A global spectral study of black hole X‐ray binaries
ABSTRACT We report on a consistent and comprehensive spectral analysis of the X-ray emission of 25 black hole X-ray binaries. All publicly available observations of the black hole binaries in the RXTE archive were analysed. Three different types of model were fitted to investigate the spectral changes occurring during an outburst. For the population, as well as for each binary and each outburst from each binary, we construct two diagnostic diagrams. The hardness intensity/luminosity diagram (HID/HLD), the X-ray colour against the flux/luminosity of the binary, is most useful when studying a single binary. However, to compare different binary systems, the disc fraction luminosity diagram (DFLD) is more useful. The DFLD uses the luminosities of the disc and power-law components to calculate the ratio of the disc luminosity to the total luminosity, resulting in a more physical value, which is analogous to the X-ray colour calculated for X-ray binaries. The tracks of the outbursts populate the DFLD more evenly than the HLD. We discuss the limitations of both diagnostic diagrams for the study of the X-ray binary outbursts and clearly illustrate how the two diagrams map on to each other for real outburst data. The similarity of the X-ray colour and disc fraction behaviour over time during an outburst originally seen in GX 339−4 data is seen in other sources' outbursts. We extract the peak luminosities in a single outburst, as well as the luminosities at the transitions away from and returning to the power-law-dominated state for each outburst. The distribution of the luminosities at the transition from the power-law to the disc-dominated state peaks at around 0.3LEdd, the same as the peak of the distribution of the peak luminosities in an outburst. Using the disc fraction to calculate the transition luminosities shows that the distributions of the luminosities for the transitions away from and returning to the power-law-dominated state are both broad and appear to overlap. Using the change in disc fraction to calculate the date when a transition occurred is not drastically different from obtaining the dates from changes in the timing behaviour of the X-ray binary. In addition, we calculate the rate of motion of an X-ray binary through the DFLD during an outburst, a diagnostic which has the potential to be used as a comparison with populations of active galactic nuclei. The fastest rate of motion is on the egress and ingress from the power-law-dominated state. A further region of increased speed through the diagram occurs in the disc-dominated state on the return to the power-law-dominated state. Finally, we compare the measured X-ray luminosities with a small number of contemporaneous radio measurements. Overall, this is the most comprehensive and uniform global study of black hole X-ray binaries to date.
- SourceAvailable from: icc.ub.edu[Show abstract] [Hide abstract]
ABSTRACT: We discuss the nature of the X-ray emitting plasma of black hole binaries. It is well known that the temperature and optical depth of the Comptonising electrons of the X-ray corona of black hole binaries can be measured using spectroscopy in the 1 keV-1 MeV energy band. We emphasize recent developments in the modeling of high energy radiation processes which allow us to constrain other important physical parameters of the corona, such as the strength of magnetic field, or the temperature of the ions. The results appear to challenge current accretion models. In particular, standard advection dominated accretion flow do not match the observed properties of bright hard state X-ray binaries such as Cygnus X-1 or GX 339-4. On the other hand, we find that all the data would be consistent with a multi-zone magnetically dominated hot accretion flow model. We also emphasize that besides the usual spectral state transitions observed at luminosities above a few percent of Eddington, there is observational evidence for at least two additional, more subtle, radiative transitions occuring at lower luminosities.International Journal of Modern Physics Conference Series. 01/2010;
