloni (2010).The accretion onto the compact object is what drives their lu-minosity in X-rays, which arise from the disc, the corona and eventhe jet (Russell et al. 2010). Studying emission from the disc al-lows the accretion process, and also the behaviour of the mate-rial within the disc as it approaches close to the compact objectto be investigated. The standard theory of accretion discs fromShakura & Sunyaev (1973) shows that the accreting material willform a geometrically thin, but optically thick disc, the inner extentof which depends on the spin of the black hole.Previous studies on the behaviours of the BHXRB accre-tion discs have selected those observations where the disc wasdominant, in order to ensure that the disc parameters were well c (cid:13) Dunn, Fender, K¨ording, Belloni & Merloni determined (Gierli´nski & Done 2004; Done et al. 2007). This al-lowed a detailed study of the disc emission from well characterisedBHXRBs to be carried out. Using the full archival coverage of the
RXTE satellite, which has been observing BHXRBs for 13 years,we present a study of all observations in which a disc was detectedusing the analysis of Dunn et al. (2010). This allows us to investi-gate the properties of the disc in the transition periods, between thefully disc-dominated and powerlaw-dominated states, as well as inthe disc dominated states.In Sections 2 and 3 we recap the data reduction proceedurepresented in Dunn et al. (2008, 2010) and the final BHXRBs whichwere selected for this study. The behaviour of the disc’s temper-ature and luminosity are discussed in Section 5. The deviationsfrom the expected behaviour of the disc luminosity and tempera-ture are presented in Section 6, where the inner radius of the discis investigated, and Section 7, where larger departures are linkedto the colour temperature correction. In Section 8 we investigatethe limits which can be placed on the distances, masses and spinsof the BHXRBs from the observations. The degeneracy of the bro-ken powerlaw model with the disc model, and the evolution of thepowerlaw in the hard state are presented in Sections 9 and 10. In the analysis of the disc properties of the sample of BHXRBspresented in this work we use the analysis of
RXTE data de-tailed in Dunn et al. (2010). We recap the main points, but referto Dunn et al. (2008, 2010) for more details.We use all the available data publicly available in the
RXTE archive . This gave a baseline of around 13 years to study the evolu-tion of the disc properties during the numerous outbursts observedwithin that time. All data were subjected to the same data reductionprocedure, in order to minimise differences arising from differentdata reduction routines.Both the Proportional Counter Array ( PCA ) and High EnergyX-ray Timing Experiment (
HEXTE ) data were required when fit-ting the spectra, as the
HEXTE data allows the powerlaw to be con-strained at high energy when the
PCA data are dominated by thedisc. We followed the procedure outlined in the
RXTE
Cookbook using the tools from HEASOFT version 6.6.2.To reduce variations the between observations further, we onlyuse the data from Proportional Counter Unit (PCU) 2 on the PCA as this has been on throughout the
RXTE mission. Our analysis con-centrates on the bright periods when the BHXRBs are in outburst,and so we use the bright model background for all data. Lowercount rates are more likely in the inter-outburst periods, and so thischoice of a single background is unlikely to bias our results.In order to proceed with the spectral fitting, we require a
PCA observation with at least 1000 background subtracted counts, anda
HEXTE observation with either Cluster A or B (or both) with atleast 2000 background subtracted counts. The other
HEXTE clusterhas to have at least a positive number of counts This count restric-tion is in place to try to ensure that the spectra which are fitted are of Rossi X-ray Timing Explorer The cut-off date used was the 4 August 2009, as in Dunn et al. (2010). http://rxte.gsfc.nasa.gov/docs/xte/recipes/cook_book.html http://heasarc.gsfc.nasa.gov/lheasoft/ The background subtraction procedure for
HEXTE can result in negativenumbers of foreground counts for low fluxes. good quality and fit within a reasonable time with well-constrainedparameters.The spectra were fitted in
XSPEC (v12.5.0an). In order to studythe disc parameters in detail, we needed to analyse the spectra to thelowest energies possible. The relation between the channel num-bers of the
PCA instrument and the energies they correspond tohas drifted over the 13 years of the mission. However, all channelsbelow number 7 are not well calibrated for spectral analysis. Wetherefore choose to ignore
PCA channels , which correspondsto around , but the exact energy has drifted over time (see the RXTE documentation). We also ignore
PCA data >
25 keV , and
HEXTE data <
25 keV and >
250 keV .To be able to characterise the state of the BHXRBs as theygo through an outburst we fit three types of base model - unbrokenpowerlaw (
POWER , PL), broken powerlaw (
BKNPOWER , BPL) andpowerlaw + disc (
POWER + DISKBB , DPL). These allow the studyof the non-thermal component using the
POWER / BKNPOWER pa-rameters, and the disc using the
DISKBB parameters. To study thepresence and change in the iron line we add an optional . gaussian feature to all these spectra, giving in total six modelswhich were fitted. The low energy sensitivity of RXTE is insuffi-cient to allow the N H to be determined from the spectra, and so wefix this value to the accepted value for each BHXRB (see Table 1).From the six fitted models, we select the best fitting one on χ terms. However if this is not the simplest model, we then deter-mine whether the increase in complexity of the model is significantusing an F -test with P < . as the significance level. For thecomplete routine see Dunn et al. (2010), but a quick outline is de-scribed below. When the best fitting model is complex but containsno gaussian component, we test this best fitting model against thesimple powerlaw result. If the best fitting model is complex andcontains a gaussian component we first test whether the underlyingcomplex continuum model is an improvement over the simple pow-erlaw, and if it is we test whether a line is required in this complexmodel. When the complex continuum is not an improvement overthe simple powerlaw a number of further steps are performed, asdetailed in Dunn et al. (2010).Once the best fitting model has been selected, we further cutthe observation number by removing any observation whose −
10 keV flux is less than × − erg s − , where the flux was notwell determined or where the powerlaw was not well constrained(even if the disc was). The flux cut was performed to focus on theperiods in which the BHXRBs are in outburst, and so streamline thedata reduction process. We also removed those fits whose χ > . as these are spectra which are not well fit by any of the modelsavailable within our automated procedure. The distribution of the χ of the best fitting models is shown in Dunn et al. (2010) Fig.2. The majority of fits are clustered around χ ∼ , but there is alarge tail to higher values. As the spectral fitting in this work hasbeen automated, such large tail is expected. The relatively high lower energy bound for the
RXTE response lim-its our ability to detect discs when they are not dominant. The maxi-mum power emitted by the
DISKBB model occurs around . kT Disc which is usually around the lower limit of the
PCA bandpass (fordiscs at ∼ ). Therefore we rarely detect the peak of the discemission, and more usually observe the Wien tail. Using a sim-ple powerlaw to model the non-thermal continuum, even when in-cluding HEXTE data, does not allow for small breaks or curvaturewithin this component. If a disc component was included in these c (cid:13) , 000–000 Global Study of the Behaviour of Black Hole X-ray Binary Discs observations, it was found to try and fit these small curvatures in thepowerlaw rather than any true underlying disc component, result-ing in unphysical disc parameters. We therefore limited the mini-mum temperature for the disc during the fitting to k B T = 0 . .Furthermore we then penalise the χ of any model which has a k B T < . when selecting the best fitting model. We notethat in doing this we are limiting our sensitivity to low tempera-ture discs, in the intermediate and hard states for example, and areprobably excluding a few accurate disc fits. We investigate furtherdegeneracies between the disc and broken powerlaw models in Sec-tion 9.More complex models, for example Comptonization, would inprinciple give more information on the state of the system in thesedisc dominated states, as it links the non-thermal emission to thedisc temperature. However, in order to freely fit all the parametersof the Comptonization models a high signal-to-noise observationis required. Not all of our observations have sufficient counts to beable to do this; in fact very few would allow all parameters to bedetermined from the observations. Although fixing some parame-ters would allow these models to fit successfully, this goes againstthe methodology of this work, by a priori constraining parametersdifferently for different states. After all the data reduction, dead-time and selection the
15 Ms ofraw
RXTE data was trimmed to ∼
10 Ms in 3919 observations, withwell fitted spectra and high enough fluxes and counts. The sampleof objects was not designed to be complete in any way. We selectedobjects which were well known BHXRBs in the literature as wellas those which were known to have outbursts which had been wellmonitored by
RXTE . The set of BHXRBs analysed in this sample,along with their physical parameters (where known) and the finalnumber of observations used in this study are shown in Tables 1and 2.There are two notable BHXRBs which were purposely not in-cluded in this study (e.g. Cyg X1 and GRS 1915-105). These twosources were not included for a number of reasons. One was apurely practical one resulting from the shear amount of data avail-able for these sources. The reduction of all the observations in thescheme outlined above would have dominated any of the globalstudies presented both here and in Dunn et al. (2010), and selectingcertain parts would have gone against the philosophy of the study,by not including all of the available data. Secondly, the behaviourof these sources is not easily explained by the outburst model pre-sented in Fender et al. (2004). In the following sections, we use thisoutburst scheme and the states it describes to explain the behaviourof the disc and powerlaw components. As the behaviour of thesetwo well studied BHXRBs do not easily fall fit into this scheme,we actively decided to not include them in the study at this time.Many of the masses and distances are unknown or not verywell constrained. Where they are unknown we have assumed valuesof M ⊙ and respectively. These uncertainties effect the cal-culation of the Eddington Luminosities ( L Edd ) for these BHXRBswhich are used extensively throughout this analysis to scale theBHXRBs to one another. Until the distances and masses are welldetermined, there will always be some uncertainty when compar-ing between sources.The investigation presented in this work concentrates on thevariation of the disc characteristics during the outburst as thechanges in the disc parameters are the most prominent changes in
Table 2. O BSERVATION N UMBERS , T
IMES AND D ISC D ETECTIONS
Object Selected Obs Exposure Disc Detections Ms
4U 1543-47
61 0 .
