State Transitions in Bright Galactic X-ray Binaries: Luminosities Span by Two Orders of Magnitude
aa r X i v : . [ a s t r o - ph . H E ] J u l State Transitions in Bright Galactic X-ray Binaries: LuminositiesSpan by Two Orders of Magnitude
Wenfei Yu and Zhen Yan Key Laboratory for Research in Galaxies and Cosmology and Shanghai AstronomicalObservatory, 80 Nandan Road, Shanghai 200030, China. E-mail: [email protected]
ABSTRACT
Using X-ray monitoring observations with the All Sky Monitor (ASM) onboard the
Rossi X-ray Timing Explorer (RXTE) and the Burst Alert Telescope(BAT) on board the
Swift , we are able to study the spectral state transitionsoccurred in about 20 bright persistent and transient black hole and neutron starbinaries. We have confirmed that there is a correlation between the X-ray lumi-nosity corresponding to the hard-to-soft transition and the X-ray luminosity ofthe following soft state. This correlation holds over a luminosity range spanningby two orders of magnitude, with no indication of a flux saturation or cut-off. Wehave also found that the transition luminosity correlates with the rate of increasein the X-ray luminosity during the rising phase of an outburst or flare, implyingthat the origin of the variation of the transition luminosity is associated withnon-stationary accretion in both transient sources and persistent sources. Thecorrelation between the luminosity corresponding to the end of the soft-to-hardtransition and the peak luminosity of the preceding soft state is found insignif-icant. The results suggest that the hysteresis effect of spectral state transitionsis primarily driven by non-stationary accretion when the mass accretion rate in-creases rather than the mass accretion rate decreases. Our results also imply thatGalactic X-ray binaries can reach more luminous hard states during outburstsof higher luminosities and of similar rise time scales as those observed. Basedon the correlations, we speculate that bright hard state beyond the Eddingtonluminosity will be observed in Galactic binaries in the next century. We alsosuggest that some ultra-luminous X-ray sources in nearby galaxies, which stay inthe hard states during bright, short flares, harbor stellar-mass compact stars.
Subject headings: accretion, accretion disks — black hole physics —stars: X-raybinaries also Graduate School of the Chinese Academy of Sciences
1. Introduction
Observations of black hole and neutron star X-ray binaries show two main X-ray spectralstates, namely the soft state and the hard state (see the recent review by Remillard &McClintock 2006 and references therein). In the soft state, the X-ray spectrum is dominatedby a thermal component with a weak steep power-law component. In the hard state, theX-ray spectrum is well described by a single power-law component with a high-energy cut-off(see the review by Done et al. 2007). For a long time it has been believed that a change inthe instantaneous mass accretion rate around a threshold causes spectral state transitions,therefore mass accretion rate was considered as the dominant parameter in determiningspectral state transitions (e.g., Esin et al. 1997).Observations suggest that mass accretion rate is not the only parameter in determin-ing spectral state transitions. The luminosity corresponding to the hard-to-soft (here afterH-S) transition is found usually higher than that of the soft-to-hard (here after S-H) tran-sition in transient sources (Miyamoto et al. 1995; Nowak 1995; Maccarone & Coppi 2003;Gladstone et al. 2007), suggesting that the transitions between the two states do not occurat the same luminosity when transition directions are opposite. On the other hand, additionalstudies show evidence that the H-S transition luminosity is not fixed (Homan et al. 2001;Zdziarski et al. 2004), which could vary by a factor of 10 (Yu, van der Klis & Fender 2004;Yu & Dolence 2007). Many different parameters have been suggested to determine spectralstate transitions, including the size of the corona (Homan et al. 2001), the history of themass accretion rate (Homan & Belloni 2005), the history of the location of the inner diskradius (Zdziarski et al. 2004), two different flows in the accretion geometry which contributeto the non-thermal and thermal components, respectively (Smith et al. 2002), the mass inthe accretion disk (Yu, van der Klis & Fender 2004; Yu et al. 2007), and the changes in theCompton cooling and heating processes in the accretion flow involving evaporation and irra-diation (Meyer-Hofmeister et al. 2004; Liu et al. 2005), etc. These diverse suggestions likelyreflect different manifestations of the same phenomena and the same physics underneath.Usually during the rising phase of a bright outburst of a neutron star or black hole tran-sient, spectral transition from the hard state to the soft state can be seen. A hard flare beforethe H-S transition occurs in neutron star and black hole transients (see Bouchacourt et al.1984; Brocksopp et al. 2002; Yu et al. 2003, and references therein). The transition lu-minosity from the hard state to the soft state corresponds to the peak luminosity of thehard state throughout an outbursts because of hysteresis effect of spectral state transitions(Miyamoto et al. 1995). The transition does not occur at a constant luminosity nor at an ar-bitrary one. It has been found that the peak luminosity of the hard state correlates with theoutburst peak luminosity in a number of soft X-ray transients Aql X-1, XTE J1550-564, and 3 –GX 339-4 and the persistent, transient-like neutron star low mass X-ray binary 4U 1705-44(Yu, van der Klis & Fender 2004; Yu et al. 2007; Yu & Dolence 2007). The general pictureis that the brighter the initial hard state, the brighter the outburst will be, or vice versa. Anapplication of the correlation is that one can predict the outburst peak luminosity duringthe rising phase of an outburst when the H-S transition occurs (Yu, van der Klis & Fender2004; Yu et al. 2007; Yu & Dolence 2007).The origin of such a correlation is not well understood, but the correlation has importantimplications. First, the widely-accepted idea that the mass accretion rate in the accretionflow determines spectral state and state transition is not complete. In Aql X-1, Yu & Dolence(2007) showed that the correlation holds for outburst peak fluxes spanning by an orderof magnitude, with the lowest transition flux comparable to that of the S-H transition.The correlation therefore holds for low luminosity flares. This suggests that spectral statetransitions in bright outbursts or small flares could be consistently explained. Second, thecorrelation has shown no saturation towards high luminosities, which suggests that hardstates brighter than the ones currently known are possible and could be