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ABSTRACT: The relatively rapid spatial and temporal variability of the X-ray radiation from some molecular clouds near the Galactic center shows that this emission component is due to the reflection of X-rays generated by a source that was luminous in the past, most likely the central supermassive black hole, Sagittarius A*. Studying the evolution of the molecular cloud reflection features is therefore a key element to reconstruct Sgr A*'s past activity. The aim of the present work is to study this emission on small angular scales in order to characterize the source outburst on short time scales. We use Chandra high-resolution data collected from 1999 to 2011 to study the most rapid variations detected so far, those of clouds between 5' and 20' from Sgr A* towards positive longitudes. Our systematic spectral-imaging analysis of the reflection emission, notably of the Fe Kalpha line at 6.4 keV and its associated 4-8 keV continuum, allows us to characterize the variations down to 15" angular scale and 1-year time scale. We reveal for the first time abrupt variations of few years only and in particular a short peaked emission, with a factor of 10 increase followed by a comparable decrease, that propagates along the dense filaments of the Bridge cloud. This 2-year peaked feature contrasts with the slower 10-year linear variations we reveal in all the other molecular structures of the region. Based on column density constraints, we argue that these two different behaviors are unlikely to be due to the same illuminating event. The variations are likely due to a highly variable active phase of Sgr A* sometime within the past few hundred years, characterized by at least two luminous outbursts of a few-year time scale and during which the Sgr A* luminosity went up to at least 10^39 erg/s.Astronomy and Astrophysics 07/2013; · 4.48 Impact Factor
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ABSTRACT: The Galactic black hole candidate H~1743-322 exhibited two X-ray outbursts in rapid succession: one in August 2010 and the other in April 2011. We analyze archival data of this object from the PCA instrument on board RXTE (2-25 keV energy band) to study the evolution of its temporal and spectral characteristics during both the outbursts, and hence to understand the behavioral change of the accretion flow dynamics associated with the evolution of the various X-ray features. We study the evolution of QPO frequencies during the rising and the declining phases of both the outbursts. We successfully fit the variation of QPO frequency using the Propagating Oscillatory Shock (POS) model in each of the outbursts and obtain the accretion flow parameters such as the instantaneous shock locations, the shock velocity and the shock strength. Based on the degree of importance of the thermal (disk black body) and the non-thermal (power-law) components of the spectral fit and properties of the QPO (if present), the entire profiles of the 2010 and 2011 outbursts are subdivided into four different spectral states: hard, hard-intermediate, soft-intermediate and soft. We attempt to explain the nature of the outburst profile (i.e., hardness-intensity diagram) with two different types of mass accretion flow.Advances in Space Research 09/2013; 52(12). · 1.24 Impact Factor
arXiv:0912.0142v1 [astro-ph.HE] 1 Dec 2009
Mon. Not. R. Astron. Soc. 000, 000–000 (0000)Printed 1 December 2009(MN LATEX style file v2.2)
A Global Spectral Study of Black Hole X-ray Binaries
R. J. H. Dunn1,2⋆†, R. P. Fender2, E. G. K¨ ording2,3, T. Belloni4and
1Excellence Cluster Universe, Technische Universit¨ at M¨ unchen, Garching, 85748, Germany
2School of Physics and Astronomy, Southampton, University of Southampton, SO17 1BJ, UK,
3AIM - Unit´ e Mixte de Recherche CEA - CNRS - Universit´ e Paris VII - UMR 7158, CEA-Saclay, Service d’Astrophysique, F-91191
Gif-sur-Yvette Cedex, France
4INAF-Osservatorio Astronomico di Brera, Via E. Bianchi 46, I-23807 Merate (LC), Italy
1 December 2009
We report on a consistent and comprehensive spectral analysis of the X-ray emission of 25
Black Hole X-ray Binaries. All publicly available observations of the black hole binaries in
the RXTE archive were analysed. Three different types of model were fitted to investigate
the spectral changes occurring during an outburst. For the population, as well as each binary
and each outburst from each binary, we construct two diagnostic diagrams. The Hardness In-
tensity/Luminosity Diagram (HID/HLD), the X-ray colour against the flux/luminosity of the
binary is most useful when studying a single binary. However, to compare between different
binary systems, the Disc Fraction Luminosity diagram (DFLD) is more useful. The DFLD
uses the luminosities of the disc and powerlaw components to calculate the ratio of the disc
luminosity to the total luminosity, resulting in a more physical value, which is analogous
to the X-ray colour calculated for X-ray binaries. The tracks of the outbursts populate the
DFLD more evenly that the HLD. We discuss the limitations of both diagnostic diagrams for
the study of the X-ray binary outbursts, and we clearly illustrate how the two diagrams map
ontoeach otherfor real outburstdata. The similarity of the X-ray colourand Disc Fraction be-
haviourovertime duringan outburstoriginallyseen in GX 339-4datais seen in othersources’
outbursts. We extract the peak luminosities in a single outburst, as well as the luminosities at
the transitions away from- and returning to the powerlaw dominated state for each outburst.