704 1 .
59 0 .
484 1 . . . . . .
709 1 .
346 0 .
81 0 .
365 0 .
108 0 .
63 0 .
21 0 . .
123 0 .
121 0 .
15 0 .
69 0 .
471 1 .
13 0 .
48 0 .
28 0 . the spectrum during a BHXRB outburst. Our results are thereforedominated by those objects which have had outbursts well moni-tored by RXTE . Roughly this “removes” all the BHXRBs from ourstudy which have only had a few
RXTE observations. Some objectswhich have had a comparatively large number of observations arenot observed to undergo the canonical outburst structure outlinedin Section 1. These sources are less able to show what changes discundergoes during a complete outburst, but are still useful for thehard/powerlaw dominated states.
The discs around black holes are thought to be optically thick andgeometrically thin (Shakura & Sunyaev 1973). The spectrum ex-pected from this kind of disc around a non-rotating black hole iseasily calculated. It is the sum of a set of blackbody spectra, onefor each radius, R , with a characteristic temperature T eff ( R ) . Thetotal spectrum resulting from this sum is then a multicolour discblackbody, with a peak temperature T eff , max coming from close tothe innermost stable orbit. However, this spectrum is effected bythe opacity of the disc, which results in a colour temperature cor-rection factor, f col (Shimura & Takahara 1995; Merloni et al. 2000;Davis et al. 2006). This factor was shown by Shimura & Takahara(1995) to be ∼ . for almost all black hole masses and emis-sion luminosities and is discussed further in Section 7. Of course,the description of the disc may not be quite as simple as en-visaged by Shakura & Sunyaev (1973) and radiatively inefficientflows (e.g. Advection Dominated Accretion Flows, Ichimaru 1977;Narayan & Yi 1994) or slim discs (e.g. Abramowicz et al. 1988) c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni
Table 1. X- RAY B INARY P ARAMETERS
Object M BH D N H P orb M ∗ Inclination ( M ⊙ ) ( kpc) ( × cm − ) ( h ) ( M ⊙ ) ( ◦ )
4U 1543-47 . ± . (1,2) . ± . (3,4) . (2,4) . (4) . (1) (2)4U 1630-47 [10] 10 . ± . (5) > (6) − − −
4U 1957+115 [10] [5] 0 . (7) . (8) . (9) − GRO J1655-40 . ± . (10,11) . ± . (4,12) . (13) . (4) . (10) (48)GRS 1737-31 [10] [5] 6 . (14) − − − GRS 1739-278 [10] 8 . ± . (15) (15) − − − GRS 1758-258 [10] [5] 1 . (16) . (17) − − GS 1354-644 > . . ± . (1) >
27 = 33 ± (18) . (18,19) . (18) . (1) − GS 2023+338 ± (1) . ± . (4) . (4) . (4) . (1) − GX 339-4 . ± . (20) . ± . (21) . (22) . (4) . (20) 40H 1743-322 [10] [5] 2 . (23) − − − XTE J1118+480 . ± . (1,24) . ± . (25,26) . (25) . (4) . (1) (26)XTE J1550-564 . ± . (3) . ± . (4) . (27) . (4) . (3) (3)XTE J1650-500 < . ± (28) . ± . (29) . (30) . (28) − (49)XTE J1720-318 [10] (31) > ± (31) . (31) − − − XTE J1748-288 [10] > ± (32) . (33) − − − XTE J1755-324 [10] [5] 0 . (34) − − − XTE J1817-330 < ± (35) > (35) . (35) − − − XTE J1859+226 ± (36) . ± . (4) . (36) . (4) . (36) − XTE J2012+381 [10] [5] 1 . (37) − − − LMC X-1 ± (38) ± . (39) . (13) . (40) − (38)LMC X-3 ± (41) ± . (39) . (42) . (43) (41) (41)SAX 1711.6-3808 [10] [5] 2 . (44) − − − SAX 1819.3-2525 ± (46) ± (46) . (47) . (46) − (46)SLX 1746-331 [10] [5] 0 . (45) − − − Many of the objects do not have well determined distances or masses. In this case we have taken the distances to be and the masses M ⊙ . A recentcritical look at the distance estimates for GRO J1655-40 by Foellmi (2009) indicates a revised estimate of the distance of < . . References:(1) Ritter & Kolb (2003) , (2) Park et al. (2004) , (3) Orosz et al. (2002) , (4) Jonker & Nelemans (2004) , (5) Augusteijn et al. (2001) , (6) Tomsick et al. (2005), (7) Nowak et al. (2008) , (8) Thorstensen (1987) , (9) Shahbaz et al. (1996) , (10) Hynes et al. (1998) , (11) Shahbaz et al. (1999) , (12) Hjellming & Rupen(1995) , (13) Gierli´nski et al. (2001) , (14) Cui et al. (1997) , (15) Greiner et al. (1996) , (16) Pottschmidt et al. (2006) , (17) Smith et al. (2002) , (18)Casares et al. (2004) , (19) Kitamoto et al. (1990) , (20) Hynes et al. (2003) , (21) Zdziarski et al. (2004) , (22) Miller et al. (2004) , (23) Capitanio et al. (2005), (24) Wagner et al. (2001) , (25) Chaty et al. (2003) , (26) Gelino et al. (2006) , (27) Gierli´nski & Done (2003) , (28) Orosz et al. (2004) , (29) Homan et al.(2006) , (30) Miniutti et al. (2004) , (31) Cadolle Bel et al. (2004) , (32) Hjellming et al. (1998) , (33) Kotani et al. (2000) , (34) Revnivtsev et al. (1998) , (35)Sala et al. (2007) , (36) Hynes et al. (2002) , (37) Campana et al. (2002) , (38) Hutchings et al. (1987) , (39) di Benedetto (1997) , (40) Orosz et al. (2008) ,(41) Cowley et al. (1983) , (42) Haardt et al. (2001) , (43) Hutchings et al. (2003) , (44) in’t Zand et al. (2002) , (45) Wilson et al. (2003) , (46) Orosz et al.(2001) , (47) in’t Zand et al. (2000) , (48) van der Hooft et al. (1998) , (49) Sanchez-Fernandez et al. (2002) may exist. However, we concentrate on the disc model proposedby Shakura & Sunyaev (1973) in this study.We use the physical description in Gierli´nski & Done (2004);Gierli´nski et al. (1999) to calculate the relation between the discluminosity and the temperature as for a Schwarzschild black hole, L Disc L Edd ≈ . (cid:18) . f col (cid:19) (cid:18) M ⊙ (cid:19) (cid:18) kT max (cid:19) , (1)which assumes a constant inner disc radius, R in . We investigate theeffects of the black hole spin in Section 8. We include the adjust-ments to the observed disc temperature, T obs , for relativistic effectsclose to the black hole (Gierli´nski & Done 2004). We add a 4 percent temperature shift to account for the stress-free boundary layer,and also the adjustment from Zhang et al. (1997) which accountsfor the strong gravitational potential. T max = T obs /f GR ( θ, a ∗ ) ξ, where ξ = 1 . is for the stress-free boundary layer, θ is the incli-nation angle and a ∗ the dimensionless spin parameter. Out of the ∼ observations ∼ have disc detections (see Table 2).Although the number of observations in which a disc is well de-termined depends on the state of the BHXRB at the time it was observed, we show the number of disc detections so that it is clearthat a few BHXRBs have many more detections than most of theothers. Therefore our conclusions are depend more on the resultsfrom these BHXRBs.In the data reduction routine and best fitting model selectionproceedure we have been conservative in determining which ob-servations have discs (see Section 2.1). Initially we investigate thedegree to which the BHXRB discs follow the expected L − T rela-tion (Equation 1), using an f col = 1 . and assuming that the innerradius of the disc is constant. In later Sections we relax these as-sumptions.In the following, we define the Powerlaw Fraction (PLF) andthe Disc Fraction (DF) as PLF = L −
100 keV , PL L . −
100 keV , Disc + L −
100 keV , PL DF = L . −
100 keV , Disc L . −
100 keV , Disc + L −
100 keV , PL , following Dunn et al. (2010) as well as Dunn et al. (2008);K¨ording et al. (2006). These two quantities, used when creatingDisc Fraction Luminosity Diagrams, allow the natural separation ofthe outburst into two states - powerlaw and disc dominated. These c (cid:13) , 000–000 Global Study of the Behaviour of Black Hole X-ray Binary Discs correspond roughly to the hard and soft states more commonly usedin BHXRB studies. For an in depth study of the relation betweenthese state conventions see Dunn et al. (2010). We show the variation of the disc temperature with unabsorbed discluminosity for each BHXRB individually in Appendix Fig. A.1.The errorbars are only from the uncertainties arising in the spectralfitting. We do not include the uncertainties in physical parametersof the BHXRB system (e.g. mass and distance), as in many casesthe physical parameters are unknown, and would further compli-cate the diagram. We also show the theoretically expected L − T relation for f col = 1 . for each BHXRB on each diagram in Ap-pendix Fig. A.1 as the dashed black line, using the masses as shownin Table 1 (again without including the uncertainties). Also shownin Appendix Fig. A.1 is a schematic showing the motion of theBHXRB through the L − T plane as an outburst progresses. Forclarity, for the remainder of this section the theoretical L − T re-lation is that from Eq. 1 under the assumption of a constant innerdisc radius and colour correction factor.In Appendix Fig. A.1 it is clear that most of the BHXRB’sdiscs do closely follow the theoretically expected L − T relation.We fit the most disc dominated points (DF > . ) of each BHXRBwith a powerlaw in the log T − log L Disc plane, where for aconstant size black body a slope of four is expected. We show theresulting slopes in Table 3 and a histogram of their distribution inFig. 1. The best-fit Gaussian distribution to the histogram peaks ata slope of . . We select the most disc dominated observationsin order to focus on those where the disc parameters (tempera-ture and disc normalisation in XSPEC ) were very well determinedand also to exclude points close to the intermediate state, wherethe relation may not apply (similar to the selection performed inGierli´nski & Done 2004). The behaviour of the disc temperature atsmaller disc fractions, corresponding to states closer to the inter-mediate states, and are discussed in Section 7.Of the ten BHXRBs studied by Gierli´nski & Done (2004),nine are included in our study. For four of the BHXRBs, their dis-tribution of observations match between their study and those inAppendix Fig A.1 (GRS 1739-278, XTE J2012+381, LMC X-1and LMC X-3). There are many more observations of GX 339-4 presented in our study, and so it is difficult to determineany differences between the two studies. Of the remaining fourBHXRBs (GRO J1655-40, XTE J1550-564, XTE J1650-500 andXTE J1859+226), the trends observed in Gierli´nski & Done (2004)show very clear and linear ∼ T relations. However, in AppendixFig A.1 we find that, although the most disc dominated observa-tions do on the whole follow the expected L − T relation, thereare a large number of points at low disc fractions which fall “be-low” the expected L − T relation (see also Section 7). In this study,we include and show all observations in which a disc+powerlawmodel was the best fit, whereas those in Gierli´nski & Done (2004)select “disc dominated spectra” where up to 15 per cent of the totalbolometric emission can be present in a Comptonized tail. In Ap-pendix Fig A.1 we only fit those observations for which DF > . and therefore the apparent observed differences are large becauseof the plotted low disc fraction points.In a number of the BHXRBs, the statistically best fitting lineis not similar to the expected L − T relation. This mismatch inbetween the slopes of the expected L − T relation and that of thebest fit to the most disc dominated states could arise from the lim- N u m b e r Figure 1.