observed in transientsources during brighter outbursts, leaving more luminosity room for the hard state to develop.Models aiming at explaining H-S transitions or the brightest hard state a source can reachtherefore need to consider the correlation in the first place.Up to now there have been a number of transient sources seen to stay in the hard statethroughout their outbursts (e.g. the last outbursts of XTE J1550-564, see (Belloni et al.2002)). This can be understood as that the mass accretion rate have not exceeded thethreshold for state transitions predicted in the advection-dominated accretion flow (ADAF)model (e.g., Narayan & Yi 1994,1995; Esin et al. 1997). The correlation, on the other hand,suggests that a source can reach higher luminosities in the hard state than the theoreticalthreshold. The correlation and its intrinsic scatter then gives the peak luminosity of thethermal disk that is required for a transition to occur when a luminosity of the hard state isgiven; dimmer thermal disk could not develop and exist.In order to systematically study spectral state transitions to understand the origin ofthe luminosity correlation and if the correlation holds for not only transient sources butalso persistent sources, we have performed a study of the spectral state transitions that canbe seen in the long-term monitoring light curves of bright X-ray binaries from the All SkyMonitor (ASM) on board the Rossi X-ray Timing Explorer (RXTE) and the Burst AlertTelescope (BAT) on board the Swift in the 2–12 keV and the 15–50 keV energy ranges,respectively, in a period of three years. We searched for H-S transitions and S-H transitionsin all the bright X-ray binaries and identified them based on hardness ratios between the BATflux and the ASM flux. We confirmed the correlation between the luminosity corresponding 4 –to the H-S transition and the peak luminosity of the following soft state, and found thesame correlation holds for both transient and persistent sources. We also show that thetransition luminosity correlates with the rate of increase of the X-ray luminosity around theH-S transition, implying that the rate-of-increase of the mass accretion rate rather than themass accretion rate itself drives the H-S transition during outbursts or flares primarily. Thisstrongly suggests that most spectral state transitions observed in persistent and transientX-ray binaries should be explained with non-stationary accretion theories.
2. Observations and Data Analysis
Public daily averaged X-ray light curves of bright X-ray binaries were obtained with theBAT (15 −
50 keV) and the ASM (2-12 keV). Combined together, they provide a monitoringof the X-ray sky on a daily basis, capable to be used to detect state transitions in brightX-ray binaries.We have searched for H-S transitions and S-H transitions in all the bright X-ray binaries.We took data from February 12, 2005 (MJD 53413) to February 8, 2008 (MJD 54504), thetime when this study started. We used good BAT data with data flag (see Scaled MapTransient Analysis Synopsis of Swift/BAT ) ) of 0 and dither flag of 0. The X-ray fluxreported in this paper has been converted into units of Crab. We used 1 Crab = 75 count/sfor the ASM and 1 Crab = 0.23 count/s/cm for the BAT, estimated from the Crab lightcurves from the two instruments, respectively. We took advantage of the energy bandsof the ASM and the BAT, which cover primarily for the thermal spectral component andthe non-thermal spectral component, respectively. The hardness ratios between the ASMand the BAT fluxes then provide a comparison between the thermal and the non-thermalspectral components, which were proved very useful to determine spectral states. To increasedetection sensitivity, we calculated two-day averaged results. We excluded BAT or ASMaverage rates with a significance smaller than 1 σ . We studied the ASM light curve, the BAT light curve and the hardness ratio for eachsource monitored by the RXTE/ASM and the Swift/BAT. We have identified spectral statetransitions in bright neutron star and black hole binaries. The two-day averaged hardness http://heasarc.gsfc.nasa.gov/docs/swift/results/transients/Transient synopsis.html σ . In Table 1,we describe the details of the state transitions identified in fifteen neutron star LMXBs andfour black hole LMXBs. We also include the high mass X-ray binary Cyg X-3 because ofits similarity to GRS 1915+105, although it does not show clear spectral states as thoseneutron star LMXBs and the black hole binaries GX 339-4 and GRO J1655-40. Othersources could not be added because of either a lack of simultaneous BAT/ASM data or alack of identifications of state transitions.In summary, we identified H-S transitions and associated S-H transitions in fifteen neu-tron star LXMBs, four black hole LMXBs and a HMXB Cyg X-3. In order to comparethem with the state transitions in the well-known black hole binary Cygnus X-1, we alsoestimated the transition flux and the peak flux of the following soft state during its H-S transition in 1996 based on CGRO/BATSE and RXTE/ASM monitoring observations(Zhang et al. 1997). It has been suggested that an additional parameter is needed to account for state evo-lution based on studies of hysteresis (Homan et al. 2001; Smith et al. 2002). The unknownsecond parameter other than the mass accretion rate is the key for the understanding ofthe accretion geometry and the origin of spectral transitions. As suggested by the correla-tion between the luminosity of the H-S transition and the peak luminosity of the followingsoft state, the second parameter could be the surrogate of the peak luminosity of an out-burst or flare, such as the mass in the accretion disk before an outburst or flare occurs 7 –(Yu, van der Klis & Fender 2004; Yu et al. 2007). In the simplest picture that the outburstrise time scale remains approximately constant in a single source, the rate-of-increase of themass accretion rate (here after d ˙M / dt), could be the surrogate of the peak luminosity ofan outburst or flare. It is thus necessary to investigate the rate-of-change in the X-ray flux(here after dL / dt) from the observations.The idea that mass accretion rate determines spectral state is based on the assumptionof stationary accretion under which the rate-of-change in the mass accretion rate has littleeffect. During transient outbursts this does not hold since the observed source flux usuallyincreases by a factor of more than an order of magnitude in a period of a few days to a week.On the time scale of state transition, the increase of the mass accretion rate is no longersmall compared to the mass accretion rate itself.We measured the rate-of-changes of the ASM and the BAT fluxes around the H-Stransition, respectively, by calculating the ratio between the flux