The distribution of the luminosities at the transition from the powerlaw to the disc dominated
state peaks at around 0.3LEdd, the same as the peak of the distribution of the peak luminosi-
ties in an outburst. Using the disc fraction to calculate the transition luminosities shows that
the distributions of the luminosities for the transitions away from- and return to the power-
law dominated state are both broad and appear to overlap. Using the change in Disc Fraction
to calculate the date a transition occurred is not drastically different from the dates obtained
from changes in the timing behaviour of the X-ray binary. In addition, we calculate the rate of
motion of an X-ray binary through the DFLD during an outburst, a diagnostic which has the
potentialto be used as a comparisonwith populationsof active galacticnuclei.The fastest rate
of motion is on the egress and ingress from the powerlaw dominated state. A further region
of increased speed through the diagram occurs in the disc dominated state on the return to the
powerlaw dominated state. Finally we compare the measured X-ray luminosities with a small
numberof contemporaneousradio measurements.Overall this is the most comprehensiveand
uniform global study of black hole X-ray binaries to date.
Key words: accretion, accretion discs - binaries: general - ISM: jets and outflows - X-rays:
† Alexander von Humboldt Fellow
Galactic X-ray binaries (XRBs) are the sites of some of the most
energetic and exotic phenomena in the local universe, and may pro-
vide us with insights into the action of supermassive black holes
in active galactic nuclei. Their energetic influence on their sur-
c ? 0000 RAS
Dunn, Fender, K¨ ording, Belloni & Cabanac
roundings and the galaxy as a whole are only just becoming clear
(Gallo et al. 2004; Heinz et al. 2008).
Many black hole X-ray binaries (BHXRBs) spend most
of their time in a quiescent state where both the X-ray (as-
sumed to arise in the accretion flow) and radio (assumed to
arise in a jet-like outflow) emission are at a very low level.
Most binaries are discovered when they go through an outburst
phase. As described in detail in Fender et al. (2004) but see
also Nowak (1995); Done & Gierli´ nski (2003); Homan & Belloni
(2005); Remillard & McClintock (2006); Done et al. (2007);
Belloni (2009), the outburst starts in the “low-hard” state. The state
is described as “low-hard” because the BHXRB is faint and the
X-ray emission is characterised by a hard powerlaw of Γ ∼ 1.5.
The term is commonly used to indicate the time during which
the X-ray spectrum is hard, regardless of the BHXRBs bright-
ness. The radio emission in the low-hard state is characteristic of
a steady jet emitting synchrotron radiation. During the early rise
of the outburst, the X-ray and radio luminosities both increase,
but the X-ray colour of the spectrum remains hard (Corbel et al.
2000, 2003). As the outburst progresses the thermal emission from
the accretion disc rapidly becomes more prominent, until it dom-
inates the X-ray emission. This softening of the X-ray spectrum
takes place quickly compared to the rise up from quiescence. The
statewhen thedisc dominates thespectrum iscalled the“high-soft”
state. There are two intermediate states between the low-hard and
high-soft states (hard-intermediate and soft-intermediate). Not all
BHXRBs have been observed to go through both these states dur-
ing their outbursts. Some BHXRBs are not observed to do a transi-
tion and remain in the low-hard state until they return to quiescence
(Brocksopp et al. 2004; Capitanio et al. 2009).
The short timescale variability characteristics of the X-
ray emission from the BHXRBs also change during the out-
bursts. The level of the root-mean-square (rms) noise and the ap-
pearance and frequency of quasi-periodical oscillations (QPOs)
are useful for denoting a more accurate date of transition be-
tween states (see e.g. Homan & Belloni 2005; van der Klis 2006;
Remillard & McClintock 2006; Belloni 2009). The change in spec-
tral information between twoneighbouring statescan sometimes be
very slight, with no clear distinction between the two.
During the transition to the high-soft state the radio emission
has been observed to flare in some BHXRBs (Fender et al. 2004,
2009). Even if the flare is unobserved (be this the consequence
of no suitable radio observations, or no radio detection during the
transition), the radio emission is quenched on the transition to the
high-soft state Fender et al. (1999). The disc gradually fades in the
soft state and the non-thermal emission recovers. The source then
undergoes the return transition to the low-hard state at a lower lu-
minosity than the transition from the hard to the high-soft state.