The distribution of the best fitting slopes in the most disc domi-nated states. The indicated Gaussian is a least-squares fit to the histogram,and peaks at . with a width of . . GRS 1739-278, XTE J1650-500and LMC X-1 are beyond the edges of the plot (see Table 3). itations on the range of disc temperatures probed and the spectralresponse of RXTE . If only a few observations have a detected disc,then the variation in the disc temperature and luminosity may besmall, which could mask a T trend if the scatter is naturally high,for example GRS 1739-278 and LMC X-1.In a large number of cases, although the shape of the relation isclose to that of the L − T relation, the normalisations are not alwayscorrect (see Equation 1). Given the uncertainties in the masses anddistances an offset between the observed and expected behavioursis not unexpected. We also note that the expected L − T relationassumes that the black hole is not spinning. We discuss the effectsof these unknown system parameters further in Section 8.Therefore it is clear that under the assumption of a constant f col and a constant inner disc radius, R in , the majority of theBHXRBs show a variation of the disc luminosity, L Disc ˜ ∝ T inthe most disc dominated states over an order of magnitude in lu-minosity and a factor of two in disc temperature. This has beenfound by earlier studies (e.g. Gierli´nski & Done 2004; Davis et al.2006; Dunn et al. 2008), though in some cases the analysis as re-stricted to the most disc dominated (soft) states. Specifically, theratio of R in : f col is constant in these states. However, it wouldbe very strange if the dynamics of the accretion disc and the radi-ation transfer processes conspired to keep this ratio constant, andso it is likely that each quantity is itself, constant, in the disc dom-inated state. However, what of the behaviour in the less disc domi-nated states? As noted above, many of the observations at low discfractions fall “below” the expected “L-T” relation. We investigatedwhether this could result from slightly different L − T relationsfrom different outbursts of the same BHXRB, however no clearor variation was found. A number of the low disc fraction observa-tions are seen as almost perpendicular deviations from the expected L − T relation. The trend for these “spurs” is for the disc luminosityto decrease as the disc temperature increases and are observed bothat the beginning and the end of the outbursts (see e.g. 4U 1543-47and GRO J1655-40). We discuss these deviations further in Section7. There are a few cases where the best fit line to the most discdominated observations is radically different to the expected L − T relation even though there are a large number of observations, e.g. c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni
XTE J1650-500, LMC X-1. It is almost as if whatever is causing the“spurs” dominates the variation of the disc temperature and lumi-nosity in these objects. In these two BHXRBs there are two effectswhich conspire to give best-fit relations different to the expected L ∝ T . Firstly, in both of these sources the majority (if not all)of observations have the same luminosity. In XTE J1650-500 thoseobservations occur just after the disc fraction reaches . , ratherthan in the most disc dominated state of the outburst (DF > . ). Ifwe select those observations with DF > . as opposed to DF > . then the slope of the best fitting line is 9.52. Whereas in LMC X-1the only a few observations have a sufficiently high disc fraction tobe fitted, with almost no variability in the total luminosity . Sec-ondly, as seen in a number of the other BHXRBs, observations atintermediate states, or those which do not have overly strong discfractions show “spurs” running approximately perpendicular to the L − T relation. Both of these effects are combined with the scatterobserved in the the relations exhibited by other BHXRBs.Therefore, if there are few points in the most disc dominatedstates (XTE J1650-500) or there is a small variation in the lumi-nosity (LMC X-1), it is possible that the best fit relation will not beclose to the theoretically expected one. However, in XTE J1650-500, the best fit relation to the observations with DF > . is muchcloser to the expected L − T relation. In a study of the discs inBHXRBs Gierli´nski & Done (2004) also find that LMC X-1 doesnot appear to follow the relation. However the range in disc tem-peratures and luminosities in their study, like the observations pre-sented here, is comparatively small. XTE J1650-500 is also in-cluded in their study, and although they find departures from the L Disc ∝ T law, these observations have large error bars and soare consistent still with it.The theoretical L − T relation depends on the mass of theBHXRB - which can reasonably be assumed to be constant dur-ing the outburst - the f col , the colour temperature correction factor,the spin and also the inner radius of the disc, R in . The behaviourof the disc temperature and luminosity seen in Appendix Fig A.1for the majority of the observations of the BHXRBs, indicates thatover a large range in disc temperature and luminosity, both the f col and R in are relatively constant, at least in the most disc domi-nated states. There is some scatter around the best fitting relationwhich on the whole appears random with no clear secondary trend(see Fig. 1). However, in the “spurs” at the beginning and ends ofthe outbursts, the deviation from the L − T relation is large, andwe now investigate whether coherent variations either R in or f col could cause them. Only when the inner radius of the disc, R in , is constant will the discluminosity and temperature follow the expected L ∝ T relationassuming that f col is also constant. As we have shown in Section 5that for the majority of the observations the expected L − T relation We note that the not all of the best fitting models appear appropriatefor LMC X-1 in Dunn et al. (2010), as all the observations have similarX-ray colours, yet some have no disc component as seen in the Disc Frac-tion Luminosity Diagram (see K¨ording et al. (2006); Dunn et al. (2008) andDunn et al. (2010) for more details). This is likely to be the result of thesimilarity between a broken powerlaw model and a disc + powerlaw modelwhen the disc does not dominate the spectrum. This is exacerbated in LMCX-1 as the hard X-rays are also faint as a result of the large distance to theBHXRB, which make fitting the powerlaw difficult.
Table 3. D ISC T EMPERATURE F ITS
Object Exponent Points Note4U 1543-47 . ± . . ± . . ± . . ± . − GRS 1739-278 − . ± . . ± . − GS 2023+338 − GX 339-4 . ± . . ± . − XTE J1550-564 . ± . . ± .
28 2XTE J1720-318 . ± . . ± . − XTE J1817-330 . ± . . ± . . ± . − . ± .
14 3LMC X-3 . ± . − SAX 1819.3-2525 − SLX 1746-331 . ± . > . . Notes: 1 – GRS 1739-278 has very few points for the fitting.2 – XTE J1650-500 has a strange distribution of observations along theoutburst, causing the erroneous fit. 3 – LMC X-1: small range in disc tem-peratures and luminosities and the slope is not well defined. is a good description of the behaviour, then we expect that the discradius remains constant for the most disc dominated observations.To calculate the disc radius, we use the normalisation of the DISKBB model, N , from XSPEC as this explicity includes the innerradius of the disc, R in . N = (cid:20) R in D
10 kpc (cid:21) cos θ, (2)where D
10 kpc is the distance in units if
10 kpc and θ is the in-clination of the system. Where the inclination of the system is notknown (Table 1) we use θ = 60 ◦ . It is possible that the discs insome of these BHXRBs are misaligned with respect to the binary’sinclination (Maccarone 2002; Fragos et al. 2010). In Appendix FigA.1 we show the inner radius against the disc temperature for eachBHXRB. We do not include the effect of the uncertainties in thedistance and inclination in the error bars shown. We also show inAppendix Fig A.1 a schematic diagram demonstrating the motionof the BHXRB through the R in − T plane as the outburst pro-gresses. As, on the whole, the disc temperature decays during themost disc dominated stages of the outburst, the track of the BHXRBthrough the R in − T plane should be clear.As was expected from the behaviour of the disc luminosityand temperature, and from the study of GX 339-4 by Dunn et al.(2008), the majority of points are at a relatively constant inner discradius. We have chosen to plot the disc radius in kilometres on theprimary x -axis rather than R as fractions of the gravitational ra-dius, R g , as in many of the BHXRBs the masses are not accuratelyknown. The secondary x -axis shows the radii as a fraction of R g c (cid:13) , 000–000 Global Study of the Behaviour of Black Hole X-ray Binary Discs Table 4. D ISC I NNER R ADIUS F ITS
Object R in ( km) R in /R g
4U 1543-47 . +10 . − . . +0 . − .