difference ∆ F between anytwo adjacent time bins over the time interval of two days. In order to reduce the effects oflarge fluctuations from individual flux measurements, we performed numerical differentiationusing 3-point, Lagrangian interpolation to measure the rate-of-change of the X-ray flux. Foreach H-S transition, we chose a time window to investigate the rate-of-change. The timewindow used for the BAT light curve starts when the BAT flux reached half of the BATtransition flux and ends when the BAT flux reached its maximum (transition flux). For theASM light curve, the time window starts at the same start time as the time window for theBAT analysis and ends at the ASM peak. We determined the maximal rate-of-changes inthe ASM flux and the BAT flux in the above time windows, respectively, for each outburstor flare with H-S transition identified.The dL / dt in black hole binaries in the soft state or neutron star X-ray binaries in bothsoft state and hard state is an indicator of the d ˙M / dt, because for the latter the gravitationalenergy of the matter accreted by neutron stars has to be released near or on the neutronstar because of hard surface, and for the former the X-ray flux is dominated by the thermalemission from the accretion disk and is known to be a surrogate of the mass accretion ratein the disk flow. Close to the luminosity threshold for spectral transitions in the radiativeinefficient flow model (Narayan & Yi 1994, 1995), which is the most popular model forblack hole hard state, the radiation efficiency is proportional to the mass accretion rate andexpected to be close to that of the standard disk flow, so the maximal rate-of-increase offlux approximately represent the maximal rate-of-increase of the mass accretion rate duringthe rising phase of the soft state or the hard state around the spectral state transition. Thisis supported by the following analysis, showing that black hole systems and neutron starsystems fall on the same empirical correlation track (Fig. 24). 8 –
3. Results3.1. The hard-to-soft transition
We have measured the hard X-ray flux corresponding to the H-S transition and the peakflux of the following soft state in about 20 bright sources. In Figure 22 we plot the observedtransition flux and the observed peak fluxes of following soft states of these sources. Itshows a strong positive correlation with Spearman correlation coefficient 0.91 and a chancepossibility on the order of 10 − . To exclude the contribution due to diverse source distancesand compact star masses, we re-scaled the observed fluxes to intrinsic fluxes to account forthe effect from different source distances and compact star masses, using the source distancesand compact star masses with uncertainties listed in Table 1. We found a strong positivecorrelation remains.Since intrinsic or Galactic absorption affects the observed soft X-ray flux below about5 keV, we used only the ASM rate from the third channel (5-12 keV) to check if the fluxcorrelation is primarily caused by this effect. We found a correlation of high significance withSpearman correlation coefficient of 0.85 and a chance possibility of 10 − . We concluded thatintrinsic or Galactic hydrogen absorption and its potential variation does not play a role incausing the correlation between the transition fluxes and the peak fluxes.The energy spectra of Crab in the 2–10 keV band and the 15–50 keV band can bedescribed by a power-law with photon indices of -2.07 and -2.12, and normalizations of 8.26and 9.42, respectively (Kirsch et al. 2005). We can convert the ASM flux and the BAT fluxin Crab units into luminosities assuming that the Galactic binaries have similar spectralshape as well as hydrogen absorption as the Crab. The approximation is justified since inthe hard state just before a state transition, the energy spectrum is dominated by a power-law component with a power-law index in the range 1.8–2.0 and most of the binaries inour study have an N H similar to that of the Crab (4 . − . × . Figure 23 shows therelation between the luminosity corresponding to the H-S transition and the outburst peakluminosity. The Spearman coefficient is 0.85, with a chance possibility of 1 . × − . We fitthe data with a model of the form log L PS = A log L tr , H +B, where L PS and L tr , H representsthe peak luminosity of the soft state and the H-S transition luminosity, respectively. Weobtained A=1.06 ± ± PS of 0.18 ± . × − . If we fit the data with a model of the same form as above, we obtainedA=0.93 ± ± PS of 0.170 ± . × − . We obtained A=1.06 ± ± PS of 0.099 ± . × − .This suggests that the correlation between the luminosity of the H-S transition and the peakluminosity of the following soft state holds in X-ray binaries. It is worth noting that theH-S transition luminosity spans by about two orders of magnitude. As shown in the plot,the luminosity corresponding to the H-S transition in the 15–50 keV range is (0.13–8.0)%Eddington luminosity. This corresponds to an X-ray luminosity (1–200 keV) of (0.4–25)%assuming the source has a power-law spectrum with a photon index of 2 up to 200 keV whenthe H-S transition occurs. If the energy spectrum is a power-law spectrum with a cut-off at30 keV, as sometimes seen just before a H-S transition, the X-ray luminosity in 1–200 keVwould be 1/7 lower. This suggests that possible deviation from a single power-law spectrumfor the hard state would not affect our luminosity estimates significantly.The correlation is found consistent with those determined previously in the outburstsof single sources Aql X-1, GX 339-4, and XTE J1550-564 (Yu, van der Klis & Fender 2004;Yu & Dolence 2007; Yu et al. 2007). We took those fluxes measured with the RXTE ASMand HEXTE reported in these papers, converted them into Eddington units, and plottedthose data in Figure 23 and 24 for the three sources (connected with a solid line for eachsource). The distance of XTE J1550-564 was taken as 5.3 kpc and the mass of the blackhole was taken as 9.68 – 11.58 M ⊙ (Orosz et al. 2002). The distance of Aql X-1 was takenas 5 kpc, as suggested by Rutledge et al. (2001), and the mass was taken as 1.4 solar massesbecause the compact star is a neutron star. For GX 339-4 we used 5.6 kpc as its distanceand a mass of 5.8 solar masses, which correspond to the lower limits. As shown in Figure22, 23 and 24, the data measured in single sources with RXTE ASM and HEXTE follow thecorrelation track measured in this study very well.It is valuable to see where the H-S transition locates in these plots for the well-knownblack hole candidate Cygnus X-1, in which transitions are known to occur at similar luminos-ity levels (Zhang et al. 1997; Zdziarski et al. 2004). We estimated the X-ray flux of the 1996H-S transition and the peak flux of the following soft state using the ASM and the BATSEfluxes. The ASM count rate of the soft state peak after the H-S transition was about 100counts/s, approximately 1.3 Crab, while the 20 −