During this period the radio emission is observed to recover. The
brightness of the BHXRB continues to decrease as it returns to qui-
escence. See Fender et al. (2009) for a detailed study of the radio
emission during BHXRB outbursts and Corbel et al. (2000, 2003)
for the details of the radio-X-ray correlation in the hard state.
Over the past few years the importance of BHXRBs for the
evolution of the galaxy has become apparent. The discovery of
a jet blown bubble from Cyg X-1 (Gallo et al. 2004) allowed
the estimation of the kinetic energy injection into the inter-stellar
medium (Heinz & Grimm 2005; Heinz et al. 2008). Searches have
been done for other jet-blown bubbles, so far with out clear suc-
cess (Russell et al. 2006). However, it is reasonable to assume that
when exhibiting a steady radio jet, all BHXRBsinject (mechanical)
energy into their surroundings. This would have significant effect
on the evolution of the galaxy. The radiative emission from X-ray
binaries, of all types, usually dominates the X-ray emission from
non-active galaxies. The level of this X-ray binary emission has
been used as a proxy for the star formation rate of the galaxy (e.g.
Grimm et al. 2003) as well as the stellar mass (e.g. Gilfanov 2004).
The global properties of BHXRBs are also useful in fully under-
standing the links between black holes on all mass scales; in par-
ticular studying the coupling between accretion and feedback (both
radiative and kinetic), can help us to understand the broader picture
of how black holes affect their surroundings (see e.g Merloni et al.
2003, 2005; K¨ ording et al. 2006, 2008; Merloni & Heinz 2008).
For recent reviews on BHXRBs see Belloni (2009); Gilfanov
(2009); Markoff (2009); Fender (2009); Gallo (2009).
Therefore the understanding of theprocesses which occur dur-
ing thelifeof aBHXRB are important ina wider context. As thera-
dio power, and perhaps the energy injection rate, of thejet increases
dramatically during the early stages of an outburst, understanding
the outbursts of the population of BHXRBs is one way of refining
our knowledge of their impact on their surroundings.
For the study of the X-ray emission from BHXRBs, the RXTE
satellite has created an extensive archive of data on a wide variety
of these objects since its launch in December 1995. This makes a
comprehensive and easily comparable study possible, as the same
instruments (though with changes in calibration over time) have
taken all the observations. The over 13 year baseline of observa-
tions means that a number of sources have been observed going
through outbursts multiple times. This allows comparison within
as well as between sources.
Wepresent an analysis of asample of 25BHXRBswhich have
been observed by the RXTE satellite. The sample was not chosen
in any statistical way. The binaries were selected from well known
BHXRBs(or candidates) as well as those which have been well ob-
served by RXTE. We outline the data reduction scheme and model
selection in Sections 2 and 3. Our initial comparisons between the
binaries using the standard diagnostic diagrams are presented in
Section 5. Sections 6 and 7 discuss the outbursts themselves and
the properties of the transitions. The radio properties of the bina-
ries during their outbursts are a useful probe of the jet activity. The
radio observations which are sufficiently coincident with the X-ray
observations are presented in Section 8.
2 DATA SELECTION AND ANALYSIS
The data reduction scheme is very similar to that used for GX 339-
4 in Dunn et al. (2008). We briefly recap the method below and
highlight any changes from that scheme.
We used all observations of the binaries we selected which
were publicly available in the RXTE archive1. This gave around
12Ms of raw PCA exposure over an 13 year period. Not all objects
we selected had similar time coverage, some having large volumes
of observations over all 13 years, whereas others had few.
All the data were reprocessed so that all observations had the
same version of the data reduction scripts applied. Apart from the
PCA data, we also analysed the HEXTE data to constrain the pow-
erlaw slope at high energy which allows for more detailed fitting
at low energies. We use the data reduction tools from HEASOFT2
version 6.6.2. The data reduction and model fitting were automated
so that each observation was treated in exactly the same way.