4U 1630-47 . +3 . − . . +0 . − .
4U 1957+115 . +0 . − . . +0 . − . GRO J1655-40 . +2 . − . . +0 . − . GRS 1739-278 . +0 . − . . +0 . − . GRS 1758-258 . +0 . − . . +0 . − . GX 339-4 . +8 . − . . +1 . − . H 1743-322 . +2 . − . . +0 . − . XTE J1550-564 . +5 . − . . +0 . − . XTE J1650-500 . +4 . − . . +0 . − . XTE J1720-318 . +16 . − . . +1 . − . XTE J1748-288 . +1 . − . . +0 . − . XTE J1817-330 . +12 . − . . +2 . − . XTE J1859+226 . +6 . − . . +0 . − . XTE J2012+381 . +1 . − . . +0 . − . LMC X-1 . +5 . − . . +0 . − . LMC X-3 . +2 . − . . +0 . − . SLX 1746-331 . +0 . − . . +0 . − . The inner radius estimates do not include the uncertainties on the valuesor estimates on the distance or mass of the BHXRB (see Equation 2). As areminder, the inner radius of the disc is R g for a non-rotating black hole,and R g for a maximally rotating one. for comparison. We show in Table 2 the best fit inner radii for theobservations with a Disc Fraction > . .In some BHXRBs (4U 1957+115, GRS 1758-258 andSLX 1746-331) the disc radii are very small, less than
10 km orbelow R g . The innermost stable circular orbit (ISCO) for a blackhole is R g for a non-rotating black hole, where R g = GM/c = is the Schwarzschild radius. For a maximally rotating black hole,the ISCO can go down to R g . In these three BHXRBs the distances,masses and inclinations are not known, and so these effect the es-timates on the inner disc radius. From the normalisation, N , thedistance is directly proportional to the R in , the mass inversely pro-portional (when measured in units if R g ) and the inclination has a (cos θ ) − / dependence. The most change would arise if the incli-nation would increase, though increasing the distance or decreas-ing the mass would also increase the inner disc radius. However,not knowing the true values of the inner disc radius, it is difficultto determine which of these parameters should change and by howmuch. Therefore, although the estimates on the inner disc radiusare smaller than physically sensible, it is likely to be the result ofour incomplete knowledge of the system parameters.The “spurs” which were mentioned in Section 5 are also seenin the R in − T plots. If taken at face value, then they indicate thatat the end of the outburst the inner disc radius decreases as the disctemperature rises, and vice versa at the beginning of the outburst.This behaviour does not appear to be physically meaningful, as theminimum radius measured for some of the observations fall wellwithin the smallest stable orbit for a M ⊙ black hole. We dis-cuss these spurs and their possible causes further in the followingsection. F COL
CONNECTION?
As has been alluded to in the above sections, apart from the theo-retically expected L − T relation at constant disc radius R in , the other main trend is perpendicular to the L Disc ∝ T relation, lead-ing to an apparent decrease in the disc radius at the beginnings andends of the outburst. These spurs are seen in most of the BHXRBs,and were also seen in GX 339-4 in Dunn et al. (2008), XTE J1650-500 in Gierli´nski & Done (2004) and GRO J1655-40 in Done et al.(2007).The plots of R in − T in Appendix Fig. A.1 show that the discradius decreases to very small values at the beginnings and ends ofthe outbursts. It is the extent of the decreases, down to values wellbelow R g , that lead us to investigate whether changes in f col couldbe responsible. Although changing the system parameters can shiftthe location of the observations in the R in − T plane, they are un-likely to move the observations with the smallest calculated R in sufficiently far. We note that there are also points which occur atquite a distance from the main L − T relation, and also have verylow disc fractions ( . . ) and also have large uncertainties in thedisc temperature and luminosity. These are unlikely to be explainedby a variation in f col , and are discussed further in Section 9.The limited low energy response of the RXTE PCA instru-ment may restrict the accurate fitting of a disc components whenit does not dramatically dominate over the remainder of the con-tinuum. The calibrated range of the
PCA starts at around whereas the disc temperatures peak at around − . As weare therefore fitting only one side of the disc component, as thetemperature and the luminosity fade, the slight curvature could bedifficult to accurately fit especially in short observations or oneswhich have a small number of signal counts. Although some of thespurs could arise from weaknesses in our data analysis proceedure,as they have also been seen in other studies (e.g. Gierli´nski & Done2004; Done et al. 2007) it is likely that these weaknesses are notthe full explanation. However Gierli´nski & Done (2004) only usethe most disc dominated observations in their analysis. We haveemulated this approach in this study when fitting lines or findingaverages by selecting those observations with a very high disc frac-tion ( > . ). However, the plots show all the observations whichhave a detected disc component. Therefore, our plots show thesespurs, which may not have been shown in other studies where onlythe selected observations were plotted.We also note that in a study of LMC X-3 by Steiner et al.(2010), the observations from RXTE PCA
PCU-2 gave a very con-sistent value for the inner radius, a value which was also consistentwith those obtained from other detectors (e.g.
Suzaku , Swift and
XMM-Newton ). In our study we also find no evidence for the spursseen in other BHXRBs in LMC X-3, and so their study does nothelp in clarifying whether the spurs come from instrumental effects.However the close correspondence of the R in between RXTE andthe other detectors does indicate that in the disc dominated state, thespectral coverage of the
PCA is sufficient to be able to accuratelydetermine the disc parameters.In the theoretical L − T expectation, we have used a constantvalue for the colour correction, f col = 1 . (Shimura & Takahara1995). The departures from the L ∝ T law could be the resultof the variation of the value of f col . The colour correction factoraccounts for the change in the dominant emission process in the in-ner disc, and therefore is a function of L Disc . Gierli´nski & Done(2004) showed that the f col is approximately constant through-out the outburst (see also Shimura & Takahara 1995; Merloni et al.2000; Davis et al. 2006). However these were only for the most discdominated observations. Therefore it is possible that f col variationscould have occurred in the BHXRBs presented in these studies, butnot be shown in the figures. If f col is constant during the most disc c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni dominated phases of the outburst, and only those phases are shown,then any variation would not be detected.To account for these spurs, f col would decrease at the begin-ning of the outburst, and then increase on the exit of the outburst asthe BHXRB goes through the intermediate states (see the schematicin Appendix Fig. A.1). The motion off the T relation is approxi-mately perpendicular. Therefore a simple change in f col would ex-plain the deviations, without needing any further variation (of innerdisc radius, for example). It is of course possible that the disc ra-dius is not constant at the very beginnings and ends of the outburst.However, if the f col is not constant then it will be difficult to deter-mine what the true R in is in these non dominant discs observed by RXTE .We show on the L − T plane in Appendix Fig. A.1 the the-oretically expected relation for f col = 1 . but also for a range ofvalues for f col between 1.6 and 2.6. The lower limit arises fromthe initial investigation into f col by Shimura & Takahara (1995),whereas the upper comes from the best characterised BHXRB inGierli´nski & Done (2004). In cases where the values of the distanceand mass used are such so that the theoretical L − T relation is agood match to the observed L − T relation, then the spurs, shouldthey be present, mostly fall within this . < f col < . range. InAppendix Fig. A.1 we also show a schematic which indicates theroute taken by a BHXRB in this diagram.If these spurs are purely the result of changes in f col , we cancalculate the change in f col required, δf col , for the spurs to be partof the expected L − R T relation, under the assumption that thedisc radius is constant. We assume that f col = 1 . when the T relation is followed, and so adjust the normalisation of Equation1 so that the expected relation falls under the observed points at kT = 1 keV . As this normalisation is affected by the distance,mass, and inclination, which in many BHXRBs are only estimates,this simplifies our approach, without affecting our conclusions onthe variation of f col . We also note that the spin of a black hole canaffect the normalisation. We are currently assuming that the blackhole is not rotating, but discuss spinning black holes in see Section8. In Appendix Fig. A.1 we show for each BHXRB the excess f col required for the observation to lie on the T relation, δf col , againstthe powerlaw and disc fractions of the observation. In most casesthis centred on δf col = 0 . , which is by design, though where the L − T relation slope is very different from (Section 5), then theposition along the x -axis can vary.There appear to be three regions in the diagrams. The obser-vations with the largest disc fractions cluster around δf col = 0 . ,as defined by the normalisation adjustment mentioned above. The δf col remains almost constant at zero over around an order of mag-nitude change in the disc fraction. These are the observations whichscatter around the theoretically expected T relation, as the f col isconstant.As the disc fraction decreases the trend is for the observa-tions to move gradually towards progressively higher values of f col , δf col increases. These are the beginnings of the spurs, but are alsovisible as lopsidedness in the scatter around the most disc domi-nated observations in the