50 keV flux estimated from BATSE corre- 10 –sponding to the start of the transition was about 1 crab (Zhang et al. 1997). The mass ofthe black hole in Cyg X-1 is about 10.1 M ⊙ and the distance is 2.1 kpc (Massey et al. 1995).Based on these parameters, we found the transition luminosity of Cyg X-1 locates at the lowend of the transition luminosity range (see Fig. 24). The results suggest that Cyg X-1 hasalmost the lowest transition luminosity in the Galactic X-ray binaries.Based on the data shown in Fig. 24, a comparison of the correlations in the neutronstar systems and in the black hole systems can be made. GRO J1655-40 lies away frommost of the data of the correlation track. This might be because of its unusual outburstprofile or inclination angle, which does not allow consistent estimates of the fluxes. Wetook it as an outliner. We fit the data of the black hole systems including Cyg X-1, GRS1915+105, GX 339-4 and XTE J1550-564, including results from previous studies. We ob-tained A=1.04 ± ± PS of 0.28 ± ± ± PS of 0.092 ± In order to study the well-known hysteresis effect of spectral state transitions, wesearched for the S-H transitions in those outbursts or low amplitude flares in which a H-Stransition was identified.Similar to the study of the H-S transitions, we have measured the 15–50 keV fluxcorresponding to the hard state immediately after the S-H transition. The advantage ofselecting the hard state to measure transition luminosity is that we can compare the H-Stransition flux and the S-H transition flux in the same energy range and in the same spectralstate, which avoid highly uncertain bolometric corrections in the soft X-ray band for the softstate when the transition starts. The disadvantage is that we measure the hard state fluxafter the S-H transition has occurred. This is not the flux at which a source started a S-Htransition, but the flux at which a source finished a S-H transition. If the S-H transitionoccurs during a luminosity decline, which is likely true in general, the measured flux shouldbe significantly lower than the actual transition flux.We have converted the fluxes into luminosities in Eddington units and compared thetransition luminosities between the S-H and the H-S transitions of the same outbursts orflares. We confirmed the hysteresis effect of state transitions that the S-H transition lumi- 11 –nosity is generally lower than the H-S transition luminosity. This is shown in Figure 25. The15–50 keV luminosity of the S-H transition is (0.2–2.0)% Eddington luminosity, correspond-ing to an X-ray luminosity in 1–200 keV of about (0.6–6.0)% Eddington luminosity.The luminosity of the S-H transition does not show a strong correlation with the pre-ceding outburst peak flux. The corresponding Spearman correlation coefficient is 0.50, witha chance possibility of only 0.01, implying that there is low level positive correlation be-tween the two but not significant. Examination of the data suggests that the correlation arelargely contributed from 4U 1705-44, 4U 0614+091, and HETE J1900.1-2455. These datacorrespond to the upper and the lower luminosity ends of the date set, respectively. We alsonoticed that the uncertainties in our estimates of source distances and compact star massesshould bring a scatter of source luminosities by a factor of 2 or so (e.g., if source distanceestimate is uncertain by a factor of 1.4 or neutron star mass is 2.2 solar masses instead of 1.4solar masses), which would contribute to a weak positive correlation in the plot. Thereforeit is unlikely that there is a universal correlation between the S-H transition luminosity andthe outburst peak luminosity among the sources from our analysis, but a correlation in singlesources can not be ruled out (4U 1636-53, Homan 2007, private communication). It is worthnoting that the S-H transition luminosity we defined is not the actual luminosity when thetransition starts but the luminosity when the transition ends.
We know that for outbursts or flares of similar rise time scales, outburst peak luminosityand the dL / dt correlates. For outbursts or X-ray flares of different rise times, outburst peakluminosity would not correlate with the dL / dt very well. Therefore, a study of the rate ofincrease in the X-ray luminosity vs. the H-S transition luminosity relation, as compared withthe peak luminosity vs. the transition luminosity relation, would tell us which correlation isthe primary correlation. In Figure 26, we plot the relation between the dL / dt and the H-Stransition luminosity for the black hole and neutron star X-ray binaries as measured withthe ASM and the BAT. We found a strong correlation between the two. For sources with es-timates of distance uncertainties, We obtained Spearman correlation coefficients of 0.72 and0.70, and chance possibilities of 2 . × − and 7 . × − , for the ASM and the BAT mea-surements, respectively. We fit the data with a model of the form log dL / dt = A log L tr , H +B,where dL / dt represents the rate-of-increase of the X-ray luminosity in the ASM or BAT. Weobtained A=1.15 ± ± ± / dt forthe ASM and A=0.81 ± ± ± / dt and the peak luminosity of the following softstate is shown. Excluding sources without an uncertainty in the distance estimate, we foundthe Spearman correlation coefficients are 0.86 and 0.65, with chance possibilities of 1 . × − and 1 . × − , for the ASM and the BAT measurements, respectively. We fit the data witha model of the form log dL / dt = A log L PH +B. We obtained A=1.18 ± ± . ± .
001 in log dL / dt for the ASM and A=0.67 ± ± . ± .
002 for the BAT.We can not address whether it is the dL / dt or the outburst peak luminosity that pri-marily drives the correlations from the data set. However, the observations of the 2007outburst in GX 339-4 might provide an evidence that the transition luminosity and the peakluminosity of the soft state have a weaker correlation than that between the transition lu-minosity and the rate-of-increase of the luminosity. During the 2007 outburst, the sourcereached a soft X-ray peak luminosity comparable to that of the 2002-2003 outburst as seenwith the ASM, but its hard X-ray peak, as seen with the BAT, reached only half of thepeak flux of the 2002-2003 outburst. The empirical relation would predict a peak luminosityof the outburst in the ASM to be half of the observed. This suggests that the outburstpeak luminosity of the 2007 outburst deviated from the relation formed by the other threeoutbursts (Yu et al. 2007) by a factor of 2. The reason might be that the 2007 outburst hasa significantly shorter rise time, which can be seen in the ASM light curve.