1The cut-off date used to find public observations was 4 August 2009.
c ? 0000 RAS, MNRAS 000, 000–000
A Global Spectral Study of Black Hole X-ray Binaries
2.1 PCA & HEXTE Data Reduction
ThePCAand HEXTEdatawerereduced according totheprocedure
in the RXTE Cookbook3, and only a quick summary is given here.
We used only data from PCA PCU-2 as it has always been
switched on throughout the mission, and so can be used over the
entire archive of data. It is also the best calibrated of the PCUs
on RXTE. Background spectra were obtained using PCABACKEST
from new filter files created using XTEFILT, from which updated
GTI files were also created. We use only the bright model for the
background. Our aim is to perform a single data reduction routine
for all sources, and switching between the faint and bright models
may have introduced jumps into our light curves. We also ignored
the ELECTRON2 selection criterion when using MAKETIME to cre-
ate the GTI files. As our analysis concentrates on the outbursts
(bright periods) of the X-ray binaries, we do not believe that this
will bias our results. However, low flux/counts data were therefore
treated with caution. The spectra were extracted and the custom-
ary systematic error of 1 per cent was added to all spectra using
In order that the model fitting in XSPEC was reliable and rel-
atively quick, we only fitted spectra which had more that 1000
background-subtracted PCA counts. The excluded observations oc-
cur throughout the light curves of the objects, with a concentration
in the low flux periods. Our analysis concentrates on the outbursts
of the X-ray binaries rather than the quiescent periods. Therefore
excluding these low count observations, even if most were taken
during quiescence, is unlikely to bias our conclusions about the
Wherepossible, weusedboth HEXTECluster Aand Cluster B
data. Background spectra were obtained using HXTBACK. Spectra
were extracted using the routine appropriate to the data-type (Event
or Archive). Dead-time was then calculated using HXTDEAD. All
spectra for a given ObsID were then summed using SUMPHA,
and the appropriate responses and ancillary files were added in as
header key words using GRPPHA. In order to accurately determine
the slope of the high energy power-law we require HEXTE data
to be present when fitting a model. There have to be at least 2000
background-subtracted counts in one of the HEXTE clusters, with
the other having a positive number of counts4. As our analysis con-
centrates on the outbursts of the binaries, we also require PCA data
to be present to fit the soft energies, where the emission from the
accretion disc is found. We bin the HEXTE data up to match the
binning found in the Standard-2 HEXTE data products.
The spectra were fitted in XSPEC (v12.5.0an, Arnaud 1996). This
latest version of XSPEC does not allow parameters to be extracted
if there are unconstrained model components present within the fit
(anunnecessary lineor disccomponent for example). Wehave used
this to our advantage by stopping fits where a model component
is not necessary (a line component for example) as these would
cost time if the code attempted to extract errors for them, as the
parameters in these cases are usually poorly determined.
Our analysis focuses on the outbursts of the X-ray binaries. It
was therefore necessary to accurately determine the disc properties
4The background subtraction on some observations resulted in a negative
number of HEXTE counts in one of the clusters.
during the outburst, requiring that we analyse the spectra down to
the lowest possible energies. The energy boundaries corresponding
to channel numbers have changed during the lifetime of the RXTE
mission. The calibration of channel numbers ? 6 is uncertain, and
we therefore ignore all PCA channels ? 6 (which corresponds to
∼ 3keV), which allows a consistent lower bound to the spectra,
extending them to the lowest possible energies and maintaining
calibration. All PCA data greater than 25keV were also ignored.
The HEXTE data were fitted between 25 and 250keV. To inves-
tigate the evolution of the thermal and non-thermal components
during an outburst, three types of models were fitted: Powerlaw
(POWER), Broken Powerlaw (BKNPOWER) and Powerlaw + Disc
(POWER+DISCBB). This allowed us to study the evolution of the
disc and powerlaw over the outburst. As an iron line has been de-
tectedinanumber of X-raybinaries, for each of thesethree models,
a version including a Gaussian line fixed at 6.4keV was also fitted.
This gave a total of six models which were fitted to each spectrum.