plots of L Disc versus T .At around δf col = 0 . the trend in the observations flattensoff, as the disc fraction approaches zero, resulting in large changesin f col over small changes in the disc fraction. These observationsare the ones from the spurs and extend up to δf col ∼ . . The valueof f col required for these observations to lie on the T relation be-come larger with very little change in the disc fraction. The x -axesof the figures has been truncated as the observations with very lowdisc fractions which lie well below the main cluster of points have up to δf col ∼ (see Section 9). These observations are unlikelyto be explained by a varying f col and hence we do not show themin the figure.The most recent investigation into f col by Done & Davis(2008) shows that there is a positive correlation between the f col and the mass accretion rate. The effect is stronger for a proportionalcounter array (e.g. the RXTE PCA ) than for a Charge-Coupled De-vice (CCD) and shows that for an alpha disc, with α = 0 . , f col can reach values of around . for accretion rates of g / s (fora KERRBB disc model). This is lower than the f col increase in-ferred in Appendix Fig. A.1, but links the accretion rate to the f col . Although the evolution of the f col over time indicated byDone & Davis (2008) is different, the clear link between the de-viations from L − T and f col suggests a link to the accretionrate. However, it must be noted that the color correction fractionand, in general, the observed properties of the high-energy tail ofthe disc emission are quite sensitive to the vertical structure of thedisc. In particular, as discussed in more detail in Davis et al. (2005)and Done & Davis (2008), the vertical dissipation profile may bevery different in spectral states where a non-thermal (power-law)component is significantly detected, as a larger fraction of the totalaccretion power has to be released near or above the disc surface,leading to a possible increase in the estimated color correction fac-tors. Both a constant f col and a constant R in are observed whenthe disc fraction is high ( & . ), i.e. in those observations wherethe disc emission dominates over the powerlaw emission, and thedisc parameters have been well determined. However, under theassumption of a constant f col , as the disc fraction reduces the in-ferred R in decreases, which has a knock-on effect on the behaviourof the disc temperature with the luminosity. However, the drasticnature of the decrease in the R in is such, that a increase in f col may be a more reasonable explanation. If the true underlying be-haviour of the BHXRB is that the inner radius remains constant,then an increase of the f col could account for the majority of thespurs observed. During the most disc dominated parts of the outburst, the inner ra-dius of the disc and the f col are approximately constant. The es-timated disc parameters (temperature and luminosity) depend onthe physical parameters of the BHXRB system - the distance, massand spin of the black hole. However, these parameters are constantfor a particular BHXRB. Therefore, the shape that the observationsmake in the L − T plane are fixed, but their location within theplane could vary, depending on these parameters.Using the theoretical relation (Equation 1) and the data we areable to place limits on the distances and masses of the BHXRBs,in the case of a Schwarzschild black hole. From Equation 1, thetheoretically expected L − T relation is of the form of L Disc L Edd = A MT , (3)where M is the mass of the black hole. When fitting the trend inthe L − T plane for the most disc dominated states, the form is (forconstant R in and f col ) L Disc L Edd = B D M T C , (4) c (cid:13) , 000–000 Global Study of the Behaviour of Black Hole X-ray Binary Discs where T is the observed temperature, B is derived from the normal-isation of the DISKBB component in
XSPEC and D is the distance ofthe BHXRB. The dependence on M and D in these two equationsare different. As these two Equations should be equal, assuming thefitted value of C = 4 , then A M = B D M . (5)However, the slope of the fits to the L − T relation do not alwaysend up with C ∼ . Therefore, in order to remove this dependencewe calculate the match at kT = 1 keV , which is close to the tem-peratures of the observed discs.Therefore, under the assumption that R in and f col are con-stant, we can determine the distances and masses which are re-quired in order that the location of the expected L − T relationmatches those which are observed. In cases where limits have beenplaced on either the distance or mass, then we are able to constrainthe acceptable values for the mass or distance respectively. Theseloci of points in the distance-mass diagram are shown in the Ap-pendix, Fig. A.1 by the blue line, and we also show the currentbest estimates on the distances and masses and their uncertainties,where they exist. In some cases (e.g. GRS J1739-278, XTE J1650-500 LMC X-1) the fitted slope is very different to , and so there inthese cases, these loci are not reliable.In some cases the current best observational estimates on thedistances and masses do coincide with the estimates from thiswork (e.g. 4U 1543-47, GX 339-4, XTE J1720-318). However inmany cases there is no overlap between the observed estimates onthe distance and mass and those calculated here (e.g. GRO 1655-40, XTE J1550-564). Although at face value, cases where thereis no overlap would allow the distance and mass estimates to berefined, it is not quite that simple. These constraints are for anon-rotating black hole, and there is significant evidence that atleast some black holes have significant spin (see e.g. Miller et al.2009; McClintock et al. 2006; Middleton et al. 2006 and alsoFender et al. 2010 and references therein).The normalisation of the theoretically expected relation be-tween L Disc and T changes when the black hole is maximallyspinning ( a ∗ = 0 . (see e.g. Gierli´nski & Done 2004). We usea very simple parameterisation from Makishima et al. (2000) whoinclude first order effects of the black hole spin on the theoreticallyexpected relation in terms of α = R in / R S , the ratio of the inner disc radius to the Schwarzschild radius ( α =1 and α = 1 / for a non rotating and maximally rotating blackhole respectively). This appears as an α term in their version ofEquation 1. We add this correction factor into Equation 1, and alsotake into account the changes in the general relativistic correctionfactors from Zhang et al. (1997) for rotating black holes.Therefore, we show in Appendix, Fig A.1, as well as the rangeof distances and masses allowed for a non-rotating black hole, wealso show those for a maximally rotating black hole ( a ∗ = 0 . ,red line) and one for a ∗ = 0 . (green line). This results in an areain the D − M plane in which both values are allowed. We note, that,a more accurate investigation would start with a more appropriatemodel for the disc emission including the relativistic effects of theblack hole spin (e.g. KERRBB ). We have, as yet, not re-fitted allour results with such a model. These plots show that many of theBHXRBs whose distances and masses did not match the loci for anon-rotating black hole, do match if the black hole is rotating (e.g.GRO J1655-40, XTE J1550-564, XTE J1650-500, LMC X-3). The F r e q u e n c y
15 keV
Figure 2.
The distribution of the break energy for the broken power-law fits using two different binning levels. The gap between . < log E Break < . arises from the cross over of the PCA and
HEXTE instruments. eight BHXRBs which have both mass and distance estimates, areall consistent with spin values < a ∗ < . , or, alternatively theinner radii are consistent with R g < R in < R g . In fact, none ofthe estimates on the spin of the black hole require high spin values( a ∼ ). This also indicates that there are no counter-rotating discsin these BHXRBs. As the estimated spins fall in the range expectedfor Kerr black holes, this indicates that the position of R in in thedisc dominated states is mainly determined by strong gravitationaleffects.For many of the BHXRBs in this sample, either the mass or thedistance or both are unknown. If only one is known, then limits onthe other can be placed from the range allowed by the black holesspin. However, in many cases these limits are not very constrain-ing (e.g. GRS J1739-278, XTE J1720-318). If both are unknown,then the best that can be obtained is a lower limit on the distance(assuming a reasonable lower bound for the black hole mass). The limitations of the spectral response of the
RXTE PCA make theunequivocal detection of a non-dominant disc very difficult. Whenthe disc’s spectral component begins to rise above the powerlaw,the difference in the χ ν between the broken powerlaw and disc +powerlaw model is very small. It is therefore difficult to say abinitio which of the two models is the most appropriate to selectfor the observation (see Dunn et al. 2010). In our selection proce-dure we select merely on the lowest reduced χ , with some restric-tions on the model parameters. We now investigate how adaptingthe model selection proceedure affects the numbers and parametersof the discs detected.As the broken powerlaw model could mimic a disc model,especially when the break energy is low ( .
10 keV ). We showin Fig. 2 the distribution of the break energies in the observationsbest fit by the broken powerlaw model, using two different binningschemes. The gap around log E break = 1 . is the result of thecrossover between the PCA and the
HEXTE instruments at
25 keV .The main cluster of points occur at low energies, with anothersmaller cluster at around log E break = 1 . . These observationswith high break energies ( E break ∼
60 keV ) are likely to be re- c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) (cid:0) kT (cid:1) GX339f col =1.6f col =2.6 -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) (cid:2) kT (cid:3) H1743f col =1.6f col =2.6
Figure 3.