4. Conclusion and Discussion
We have performed a systematic study of the state transitions in the brightest persistentand transient X-ray binaries observed with the RXTE/ASM and the Swift/BAT during aperiod of three years. We have found that the 15–50 keV luminosity corresponding to theH-S transition is positively correlated with the peak 2–12 keV luminosity of the followingsoft state and the rate-of-increase of the X-ray luminosity in a luminosity range spanningby two orders of magnitude (Figure 24 and 26). This does not only confirm the correlationpreviously found in single sources but also reveal that there is no clear cut in the statetransitions between persistent sources and transient sources, suggesting that the observedlarge luminosity span of the H-S transition is caused by non-stationary accretion of differentscales, rather than the detailed mechanism of transient outburst and flare (e.g., inside-outor outside-in outbursts). This suggests that the additional parameter other than the massaccretion rate which determines spectral state transitions would relate to non-stationaryaccretion parameters, such as the d ˙M / dt or the initial condition such as the mass in the disk 13 –(Yu, van der Klis & Fender 2004; Yu et al. 2007). On the other hand, both correlationsshow no luminosity saturation, suggesting that we have not observed the brightest hardstate nor the brightest soft state which are permitted by physics. In other words, brighterhard states would be observed during brighter outbursts in the Galactic X-ray binaries. Suchbright hard states and outbursts in stellar mass black holes may have already been observedin ultra-luminous X-ray sources (ULXs) in nearby galaxies.We also found that the luminosity corresponding to the end of the S-H transition doesnot show significant correlation with the peak luminosity of the preceding soft state ingeneral. The transition flux as we defined is in general a few times lower than that of theH-S transition, but spans by more than one order of magnitude. This is larger than thefactor of 4 difference estimated by Maccarone (2003), but uncertainties on the masses anddistances and a narrower band used may account for the differences. The correlation between the luminosity of the H-S transition and the dL / dt tells us thatwhen there is little rate-of-increase of the X-ray luminosity, indicating little d ˙M / dt on thetransition time scale, the transition luminosity of the H-S is the lowest. This is consistentwith the low and constant transition luminosity seen in Cyg X-1 (Figure 24). Cyg X-1 staysat a rather constant flux level and shows similar transition luminosities (Zhang et al. 1997;Zdziarski et al. 2002; Wilms et al. 2006). This can be understood as that Cyg X-1 has verylittle d ˙M / dt on the time scale of spectral state transitions. The implication of the correlationshown in Fig. 24 is that the difference in the H-S transition luminosity between the persistentsources and the transient sources lies in the difference in the d ˙M / dt. Persistent sources tendto have lower d ˙M / dt in the hard state and therefore lower H-S transition luminosities; whilethe transient sources tend to have higher d ˙M / dt during outbursts. We speculate that thetransition luminosity of the S-H transition is also affected by the rate-of-decrease of the massaccretion rate, as one could imagine that the faster a fading thermal disk disappears, theearlier the source enters the hard state, leading to the hard state to occur at a relativelyhigher luminosity. Whether the S-H transition luminosity is influenced by non-stationaryaccretion is worth further investigations.The tight correlation between the transition luminosity and the dL / dt suggests thatthere are two main parameters that determine the luminosity at which the spectral statetransition occurs. One is the mass accretion rate, as generally suggested. The transitionis determined by the mass accretion rate when there is little rate-of-increase of luminosity.The mass accretion rate sets the reference luminosity of the H-S transition corresponding 14 –to zero rate-of-change of the mass accretion rate. The other is the rate-of-increase in themass accretion rate (note: whether there is strong effect of the rate-of-decrease of the massaccretion rate in the hard state is expected but not known yet, see Smith et al. 2007). InFigure 26, the slope between the transition luminosity and the dL / dt is determined. Whenthe dL / dt is known, the range of the transition luminosity can be predicted.What causes sources in the hard states to reach higher luminosities than expected ? Theanswer is non-stationary accretion. This is set up by the initial condition at the beginningof an outburst or flare. The peak flux vs. waiting time relation found in GX 339-4 suggeststhat the hard X-ray peak luminosity is proportional to the mass stored in the disk (note: inGX 339-4 the mass stored in the disk during quiescence is approximately entirely accretedduring the following outburst, see Yu et al. 2007). The correlations between the transitionluminosity and the peak luminosity of the following soft state or the dL / dt (Figure 24 and 26)indicate that the hard X-ray peak luminosity is positively correlated to the peak luminosityof an outburst or flare and the rate-of-increase of the X-ray luminosity. This links the rateof increase of the mass accretion rate to the mass stored in the disk before an outburst orflare occurs. How this link establishes is not clear.The results remind us that static accretion models are not good approximations ofthe accretion flow on the time scales when the variation of the mass accretion rate ∆ ˙ M is comparable to the mass accretion rate ˙ M itself. The stationary condition was not metduring most of the spectral state transitions during the rising phases of the outbursts orflares we studied. A complete state transition from the hard state to the soft state usuallytakes about a few days to a few weeks. As shown in Figure 26 and 27, the slope of thetrend is ∼
1, indicating that the daily increase of the X-ray luminosity during the risingphase of an outburst or flare is about 1/3 of the total luminosity itself. This indicates thatduring the rising phase of an outburst or flare, the mass accretion rate increases rapidly, andthe variation of the mass accretion rate can not be treated as a small perturbation. Thissuggests that using static accretion solutions to interpret these spectral state transitions,as those models under the assumption of stationary accretion (for example, Esin et al.1997; Meyer-Hofmeister et al. 2004;Liu et al. 2005), is questionable. The importance oftime-dependent approaches is also supported by some other observations of spectral statetransitions (Smith et al. 2002, 2007).