The powerlaws had a soft upper limit of 3keV and a hard
upper limit of 5keV. The break energy was left free throughout
the sensitivity range of RXTE, though this does allow it to mimic a
low luminosity disc (see Section5.3). Wedecided on this approach,
rather than having a higher low-energy bound for the break energy
as this is more flexible in later stages of the analysis. For the work
presented here we use the method in Section 3.1.
Noticeable variations of the hydrogen column density value
during state transitions may be observed in BHBs (see e.g
Cabanac et al. 2009; Oosterbroek et al. 1996 in GS 2023+338
(V404-Cyg)). However, as RXTE/PCAresponse falls under 2keV,
a systematic study of such variations with this instrument appears
to be difficult. Hence we decided to fix its value to the commonly
accepted value for binaries (see Table 1). Galactic absorption was
modelled using the WABS photoelectric absorption code, with val-
ues fixed to the accepted values for the binaries (see Table 1). To
obtain fluxes outside of the RXTE observing band, for the disc for
example, dummy responses were created within XSPEC.
Although GX 339-4 had a correction applied for the galactic
ridge emission (GRE) in Dunn et al. (2008), we do not apply any
such correction to any of the sources analysed here. We did inves-
tigate whether it was possible to determine the level of any such
correction from the RXTE data itself. In some cases (4U 1543-47,
XTE J1550-564, XTE J1650-500, GX339-4 and H 1743-322) this
was indeed possible - in some cases even being able to constrain
the line parameters. However in all the other sources, there did
not appear to be any RXTE observations in periods of quiescence
where the source was not detectable over the background (in terms
of background subtracted counts per second per PCU). Rather than
applying the GRE correction to only those sources where it was
possible to determine the level of correction from the RXTE data,
or even those where measures using other observatories have been
published, we decided to not apply any correction at all. The level
of the GRE during an outburst of an BHXRB is very low. Compar-
ing our results from GX 339-4 in this analysis to that presented in
Dunn et al. (2008) the average flux difference is 2.27 per cent, with
95 per cent of the observations having a flux difference of less than
5 per cent. Therefore our decision to standardise the spectral fit-
ting across all objects by not applying a GRE correction should not
affect any conclusions drawn about the outbursts of the BHXRBs.
Any future work on the decays of the outbursts will need to take the
GRE into account, and as such any correction will be applied then.
We encountered some difficulty in fitting discs reliably, espe-
cially when the sources are in the intermediate states. The response
of RXTEisonly reliabledown to∼ 3keV,whereas thediscsweare
c ? 0000 RAS, MNRAS 000, 000–000
Dunn, Fender, K¨ ording, Belloni & Cabanac
trying to measure have temperatures of around 1keV or less. We
set the minimum disc temperature to kBT = 0.1keV in XSPEC to
prevent discs from being fit at very low temperatures. It is likely
that in cases where this occurred, the disc was being fit to take into
account of any curvature in the powerlaw slope rather than to a
true disc component. Before selecting the best fitting model we pe-
nalisedtheχ2ofdisc modelswhichhad kBT < 0.4keV asinearly
results from the fitting procedure indicated that few discs are de-
tected in RXTE data with temperatures lower than kBT < 0.4keV.
In doing this we note that we are likely to have excluded a few disc
fits that were reliable.
Although a more complicated model, COMPTT for example,
would give more information on the state of the accretion disc and
its surroundings there are difficulties with using these models. The
models used in this analysis are simple, and so can be fit to ob-
servations with low numbers of counts. More complicated models
requiremorecounts toenableacompletefittobemade. Inour anal-
ysis of GX 339-4 we find that although COMPTT does fit well to the
high luminosity hard-state observations with the highest number of
counts (Dunn et al. 2008). But in the soft state, even the observa-
tions with the highest number of counts are unable to constrain all
the parameters. To use more complicated models restrict the num-
bers of observations we could use inour analysis, and so the picture
arising from this work would be less complete.
The DISKBB model is a comparatively simplistic model and
does not include effects on the disc spectrum from the gravitational
potential or from the disc atmosphere. In the PCA pass-band, when
the discs are at low temperatures, this is unlikely to be of concern.
However for higher temperature and brighter, more dominant discs,
the resulting distortion of the disc emission may not be well fit by
the DISKBB model. But, for the reasons noted above, we still use
the DISKBB model rather than adding in further model parameters.