The variation of the disc luminosity with the disc temperaturefor GX 339-4 and H 1743-322 when penalising the χ of broken powerlawmodels which have a break energy <
15 keV . For comparison plots seeAppendix Fig. A.1. liable fits to a true break in the spectrum. However, those whichfall below around E break ∼
10 keV could be the result of a non-dominant disc mimicking a broken powerlawWe redo the model selection proceedure but penalise the bro-ken powerlaw models where the break energy is lower than
15 keV .In some cases only one of the two powerlaw fits (with and withoutline) has a break energy <
15 keV , and then the remaining bro-ken powerlaw fit is still allowed. However, this only occurs in rarecases. The other two remaining options are then single powerlaw ordisc+powerlaw models (each with and without a line). We expectthat this will have most effect in the intermediate states, where non-dominant discs are expected, rather than in the most disc dominatedstates where L ∝ T .In Fig. 3 we show the L − T plane for GX 339-4 and H 1743-322 as an example to show the increase in the number of observa-tions which have a low disc fraction. These extra observations ap-pear below the T relation, and the spurs appear to merge in withthem. Most of these observations have large uncertainties in boththe disc temperature and luminosity.Doing the converse on the selection procedure - favouring thebroken powerlaw models in these situations - removes most of theobservations with a disc detection at very low disc fractions (lowerright in the L − T plane) in Appendix Fig. A.1. Although this is may be a more conservative selection procedure (no discs detectedwhen they may be uncertain), it is less informative on the behaviourof the BHXRBs on the transitions between the different states.It is therefore difficult to determine what the appropriate se-lection procedure is when broken powerlaw and disc models areboth good fits to the data. The spectral resolution and low energyrange of the RXTE PCA are very limiting in this case. Future inves-tigations or instruments may aid in pin-pointing the disc behaviourin the transition regions
10 POWERLAW EVOLUTION
Using the Disc Fraction Luminosity Diagram (DFLD) to investi-gate the behaviour of a BHXRB during an outburst restricts whatinformation can be extracted about the variation of the powerlawcomponent, especially in the hard/powerlaw-dominated state. Inthis state, the variation in the powerlaw slope or break energy donot effect the disc fraction, and so all observations fall on a singleline. In Appendix Fig. A.2 we show the DFLDs for the X-ray bi-nary in question, where the colourscale shows the variation of thepowerlaw slope (below the break if it is a broken powerlaw). Weshow in the neighbouring panel, the powerlaw slope against the to-tal luminosity for those observations with a disc fraction of < . (powerlaw fraction > . ). This allows the change in the powerlawslope to be tracked in the powerlaw dominated state. In a number ofbinaries there are insufficient observations in the hard state to de-termine any trend with time. Also, 4U 1630-47, the variation of thepowerlaw slope appears complex, with no easily discernable globaltrend. However, the outburst structure in this BHXRB is also com-plex and so this variation is expected (see Dunn et al. 2010).In the majority of BHXRBs, in the low luminosity “stalk”,the powerlaw slope increases as the luminosity falls – the spectrumsoftens. This has been seen in the HIDs of the BHXRBs before,as a change in the X-ray colour. The re-emergence of the disc atvery low luminosities has been observed in deep pointed observa-tions and may also play a role in the softening of the spectrum atlow luminosities (see Cabanac et al. 2009). However, at these lowluminosities the effects of the Galactic Ridge Emission (GRE) playa role. None of the BHXRBs were fitted with a model which takesinto account the effects of the GRE in their vicinity (Dunn et al.2010). At low luminosities, the GRE can have an appreciable effecton the shape and flux of the spectrum. However, the curvature inthe stalk was seen in the study of GX 339-4 by Dunn et al. (2008),where the GRE was added to the model spectrum as a fixed com-ponent. Therefore only part of the softening at low luminosities canbe explained by the GRE.However, at the top of the powerlaw dominated state in someBHXRBs, there is an increase in the powerlaw slope. The increasein Γ has been observed as the BHXRB enters the soft or disc-dominated state. However, in these Figures, the Γ increases far be-yond what has been observed in other studies of these BHXRBs, us-ing the same data (e.g. Motta et al. 2009). The likeliest explanationis that the broken powerlaw is accounting for a rising disc, whichis not being well fit by a disc model. What can also be seen is thatthese softer powerlaw slopes are from broken powerlaws, and theyhave a comparatively low break energy. As noted in Dunn et al.(2010) and Section 9 there is a possibility for the broken powerlawto mimic the disc (and powerlaw) model. It is probable that as thedisc rises in luminosity the limited spectral range of the RXTE PCA means that the curvature of the disc cannot be determined, and the c (cid:13) , 000–000 Global Study of the Behaviour of Black Hole X-ray Binary Discs broken powerlaw resulted being a better fit. Restricting the power-law break to being above the peak mentioned in Section 9 wouldprevent this occurring. However, the accuracy of the fitted disc pa-rameters is not clear. Therefore, the softening of the powerlaw onthe transitions to the disc-dominated state is likely to be the resultof the limitations of the RXTE PCA .
11 SUMMARY
We have investigated the behaviour of the disc and powerlaw com-ponents in the 25 BHXRBs presented in Dunn et al. (2010). In themajority of BHRXBs in which at least most of an outburst has beenobserved, the disc luminosity scales close to T in the most discdominated observations. This behaviour had been seen in otherstudies (e.g. Gierli´nski & Done 2004). The scaling of T impliesthat both the disc’s inner radius, R in and the colour correction fac-tor, f col are relatively constant in the most disc dominated states.A number of BHXRBs do not show a clear T relation, but thesecould be the result of the limitations of the model fitting routine orthe frequency of observations.However, in observations where the disc is no longer overlydominant, there are deviations from the T law. If interpreted aschanges in the disc’s inner radius, these deviations imply that thedisc is moving inwards at the end of an outburst, and outwards at thebeginning of the outburst. Although we do not rule this behaviourout, it seems an unlikely scenario. If these deviations are attributedto changes in the colour correction factor, then f col rises as the discfraction decreases.There are a number of observations in which the disc param-eters determined are unlikely to be explained by reasonable valuesfor the disc radius or the f col . The spectral fits for these observa-tions tend to have χ values which are very similar to those for thebroken-powerlaw model, which makes selecting the most appropri-ate model difficult. This also makes determining the true behaviourof the disc temperature, radius and f col in these intermediate statesdifficult.The luminosity of the disc in Eddington units can be calcu-lated from theoretical arguments from the BHXRB parameters andthe disc temperature. When calculating the observed luminosity thedistance of the BHXRB system also enters the calculation. Thecombination of these two calculations allows the ratio of D/M tobe estimated from the L − T relation of the BHXRB disc. We havetherefore placed limits on the range values of D and M values al-lowed for different values of the spin of the black hole. ACKNOWLEDGEMENTS
REFERENCES