Because of the hysteresis effect of state transitions (Miyamoto et al. 1995; Nowak 1995;Maccarone & Coppi 2003; Gladstone et al. 2007), the brightest hard state is usually reached 15 –during the rising phase of an outburst in transient X-ray binaries (Bouchacourt et al. 1984;Brocksopp et al. 2001; Yu et al. 2003). In our systematic study of the H-S transition in thebright X-ray binaries, the correlations do not show a flux saturation or cut-off at either endof the X-ray luminosity range, as shown in Figure 24 and 26, suggesting that the maximumluminosity that is permitted in the hard state has not been observed in the Galactic X-raybinaries.In the Galactic X-ray binaries we studied, the maximum transition luminosity in the15–50 keV range is about 7–8% L E (assume Cyg X-3 is not a neutron star system). Thiscorresponds to about ∼
25% Eddington luminosity in the energy range 1–200 keV assuminga power-law spectrum with photon index 1.8–2.0. If we consider that the hard X-ray peakflux of the 2002-2003 outburst of the black hole transient GX 339-4 is about twice of that ofthe 2006 outburst, the maximum H-S transition luminosity observed in the Galactic X-raytransients in the past decade is around 30% (see also Zdziarski et al. 2004).How bright a black hole hard state can be ? What does the empirical relations tellus about the brightest hard state ? Based on Figure 24, hard states could reach higherpeak luminosities in Eddington unit during outbursts or flares of higher peak luminosities.Therefore the chance to observe a much brighter hard state in these Galactic sources lies inwhether there would be much brighter outbursts in future.We can roughly estimate the chance for us to observe a source in the hard state atthe Eddington luminosity. In the past ten years or so we likely detected outbursts in theGalactic X-ray binaries on the order of 100 with peak luminosities higher than about 1%L E . One out of these outbursts reaches 30% L E (e.g., the 2002–2003 outburst in GX 339-4).Assuming the distribution of outburst peak luminosity is of the form N (L p )= A L p α , where Ais the normalization and α is the index, the chance for us to detect a hard state at Eddingtonluminosity would be (1 . / . α times the chance for us to see an outburst of 30% L E – whichis one in ten years. If α is close to -1, then we would observe an outburst with the hardstate reaching the L E in about 30 years’ time. If α is close to -1.5, then we would observean outburst with the hard state reaching the L E in about 60 years (see Grimm et al. 2002for Galactic X-ray binary luminosity function). Similar estimate would apply to galaxiessimilar to our own. If α is in the range -1 – -1.5, we would observed an X-ray binary in thehard state at the Eddington luminosity in about 3–6 galaxies during a period of ten years.This would account for some of the ultra-luminous X-ray sources (ULXs) seen in brighthard states in nearby galaxies. We found that the outburst sample in our current study isnot enough for a determination of the distribution of the outburst peak luminosity. Futurestatistical studies of transient outbursts would determine the distribution and give a certain,quantitative answer. 16 –Based on the empirical relations, the outbursts or flares during which a much brighterhard state can be seen are those having a larger rate-of-increase of the luminosity than whathave been seen in these Galactic sources. To have a larger rate-of-increase of the luminosity,an outburst or flare should either reach higher peak luminosity within a similar rise timeas the outbursts seen in the Galactic transients, or reach similar peak luminosity within ashorter rise time. Specific prediction about the interesting source GX 339-4 can be made.Based on the empirical relation between the peak flux of the hard state and the outburstwaiting time (Yu et al. 2007), GX 339-4 will reach the Eddington luminosity in the hard stateduring a future outburst after being inactive for ten years. It worth noting that the peakflux vs. waiting time relation reported in Yu et al. (2007) was based on BATSE monitoringobservations. Source activities below about 0.1 Crab did not obviously affect the empiricalrelation. Therefore if GX 339-4 stays inactive (below 0.1 Crab) for more than 10 years,the peak flux of the hard state in the next outburst would reach beyond the Eddingtonluminosity.Have super-Eddington outbursts with similar rise or decay time scales as those of theGalactic transients been observed in sources in nearby galaxies ? The answer is yes. Wehave performed a study of the bright outbursts of the Galactic X-ray binaries seen withthe RXTE/ASM and found that the shortest e-folding rise time scale in each outburst ison average about 2 days. There is evidence that the shortest characteristic rise or decaytimescales during the X-ray flares of some ULXs are comparable. One of the best examplesis seen in NGC 1365 X-1, which declined in luminosity with an e-folding time scale of about3 days during a series Chandra/ACIS snapshots (Soria et al. 2007). Another example is asupersoft source in M 101, which showed an outburst to the soft state with an e-folding timescale around 1–2 days (Kong et al. 2004). Yet another example is a ULX in M82: a fewX-ray flares were seen emerging from a 62-day flux modulation (Kaaret et al. 2006). Wehave investigated the RXTE/PCA light curve and found that the e-folding rise and decaytimescales being about 2 − / dt instellar-mass black hole or neutron star X-ray binaries. Our study provides an additionalevidence that some of the ULXs contain stellar mass compact stars. A number of hard state outbursts have been observed in X-ray transients, such asXTE J1550-564, XTE J1118-480, IGR J17497-281, SWIFT J1753.5-0127, and Aql X-1 17 –(Belloni et al. 2002; Brocksopp et al. 2004; Rodriguez et al. 2006, 2007; Ramadevi & Seetha2007). In the framework that mass accretion rate determines spectral state transitions, thesehard state outbursts can only be explained as that the mass accretion rate threshold is notreached. Then brighter outbursts with the hard state exceeding the threshold, roughly of1-2% L E in 1–200 keV corresponding to the transition luminosity of Cyg X-1 (see Fig. 24),can not be explained.The correlations shown in Fig. 24 and Fig. 26 provide an explanation of bright hardstate outburst. In the plot of Fig. 26, the data defines a band of the transition regime (with ahalf width as the intrinsic scatter) in the transition luminosity of the hard state vs. the rate-of-increase of the luminosity relation. Two theoretical possibilities therefore can be inferredfor when the state transitions do not occur. One is that these sources stay in the lower-rightregime below the transition regime and have had lower rate-of-increase of the luminosity inthe recent past in relative to their peak luminosities of the hard states. Combined with thecorrelation shown in Fig. 24, the occurrence of hard state outburst is because of low dL / dt inthe recent past which does not permit the source to reach a soft state of which the luminosityshould follow the relation defined in Fig. 24, i.e., soft state of lower luminosity can not exist.The other possibility is that the sources stay in the upper-left