3.1 Selecting the best fitting model
Out best-fitting model-selection routine has changed subtly from
that outlined in Dunn et al. (2008). We show the flowchart used in
Fig. 1 and outline the procedure here. We still initially select the
model with the lowest reduced χ2. If this is the simple powerlaw
(SP),then that isthe best fittingmodel, asit isalso the simplest. If it
is the simple powerlaw + gaussian line (SPG) then we test whether
the gaussian component is an accurate description of a true iron
line in the data. The scheme for this “line test” is identical to that
described in Dunn et al. (2008)5.
If this best fitting model is a broken powerlaw (BP) or a
disc+powerlaw model (DP), we test whether using this more com-
plex continuum model is a significant enough an improvement over
a simple unbroken powerlaw, by performing an F-test. If the F-
statistic probability P < 0.001 then we select the more complex
However, if the best fitting model is BP (or DP) and contains
a gaussian (BPG or DPG respectively), then the following is done.
If the χ2of the BP (or DP) without the line is less than that of
theSP,thenthese continuum models aretested against each other to
see if the more complicated model is necessary. Then subsequently
5An F-test using P < 0.001 as the significance level combined with
the normalisation of the line and its uncertainty (Nline> 3σNline). Both
criteria have to be satisfied for the line to be taken as real. Also, if the line
width, σ > 2keV then this was taken to mean that the line was not well
constrained, and the line deemed to be not real.
BROKEN POWERLAW or
Best fitting is
BROKEN POWERLAW + LINE or
DISC+POWERLAW + LINE Selected
POWERLAW + LINE Selected
Best fitting model onχ2
Figure 1. Decision Tree for selecting the best model.
the addition of the line component is tested on the result of the
If, however, the χ2of BP (or DP) is greater than that of the
SP, then firstly the existence of the line is tested between SP and
SPG. Then if the line is necessary in SPG, the BPG (or DPG) are
tested against SPG. If SPG is the best fitting model, then we use
the SPG model fit as the best fitting. If the best fitting model is
BPG (or DPG), then if the line is well defined (σ < 2keV) in both
the complicated (BPG or DPG) and SPG models, then the BPG (or
DPG) are chosen. If the line is only well defined in the SPG model,
then this is chosen, else the SP model is taken as the best fit.
However, if the line is not necessary in the SP models, then
although it is not a fair test, then BPG (or DPG) are tested against
SP.If SP is the best fittingmodel, then this is a reliable result. How-
ever, if BPG (or DPG) are the best fitting model, then only if the
line is well defined (σ < 2keV) in both the BPG (or DPG) and
SPG models, then the BPG (or DPG) are chosen. Else the best fit-
ting model is SP. All observations with this final set are noted so
they can be investigated at a later stage if necessary.
The new feature of XSPEC where fits are terminated if there
are unnecessary model components present, allows us to stream-
line the model selection procedure. These model “fits” are auto-
matically removed from those available to be selected as they are
set to have a very high chi-squared value and so are not selected by
the routine as a best fit.
We note that we may be missing non-dominant disc compo-
c ? 0000 RAS, MNRAS 000, 000–000
A Global Spectral Study of Black Hole X-ray Binaries
nents in, for example, the hard state. Even though we fit all ob-
servations with a powerlaw + disc model, the lack of sensitivity
of the RXTE PCA below ∼ 3keV makes detecting non-dominant
discs difficult. Therefore even if no significant disc is detected in
our analysis, there may be discs present at a very low level in the
hard and intermediate states – absence of evidence does not imply
evidence of absence.
We also note that we are attempting to fit a line component
with a gaussian at a fixed energy, whereas deeper spectra with
higher resolution (from e.g.Chandra or XMM-Newton) are bet-
ter fit with relativistically blurred line whose peak energy varies
(e.g.Miller et al. 2004). The results from the line parameters will
appear in a forthcoming publication. However, we do not select
models where the line parameters (usually the line width) are not
well constrained6, even if these are the best fitting.