Abramowicz M. A., Czerny B., Lasota J. P., Szuszkiewicz E.,1988, ApJ, 332, 646Augusteijn T., Kuulkers E., van Kerkwijk M. H., 2001, A&A, 375,447Belloni T. M., 2010, in Lecture Notes in Physics, Berlin SpringerVerlag, Vol. 794, Lecture Notes in Physics, Berlin Springer Ver-lag, T. Belloni, ed., pp. 53–+Cabanac C., Fender R. P., Dunn R. J. H., K¨ording E. G., 2009,MNRAS, 396, 1415Cadolle Bel M., Rodriguez J., Sizun P., Farinelli R., Del Santo M.,Goldwurm A., Goldoni P., Corbel S., Parmar A. N., KuulkersE., Ubertini P., Capitanio F., Roques J.-P., Frontera F., Amati L.,Westergaard N. J., 2004, A&A, 426, 659Campana S., Stella L., Belloni T., Israel G. L., Santangelo A.,Frontera F., Orlandini M., Dal Fiume D., 2002, A&A, 384, 163Capitanio F., Ubertini P., Bazzano A., Kretschmar P., ZdziarskiA. A., Joinet A., Barlow E. J., Bird A. J., Dean A. J., JourdainE., De Cesare G., Del Santo M., Natalucci L., Cadolle Bel M.,Goldwurm A., 2005, ApJ, 622, 503Casares J., Zurita C., Shahbaz T., Charles P. A., Fender R. P.,2004, ApJ, 613, L133Chaty S., Haswell C. A., Malzac J., Hynes R. I., Shrader C. R.,Cui W., 2003, MNRAS, 346, 689Corbel S., Fender R. P., Tzioumis A. K., Nowak M., McIntyre V.,Durouchoux P., Sood R., 2000, A&A, 359, 251Corbel S., Nowak M. A., Fender R. P., Tzioumis A. K., MarkoffS., 2003, A&A, 400, 1007Cowley A. P., Crampton D., Hutchings J. B., Remillard R., Pen-fold J. E., 1983, ApJ, 272, 118Cui W., Heindl W. A., Swank J. H., Smith D. M., Morgan E. H.,Remillard R., Marshall F. E., 1997, ApJ, 487, L73+Davis S. W., Blaes O. M., Hubeny I., Turner N. J., 2005, ApJ, 621,372Davis S. W., Done C., Blaes O. M., 2006, ApJ, 647, 525di Benedetto G. P., 1997, ApJ, 486, 60Done C., Davis S. W., 2008, ApJ, 683, 389Done C., Gierli´nski M., 2003, MNRAS, 342, 1041Done C., Gierli´nski M., Kubota A., 2007, AAAR, 15, 1Dunn R. J. H., Fender R. P., K¨ording E. G., Belloni T., CabanacC., 2010, MNRAS, 403, 61Dunn R. J. H., Fender R. P., K¨ording E. G., Cabanac C., BelloniT., 2008, MNRAS, 387, 545Fender R., Gallo E., Russell D., 2010, ArXiv e-printsFender R. P., Belloni T. M., Gallo E., 2004, MNRAS, 355, 1105Foellmi C., 2009, New Astronomy, 14, 674Fragos T., Tremmel M., Rantsiou E., Belczynski K., 2010, ApJ,719, L79Gelino D. M., Balman S¸ ., Kızılo˘glu ¨U., Yılmaz A., Kalemci E.,Tomsick J. A., 2006, ApJ, 642, 438Gierli´nski M., Done C., 2003, MNRAS, 342, 1083—, 2004, MNRAS, 347, 885Gierli´nski M., Maciołek-Nied´zwiecki A., Ebisawa K., 2001, MN-RAS, 325, 1253Gierli´nski M., Zdziarski A. A., Poutanen J., Coppi P. S., EbisawaK., Johnson W. N., 1999, MNRAS, 309, 496Greiner J., Dennerl K., Predehl P., 1996, A&A, 314, L21Haardt F., Galli M. R., Treves A., Chiappetti L., Dal Fiume D.,Corongiu A., Belloni T., Frontera F., Kuulkers E., Stella L., 2001,ApJS, 133, 187Hjellming R. M., Rupen M. P., 1995, Nature, 375, 464 c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni
Hjellming R. M., Rupen M. P., Mioduszewski A. J., Smith D. A.,Harmon B. A., Waltman E. B., Ghigo F. D., Pooley G. G., 1998,in Bulletin of the American Astronomical Society, Vol. 30, Bul-letin of the American Astronomical Society, pp. 1405–+Homan J., Belloni T., 2005, APSS, 300, 107Homan J., Wijnands R., Kong A., Miller J. M., Rossi S., BelloniT., Lewin W. H. G., 2006, MNRAS, 366, 235Hutchings J. B., Crampton D., Cowley A. P., Bianchi L., Thomp-son I. B., 1987, AJ, 94, 340Hutchings J. B., Winter K., Cowley A. P., Schmidtke P. C., Cramp-ton D., 2003, AJ, 126, 2368Hynes R. I., Haswell C. A., Chaty S., Shrader C. R., Cui W., 2002,MNRAS, 331, 169Hynes R. I., Haswell C. A., Shrader C. R., Chen W., Horne K.,Harlaftis E. T., O’Brien K., Hellier C., Fender R. P., 1998, MN-RAS, 300, 64Hynes R. I., Steeghs D., Casares J., Charles P. A., O’Brien K.,2003, ApJ, 583, L95Ichimaru S., 1977, ApJ, 214, 840in’t Zand J. J. M., Kuulkers E., Bazzano A., Cornelisse R., CocchiM., Heise J., Muller J. M., Natalucci L., Smith M. J. S., UbertiniP., 2000, A&A, 357, 520in’t Zand J. J. M., Markwardt C. B., Bazzano A., Cocchi M., Cor-nelisse R., Heise J., Kuulkers E., Natalucci L., Santos-Lleo M.,Swank J., Ubertini P., 2002, A&A, 390, 597Jonker P. G., Nelemans G., 2004, MNRAS, 354, 355Kitamoto S., Tsunemi H., Pedersen H., Ilovaisky S. A., van derKlis M., 1990, ApJ, 361, 590K¨ording E. G., Jester S., Fender R., 2006, MNRAS, 372, 1366Kotani T., Kawai N., Nagase F., Namiki M., Sakano M.,Takeshima T., Ueda Y., Yamaoka K., Hjellming R. M., 2000,ApJ, 543, L133Maccarone T. J., 2002, MNRAS, 336, 1371Makishima K., Kubota A., Mizuno T., Ohnishi T., Tashiro M.,Aruga Y., Asai K., Dotani T., Mitsuda K., Ueda Y., Uno S., Ya-maoka K., Ebisawa K., Kohmura Y., Okada K., 2000, ApJ, 535,632McClintock J. E., Shafee R., Narayan R., Remillard R. A., DavisS. W., Li L., 2006, ApJ, 652, 518Merloni A., Fabian A. C., Ross R. R., 2000, MNRAS, 313, 193Middleton M., Done C., Gierli´nski M., Davis S. W., 2006, MN-RAS, 373, 1004Miller J. M., Fabian A. C., Reynolds C. S., Nowak M. A., HomanJ., Freyberg M. J., Ehle M., Belloni T., Wijnands R., van der KlisM., Charles P. A., Lewin W. H. G., 2004, ApJ, 606, L131Miller J. M., Reynolds C. S., Fabian A. C., Miniutti G., GalloL. C., 2009, ApJ, 697, 900Miniutti G., Fabian A. C., Miller J. M., 2004, MNRAS, 351, 466Motta S., Belloni T., Homan J., 2009, MNRAS, 400, 1603Narayan R., Yi I., 1994, ApJ, 428, L13Nowak M., Juett A., Homan J., Yao Y., Wilms J., Schulz N.,Canizares C., 2008, in AAS-High Energy Astrophysics Division,Vol. 10, AAS-High Energy Astrophysics Division, pp. 14.04–Orosz J. A., Kuulkers E., van der Klis M., McClintock J. E., Gar-cia M. R., Callanan P. J., Bailyn C. D., Jain R. K., RemillardR. A., 2001, ApJ, 555, 489Orosz J. A., McClintock J. E., Remillard R. A., Corbel S., 2004,ApJ, 616, 376Orosz J. A., Polisensky E. J., Bailyn C. D., Tourtellotte S. W., Mc-Clintock J. E., Remillard R. A., 2002, in Bulletin of the Ameri-can Astronomical Society, Vol. 34, Bulletin of the American As-tronomical Society, pp. 1124–+ Orosz J. A., Steeghs D., McClintock J. E., Torres M. A. P.,Bochkov I., Gou L., Narayan R., Blaschak M., Levine A. M.,Remillard R. A., Bailyn C. D., Dwyer M. M., Buxton M., 2008,astro-ph/0810.3447Park S. Q., Miller J. M., McClintock J. E., Remillard R. A.,Orosz J. A., Shrader C. R., Hunstead R. W., Campbell-WilsonD., Ishwara-Chandra C. H., Rao A. P., Rupen M. P., 2004, ApJ,610, 378Pottschmidt K., Chernyakova M., Zdziarski A. A., Lubi´nski P.,Smith D. M., Bezayiff N., 2006, A&A, 452, 285Remillard R. A., McClintock J. E., 2006, ARA&A, 44, 49Revnivtsev M., Gilfanov M., Churazov E., 1998, A&A, 339, 483Ritter H., Kolb U., 2003, A&A, 404, 301Russell D. M., Maitra D., Dunn R. J. H., Markoff S., 2010, MN-RAS, 620Sala G., Greiner J., Ajello M., Bottacini E., Haberl F., 2007, A&A,473, 561Sanchez-Fernandez C., Zurita C., Casares J., Castro-Tirado A. J.,Bond I., Brandt S., Lund N., 2002, IAU Circ., 7989, 1Shahbaz T., Smale A. P., Naylor T., Charles P. A., van Paradijs J.,Hassall B. J. M., Callanan P., 1996, MNRAS, 282, 1437Shahbaz T., van der Hooft F., Casares J., Charles P. A., vanParadijs J., 1999, MNRAS, 306, 89Shakura N. I., Sunyaev R. A., 1973, A&A, 24, 337Shimura T., Takahara F., 1995, ApJ, 445, 780Smith D. M., Heindl W. A., Swank J. H., 2002, ApJ, 578, L129Steiner J. F., McClintock J. E., Remillard R. A., Gou L., YamadaS., Narayan R., 2010, ApJ, 718, L117Thorstensen J. R., 1987, ApJ, 312, 739Tomsick J. A., Corbel S., Goldwurm A., Kaaret P., 2005, ApJ,630, 413van der Hooft F., Heemskerk M. H. M., Alberts F., van Paradijs J.,1998, A&A, 329, 538Wagner R. M., Foltz C. B., Shahbaz T., Casares J., Charles P. A.,Starrfield S. G., Hewett P., 2001, ApJ, 556, 42Wilson C. A., Patel S. K., Kouveliotou C., Jonker P. G., van derKlis M., Lewin W. H. G., Belloni T., M´endez M., 2003, ApJ,596, 1220Zdziarski A. A., Gierli´nski M., Mikołajewska J., Wardzi´nski G.,Smith D. M., Harmon B. A., Kitamoto S., 2004, MNRAS, 351,791Zhang S. N., Cui W., Chen W., 1997, ApJ, 482, L155+
APPENDIX
For each BHXRB in our sample we show in Fig. A.1
TOP LEFT thedisc temperature as a function of the disc luminosity, along withthe theoretically expected relation for the case that the BH is notrotating for a variety of values for f col . The f col = 1 . line isdepicted thicker than the rest, which increment in . intervals. Theline which best fits the most disc dominated spectra is shown, aswell as its slope. We show TOP RIGHT the region in the distance-mass plane which is allowed by the theoretical expectation of theluminosity-temperature relation and the observed data points. Thebest determined values for the distance and mass along with theiruncertainties are also shown where available.In the
BOTTOM LEFT we show the variation of the disc radius( R in ) with the disc temperature. The colourscale is the disc frac-tion. The line is the average of the disc radii for the observationswhich have a disc fraction > . . The variation of the f col with the c (cid:13) , 000–000 Global Study of the Behaviour of Black Hole X-ray Binary Discs -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) (cid:4) kT col =1.6f col =2.6 R inner (km) D i s c T e m p , k e V R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 (cid:5) f col L P L / ( L D i s c + L P L ) L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1.