regime in Fig. 26 and havelower peak luminosity of the hard state in relative to the rate-of-increase of the luminosity,suggesting that the hard state outbursts are due to lower peak luminosities in relative tothe dL / dt. This indicates a potentially existing, but special regime of the hard state underviolent conditions of the accretion flow, which may account for not only bright hard state inGalactic binaries but also those seen in ULXs. Combined with the correlation in Fig. 24, theoccurrence of hard state outburst is because the source has a low luminosity in relative tothe dL / dt. Such hard states can sustain for some time but not forever since otherwise thiswould lead to an infinite luminosity. Therefore thermal disk with a luminosity higher thanthe value predicted in the relation in Fig. 24 can not develop. Whether this case is relatedto the occurrence of very high state or intermediate state in black hole systems is unclear,but clearly deserves further studies.Two hard state outbursts around MJD 53926 and 54618 (outside the time range of ouranalysis) in 4U 1608-52 can be seen in the ASM and BAT light curves. We can determine thepeak flux of the hard state and the maximum rate-of-increase of the fluxes since the sourcesreached half of their peak fluxes for the two outbursts. The maximum rate-of-increase of theX-ray flux as seen in the ASM and BAT during these hard state outbursts is statisticallylower by a factor of 4 compared with the outbursts during which the H-S transition occursaround MJD 54270 and 54400, but comparable to that occurred around MJD 53650. Thisseems to suggest that our approach with maximum rate-of-increase of the X-ray flux is toosimple to reveal the nature of hard state outburst. 18 –
5. Summary
We have studied spectral state transitions in the brightest persistent and transientGalactic X-ray binaries seen with the X-ray monitoring observations of the RXTE/ASM andthe Swift/BAT. We have confirmed that the luminosity of the H-S transition is correlatedwith the peak luminosity of the following soft state, and found that the correlation holds forboth persistent sources and transient sources in a luminosity range spanning by two orders ofmagnitude. We have also found the rate-of-increase of the luminosity is correlated with thetransition luminosity or the peak luminosity of the following soft state. The results implythat state transitions occur in a large range of mass accretion rates and the majority ofthe H-S transitions observed are strongly influenced by non-stationary accretion. The mainresults can be summarized as follows: • Both correlations do not show high luminosity saturation or low luminosity cut-off,suggesting that we have not observed the brightest hard state nor the dimmest softstate in the Galactic black hole or neutron star soft X-ray binaries. An outburstreaching the Eddington luminosity in the hard state would be observed in GX 339-4 ifthe source stays below ∼ • The correlations suggest that brighter hard state could be reached during the risingphase of a brighter outburst with similar rise time or similarly bright outburst withshorter rise time in stellar-mass black hole or neutron star transients. Several ULXsshowing short-duration hard flares therefore likely harbor stellar-mass compact stars. • The two correlations are dependent. The correlation between the rate-of-increase ofX-ray luminosity and the H-S transition luminosity could introduce the correlationbetween the peak luminosity of the following soft state and the transition luminosityif the rise time scales are similar among outbursts or flares in single sources and acrosssources. • The luminosity of the H-S transition is shown to correlate with the rate-of-increaseof the luminosity, suggesting that it is non-stationary accretion, characterized by therate-of-increase of the mass accretion rate, determines the variation of the transitionluminosity. Combined with the results obtained from GX 339-4 (Yu et al. 2007), therate-of-increase of the mass accretion rate is nearly proportional to the mass in theaccretion disk involved in an outburst or flare. Cygnus X-1 is at the low luminosity endin the correlation tracks, consistent with previous suggestions that its mass accretionrate is in a narrow range which leads to low rate-of-increase of the mass accretion rate. 19 –The schematic picture concerning the allowed regimes of the luminosities of the H-Stransition and the hard state is shown in Fig. 28. The light curves of two assumed outburstsof the same source are shown. The solid curve represents the X-ray light curve of a brighteroutburst while the dashed line represents that of a weaker one. The allowed regimes for thehard state (gray) or the soft state (white) are shown based on our results. The maximumluminosity permitted in either the hard state or the soft state is yet unknown. The popularpicture based on the idea that the mass accretion rate determines spectral state predicts thatthe H-S and the S-H transitions occur at a constant luminosity L , below which a sourcestays in the hard state. An additional hard state regime is on the rising phase of an outburstor flare in X-ray binaries based on the empirical correlations. The schematic picture showsthat much brighter hard state can be reached during bright, short outbursts in stellar-massblack hole and neutron star binaries in our Galaxy. We infer that Galactic binaries mayturn into ULXs during shorter, brighter outbursts. The picture also suggests that hysteresiseffect of state transitions is mainly caused by the H-S transition strongly influenced by non-stationary accretion characterized by the rate-of-increase of the mass accretion rate, of whichthe initial condition may be described by the mass in the accretion disk.We would like to thank the RXTE and the Swift Guest Observer Facilities at NASAGoddard Space Flight Center for providing the RXTE/ASM products and the Swift/BATtransient monitoring results. We thank the anonymous referee for useful comments andsuggestions. WY would also like to thank Roberto Soria of University College London andAlbert Kong of National Tsing Hua University for sharing their studies on ultra-luminous X-ray sources, D. M. Smith of University of California at San Diego for sharing his work beforepublication, and Thomas Maccarone of University of Southampton and Diego Altamiranoof University of Amsterdam for comments and careful reading of the manuscript. WYappreciate useful discussions with Chris Done, Robert Fender, Tomaso Belloni, Jean Swank,Ron Remillard, John Tomsick, Joern Wilms, and Mike Nowak. This work was supported inpart by the National Natural Science Foundation of China (10773023, 10833002), the OneHundred Talents project of the Chinese Academy of Sciences, the Shanghai Pujiang Program(08PJ14111), the National Basic Research Program of China (973 project 2009CB824800),and the starting funds at the Shanghai Astronomical Observatory. The study has made useof data obtained through the High Energy Astrophysics Science Archive Research CenterOnline Service, provided by the NASA/Goddard Space Flight Center. 20 – REFERENCES
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This preprint was prepared with the AAS L A TEX macros v5.2.