Any observation with a 3 − 10keV flux from the best fitting
model of less than 1 × 10−11erg s−1was discarded from further
analysis, as were ones where the flux was not well determined (the
error on the 3 − 10keV flux was larger than the flux itself). It was
noted that in some cases, although the flux was high enough and
well determined, some of the model parameters were not, espe-
cially in the soft state, were the powerlaw parameters may be diffi-
cult to determine if the disc is very strong. We therefore excluded
these observations from the analysis presented here, however as the
disc was fitted successfully, they may be included in a future paper
on the disc properties.
Even after this level of selection some spectra still were not
well fit by any of the models. To remove the parameters obtained
from these poor fits we cut at χ2< 5.0.
This selection procedure resulted in a final list of 3919 ob-
servations, corresponding to ∼ 10Ms, with well fitted spectra and
high enough fluxes and counts. We extract a range of parameters
and fluxes for different energy bands and model components which
are presented and analysed further the following sections.
The distribution of the reduced χ2from all the observations
is shown in Fig. 2. There is a clear peak at χ2= 1 with a tail ex-
tending to higher values of χ2, 60.1 per cent of the model fits have
0.8 ? χ2? 1.2 and 90.2 per cent between 0.7 ? χ2? 2.0. Our
average number of degrees of freedom per spectrum is 111.4. We
show on Fig. 2 the expected distribution for 111 degrees of free-
dom. Given the automatic nature of the data reduction procedure
used in this analysis, this tail to higher values of χ2is expected.
A manual investigation into some of the models with a high χ2
showed that these observations are a mix of low counts data and
occasions where the automated fitting routine failed to find the best
fitting model, leaving a poorly-fit simple powerlaw (+gaussian) as
theonlymodel withfittedparameters. However, thefractionof high
χ2values is reasonably small.
4 SELECTED OBJECTS
In our analysis we primarily aimed to select those objects which
appear to have been observed regularly with RXTE. However, some
of the objects only have a few observations taken with RXTE. In
some cases, although there are many observations, only few pass
the counts, flux and model fitting criteria to be analysed further.
This sample of X-ray binaries was not intended to be complete in
6Those observations where the line width is unconstrained or if the value
of the line width is greater than 2keV.
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Figure 2. The distribution of reduced χ2from all the observations. The in-
set shows an enlargement around the peak of the distribution. The selection
of χ2< 5.0 has been applied when creating this plot. We show on top a
the χ2distribution using 111 degrees of freedom.
any way, however, we have attempted to include all BHXRBs with
well studied outbursts.
InTable 1welist themasses, distances, NHvalues of the bina-
ries studied in this work. We also summarise the number and total
exposure of the X-ray observations used (Table 2). Many of the
masses and distances are not well determined, and in these cases
we have assumed the distances to be 5kpc and the masses 10M⊙.
The uncertainties in distances and masses affect the calcula-
tion of the Eddington Luminosity for these sources. As the major-
ity of relations and diagrams in this work use LEdd to scale the
observables, allowing the different binaries to be compared with
one another. Without well determined distances and masses then
any relation obtained for the ensemble of binaries will be uncertain
to some degree.
We note that there is a large range in the number of obser-
vations per binary (from almost 700 to less than 10). Therefore in
parts of thisanalysis where the population as a whole is studied, the
results will be strongly influenced by those BHXRBs with many
observations. However, those BHXRBs with the most observations
also tend to be the ones which go through clear outbursts. We also
look at the lightcurves to “pre-identify” outbursts, which can then
be compared, either to other outbursts from the same source, or to
ones from different sources.
The full PCA lightcurve of from all the objects over the full
13 years of the RXTE mission is shown in Fig. 3. The level of ac-
tivity from X-ray binaries can easily be seen. Although this plot is
in terms of the Eddington ratio, most sources are between 5 and
10kpc away, so the overall variation in X-ray flux is a factor of
four greater. Even with this incomplete sample and the restrictions
on which observations are analysed in this work, there are few peri-
ods when no BHXRB is radiating at a significant fraction of LEdd.
5 POPULATION STUDY: GLOBAL PROPERTIES OF
Having analysed this large sample of X-ray binaries we now look
at their global properties using well characterised methods.
c ? 0000 RAS, MNRAS 000, 000–000