Schematic figures of
LEFT : Disc luminosity against disc temperature,
MIDDLE : Disc radius against disc temperature and
RIGHT : the excess δf col required against the disc fraction. The arrows show the motion through the diagram. In the right-hand figure, the offset between the inward and outward tracksare for clarity only. -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) (cid:6) kT (cid:7) col =1.6f col =2.6 Distance (kpc) M a ss ( M (cid:8) ) a=0a=0.998 a=0.5 R inner (km) D i s c T e m p , k e V R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 (cid:9) f col L P L / ( L D i s c + L P L ) L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) 4U 1543-47
TOP LEFT
We show the Luminosity of the disc as a function of the temperature of the
DISCBB component in
XSPEC . The colourscale is the disc fraction of the observation. The theoretical L − T relations are shown by the sets of dotted line for a number of values of f col . The solid lineshows the fit to the most disc dominated states (Disc Fraction > . ). TOP RIGHT
We show the range of distances and masses allowed, if the observations areto match the theoretical relation. The blue line is for a non-rotating black hole, and the direction for increasing a is shown. The dashed and dotted lines showthe current values and uncertainties on the masses and distances where available. BOTTOM LEFT
We show the variation of the inner disc radius ( R in ) withthe disc temperature. The colour scale is the disc fraction of the observation. The solid line shows the average R in of the most disc dominated states (DiscFraction > . ). BOTTOM RIGHT
The excess the colour correction required, δf col , with the disc fraction. The disc temperature is the colour scale. disc fraction is show in the BOTTOM RIGHT . The disc temperatureis the colour scale.By comparing all three of the scatter plot figures, the be-haviour of the disc in the BHXRB in the outburst becomes clearer. c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) (cid:10) kT (cid:11) col =1.6f col =2.6 Distance (kpc) M a ss ( M (cid:12) ) a=0a=0.998 a=0.5 R inner (km) D i s c T e m p , k e V R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 (cid:13) f col L P L / ( L D i s c + L P L ) L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) 4U 1630-47 -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) (cid:14) kT (cid:15) col =1.6f col =2.6 Distance (kpc) M a ss ( M (cid:16) ) a=0a=0.998 a=0.5 R inner (km) D i s c T e m p , k e V R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 (cid:17) f col L P L / ( L D i s c + L P L ) L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) 4U 1957+115 c (cid:13) , 000–000
Global Study of the Behaviour of Black Hole X-ray Binary Discs -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) (cid:18) kT (cid:19) GRO1655f col =1.6f col =2.6
Distance (kpc) M a ss ( M (cid:20) ) a=0a=0.998 a=0.5 GRO1655 R inner (km) D i s c T e m p , k e V GRO1655
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 (cid:21) f col L P L / ( L D i s c + L P L ) GRO1655 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) GRO J1655-40 -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) (cid:22) kT (cid:23) (cid:24) GRS1739f col =1.6f col =2.6
Distance (kpc) M a ss ( M (cid:25) ) a=0a=0.998 a=0.5 GRS1739 R inner (km) D i s c T e m p , k e V GRS1739
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 (cid:26) f col L P L / ( L D i s c + L P L ) GRS1739 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) GRS 1737-31c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) (cid:27) kT (cid:28) GRS1758f col =1.6f col =2.6
Distance (kpc) M a ss ( M (cid:29) ) a=0a=0.998 a=0.5 GRS1758 R inner (km) D i s c T e m p , k e V GRS1758
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 (cid:30) f col L P L / ( L D i s c + L P L ) GRS1758 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) GRS 1758-258 -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) (cid:31) kT GX339f col =1.6f col =2.6
Distance (kpc) M a ss ( M ! ) a=0a=0.998 a=0.5 GX339 R inner (km) D i s c T e m p , k e V GX339
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 " f col L P L / ( L D i s c + L P L ) GX339 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) GX 339-4 c (cid:13) , 000–000
Global Study of the Behaviour of Black Hole X-ray Binary Discs -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) kT $ H1743f col =1.6f col =2.6
Distance (kpc) M a ss ( M % ) a=0a=0.998 a=0.5 H1743 R inner (km) D i s c T e m p , k e V H1743
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 & f col L P L / ( L D i s c + L P L ) H1743 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) H 1743-322 -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) ’ kT ( J1550f col =1.6f col =2.6
Distance (kpc) M a ss ( M ) ) a=0a=0.998 a=0.5 J1550 R inner (km) D i s c T e m p , k e V J1550
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 * f col L P L / ( L D i s c + L P L ) J1550 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) XTE J1550-564c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) + kT , J1650f col =1.6f col =2.6
Distance (kpc) M a ss ( M - ) a=0a=0.998 a=0.5 J1650 R inner (km) D i s c T e m p , k e V J1650
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 . f col L P L / ( L D i s c + L P L ) J1650 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) XTE J1650-500 -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) / kT J1720f col =1.6f col =2.6
Distance (kpc) M a ss ( M ) a=0a=0.998 a=0.5 J1720 R inner (km) D i s c T e m p , k e V J1720
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 f col L P L / ( L D i s c + L P L ) J1720 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) XTE J1720-318 c (cid:13) , 000–000
Global Study of the Behaviour of Black Hole X-ray Binary Discs -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) kT J1748f col =1.6f col =2.6
Distance (kpc) M a ss ( M ) a=0a=0.998 a=0.5 J1748 R inner (km) D i s c T e m p , k e V J1748
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 f col L P L / ( L D i s c + L P L ) J1748 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) XT J1748-288 -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) kT J1817f col =1.6f col =2.6
Distance (kpc) M a ss ( M ) a=0a=0.998 a=0.5 J1817 R inner (km) D i s c T e m p , k e V J1817
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 : f col L P L / ( L D i s c + L P L ) J1817 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) XTE J1817-330c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) ; kT < J1859f col =1.6f col =2.6
Distance (kpc) M a ss ( M = ) a=0a=0.998 a=0.5 J1859 R inner (km) D i s c T e m p , k e V J1859
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 > f col L P L / ( L D i s c + L P L ) J1859 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) XTE J1859+226 -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) ? kT @ J2012f col =1.6f col =2.6
Distance (kpc) M a ss ( M A ) a=0a=0.998 a=0.5 J2012 R inner (km) D i s c T e m p , k e V J2012
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 B f col L P L / ( L D i s c + L P L ) J2012 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) XTE J2012+381 c (cid:13) , 000–000
Global Study of the Behaviour of Black Hole X-ray Binary Discs -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) C kT D E LMC_X1f col =1.6f col =2.6
Distance (kpc) M a ss ( M F ) a=0a=0.998 a=0.5 LMC_X1 R inner (km) D i s c T e m p , k e V LMC_X1
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 G f col L P L / ( L D i s c + L P L ) LMC_X1 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) LMC X-1 -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) H kT I LMC_X3f col =1.6f col =2.6
Distance (kpc) M a ss ( M J ) a=0a=0.998 a=0.5 LMC_X3 R inner (km) D i s c T e m p , k e V LMC_X3
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 K f col L P L / ( L D i s c + L P L ) LMC_X3 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) LMC X-3c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni -3 -2 -1 L D i s c / L E dd (L Disc /L Edd ) L kT M SLX1746f col =1.6f col =2.6
Distance (kpc) M a ss ( M N ) a=0a=0.998 a=0.5 SLX1746 R inner (km) D i s c T e m p , k e V SLX1746
R/R g -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 O f col L P L / ( L D i s c + L P L ) SLX1746 0.990.900.00 L D i s c / ( L D i s c + L P L ) Disc (keV)
Figure A.1. (cont) SLX 1746-331 c (cid:13) , 000–000
Global Study of the Behaviour of Black Hole X-ray Binary Discs L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s L Disc /(L
Disc +L PL ) PQR S T U L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s L Disc /(L
Disc +L PL ) VW L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s L Disc /(L
Disc +L PL ) XY Figure A.2.
The DFLDs with the colour scale showing the powerlaw slope. Also shown in the side panel is the powerlaw slope (below the break whereappropriate) for the observations with a disc fraction < . , along with the break energy for the broken powerlaw (where it occurs). TOP : 4U 1543-47,
MIDDLE : 4U 1630-47,
BOTTOM : 4U 1957+115.c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s GRO1655 L Disc /(L
Disc +L PL ) Z[ L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s GX339 L Disc /(L
Disc +L PL ) \] L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s H1743 L Disc /(L
Disc +L PL ) ^_ Figure A.2. (cont)
TOP : GRO J1655-40,
MIDDLE : GX 339-4,
BOTTOM : H 1743-322.c (cid:13) , 000–000
Global Study of the Behaviour of Black Hole X-ray Binary Discs L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s J1118 L Disc /(L
Disc +L PL ) ‘a L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s J1550 L Disc /(L
Disc +L PL ) bc L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s J1650 L Disc /(L
Disc +L PL ) de Figure A.2. (cont)
TOP : XTE J1118+480,
MIDDLE : XTE J1550-564,
BOTTOM : XTE J1650-500.c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s J1720 L Disc /(L
Disc +L PL ) fg L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s J1748 L Disc /(L
Disc +L PL ) hi L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s J1817 L Disc /(L
Disc +L PL ) jk Figure A.2. (cont)
TOP : XTE J1720-318,
MIDDLE : XTE J1748-288,
BOTTOM : XTE J1817-330.c (cid:13) , 000–000
Global Study of the Behaviour of Black Hole X-ray Binary Discs L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s J1859 L Disc /(L
Disc +L PL ) lm L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s LMC_X1 L Disc /(L
Disc +L PL ) no L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s LMC_X3 L Disc /(L
Disc +L PL ) pq Figure A.2. (cont)
TOP : XTE J1859+226,
MIDDLE : LMC X-1,
BOTTOM : LMC X-3.c (cid:13) , 000–000 Dunn, Fender, K¨ording, Belloni & Merloni L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s SAX1711 L Disc /(L
Disc +L PL ) rs L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s SAX1819 L Disc /(L
Disc +L PL ) tu L PL /(L Disc +L PL ) L D i s c + L P L , e r g/ s SLX1746 L Disc /(L
Disc +L PL ) vw Figure A.2. (cont)
TOP : SAX 1711.6-3808,
MIDDLE : SAX 1918.3-2525,