24 –Fig. 1.— The distribution of the BAT/ASM hardness ratio on time scale two days for thebright neutron star LMXBs and black hole binaries in which spectral state transitions weredetected. 4U 1608-52 and GX 339-4 are the best examples showing distinct spectral statesfor neutron stars and black holes, respectively. Data of GRS 1915+105 were not includedin the statistics of black hole binaries. The hardness thresholds for the soft states and thehard states which were used in our analysis are marked as dotted-lines and dashed-lines,respectively. 25 –Fig. 2.— X-ray monitoring observations of 1A 1742-294 in 2–12 keV with the ASM and15–50 keV with the BAT. 26 –Fig. 3.— X-ray monitoring observations of 2S 0918-549 in 2–12 keV with the ASM and15–50 keV with the BAT. 27 –Fig. 4.— X-ray monitoring observations of 4U 0614+091 in 2–12 keV with the ASM and15–50 keV with the BAT. 28 –Fig. 5.— X-ray monitoring observations of 4U 1323-62 in 2–12 keV with the ASM and 15–50keV with the BAT. 29 –Fig. 6.— X-ray monitoring observations of 4U 1608-52 in 2–12 keV with the ASM and 15–50keV with the BAT. 30 –Fig. 7.— X-ray monitoring observations of 4U 1636-53 in 2–12 keV with the ASM and 15–50keV with the BAT. 31 –Fig. 8.— X-ray monitoring observations of 4U 1702-429 in 2–12 keV with the ASM and15–50 keV with the BAT. 32 –Fig. 9.— X-ray monitoring observations of 4U 1705-44 in 2–12 keV with the ASM and 15–50keV with the BAT. 33 –Fig. 10.— X-ray monitoring observations of 4U 1728-34 in 2–12 keV with the ASM and15–50 keV with the BAT. 34 –Fig. 11.— X-ray monitoring observations of 4U 1820-30 in 2–12 keV with the ASM and15–50 keV with the BAT. 35 –Fig. 12.— X-ray monitoring observations of EXO 0748-676 in 2–12 keV with the ASM and15–50 keV with the BAT. 36 –Fig. 13.— X-ray monitoring observations of GRS 1724-308 in 2–12 keV with the ASM and15–50 keV with the BAT. 37 –Fig. 14.— X-ray monitoring observations of HETE J1900.1-2455 in 2–12 keV with the ASMand 15–50 keV with the BAT. 38 –Fig. 15.— X-ray monitoring observations of SAX J1712.6-3739 in 2–12 keV with the ASMand 15–50 keV with the BAT. 39 –Fig. 16.— X-ray monitoring observations of SAX J1747.0-2853 in 2–12 keV with the ASMand 15–50 keV with the BAT. 40 –Fig. 17.— X-ray monitoring observations of GRO J1655-40 in 2–12 keV with the ASM and15–50 keV with the BAT. 41 –Fig. 18.— X-ray monitoring observations of GRS 1915+105 in 2–12 keV with the ASM and15–50 keV with the BAT. The hardness ratios for the hard state are lower than other blackhole binaries. In order to include the transition from the hard state to the soft state aroundDay 60 as the second transition sample, we lower the hardness ratio threshold for the hardstate to 0.6. 42 –Fig. 19.— X-ray monitoring observations of GX 339-4 in 2–12 keV with the ASM and 15–50keV with the BAT. 43 –Fig. 20.— X-ray monitoring observations of XTE J1856+053 in 2–12 keV with the ASMand 15–50 keV with the BAT. 44 –Fig. 21.— X-ray monitoring observations of Cyg X-3 in 2–12 keV with the ASM and 15–50keV with the BAT. The thresholds for spectral states in black hole systems were used. 45 –Fig. 22.— The observed BAT fluxes when the H-S transitions occurred and the correspondingASM peak fluxes of the following soft states. Data connected with a straight line were takenfrom previous studies of Aql X-1 (Yu & Dolence 2007), GX 339-4 (Yu et al. 2007), and XTEJ1550-564 (Yu, van der Klis & Fender 2004) with pointed observations, respectively. 46 –Fig. 23.— The correlation between the transition luminosity (15–50 keV, ergs/s) and thecorresponding peak luminosity of the following soft state (2–12 keV, ergs/s). The luminositieswere estimated based on the X-ray energy spectrum of the Crab (Kirsth et al. 2005). Dataconnected with a solid line were from previous studies with pointed observations of singlesources, see Fig. 22. 47 –Fig. 24.— The correlation between the transition luminosity (15–50 keV) and the peakluminosity of the following soft state (2–12 keV) in Eddington units. Source distances andmasses used are listed in Table 1. Data point for Cygnus X-1 is based on CGRO/BATSEand RXTE/ASM observations in 1996 (Zhang et al. 1997). Data connected by a solid linewere from previous single source studies, as those in Fig. 22. Notice that 2S 0918-549, CygX-1, GRS 1915+105, 4U1820-30, and 4U 1705-44 are at both ends of the correlation withrather accurate distance estimates, indicating that the luminosity of the H-S transition spansby two orders of magnitude. 48 –Fig. 25.— Comparison between the luminosities of the hard-to-soft and the soft-to-hardtransitions associated with the same outbursts or flares. Filled and unfilled symbols representthose of the hard-to-soft transitions and the soft-to-hard transitions, respectively. 49 –Fig. 26.— The correlation between the luminosity of the hard-to-soft transition and themaximum rate-of-increase of the X-ray luminosity around the hard-to-soft transition. 50 –Fig. 27.— The correlation between the peak luminosity of the soft state and the maximumrate-of-increase of the X-ray luminosity around the hard-to-soft transition. 51 –Fig. 28.— A schematic picture of the regimes of the hard state. Two assumed transient out-bursts of different peak luminosities are shown as solid curve and dashed curve, respectively.When a source is under stationary accretion, spectral transitions between the hard state andthe soft state occurs at a nearly a constant luminosity L , as expected from the frameworkthat the mass accretion rate determines spectral states. When a source is undergoing anoutburst or flare, the hard-to-soft transition occurs at a luminosity above L . The additionalluminosity roughly proportional to ∆ L ∆ T . The soft-to-hard transitions are expected to occuraround L , but effect of non-stationary accretion may exist as well (see e.g., Smith et al.2007). 52 –Table 1. List of the sources with H-S transitions identified and parameters used* Source Distance Mass H2S S2H References(kpc) ( M ⊙ )1A 1742-294 8.0 1.4 3 0 B´elanger et al. (2006)2S 0918-549 4.1-5.4 1.4 3 0 in’t Zand et al. (2005)4U 0614+091 3 1.4 2 1 Brandt et al. (1992)4U 1323-62 10 1.4 3 1 Parmar et al. (1989)4U 1608-52 4.1 ± ± ± +0 . − . ± ± ± ± ± ± ± ± ≥ ≥ ± ∗∗