Yangsen Yao

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Studying the Accretion Disks in Black Hole
X-ray Binaries with Monte-Carlo Simulations
Yangsen Yao∗, Shuang Nan Zhang∗ and Xiaoling Zhang∗
∗University of Alabama in Huntsville and National Space Science and Technology Center,
Physics Department, Huntsville, AL 35899, USA
Abstract. Understanding the properties of the hot corona is very important for studying the ac-
cretion disks in black hole X-ray binary systems. Using the Monte-Carlo technique to simulate the
inverse Compton scattering process between disk photons and electrons in the hot corona, we have
produced two table models in the XSPEC package. Applying themodels to the broad-band Bep-
poSAX observations of the black hole candidate XTE J2012+381, we demonstrate the power of this
table model. Our results indicate that the electron distribu ion in the corona has a powerlaw shape
with a spectral index around 4 and the size of the corona is just several tens of gravitational radius
and the inclination angle of the disk is around 60 degrees.
INTRODUCTION
The spectrum of a black hole X-ray binary system usually consists of two components
(see Zhang, et al. 1997 for a review and references therein):blackbody-like component
and powerlaw-like component. The blackbody-like component turns off above 20 keV
and is believed to be emitted from the accretion disk. The powerla -like component
can extend up to 200 keV and is believed to be produced in a hot cor na around the
black hole through the inverse Compton scattering process btween the disk photons and
electrons in the corona. This process can be described by theKompaneets’s equation,
which is a non-linear diffusion equation and very difficult for analytical solutions.
Analytic solutions have been worked out by Sunyaev and Titarchuk (1980) and
Titarchuck (1994) based on these assumptions: 1) uniform corona with either spheri-
cal or disk geometry; 2) seed photons are emitted in the center of he corona; 3) the seed
photon distribution follows the Wien form; 4) the thermal temperature of electrons in the
corona is much higher than the Wien temperature of the seed photons. However, some
or all of these assumptions are not appropriate for black hole binary systems.
In the X-ray astronomy community, the multi-color blackbody (Mitsuda et al., 1984;
Makishima et al., 1986;diskbb in XSPEC) plus a powerlaw model has been employed
traditionally to fit the energy spectra of the black hole X-ray binary systems; this model
is non-physical and unreasonable as we pointed out in our previous paper (Zhang et al.,
2001).
In this paper, we use the Monte-Carlo technique to simulate the inverse Compton
process in the corona; two powerful table models (as the standard model inXSPEC
package) have been built up based on our simulation results.Using these table models
to fit the data on XTE J2012+381 with BeppoSAX, we estimated several physical
parameters of the accretion disk and corona.
MONTE-CARLO SIMULATIONS
In our simulations, we assume that the accretion disk is the Keplerian disk, and during
the accretion process, the potential energy loss of the accreted material is radiated away
in blackbody radiation. Therefore, the temperature distribu ion along the accretion disk
is T ∝ r−3/4. The corona may take either spherical or disk geometry; the electron density
distribution in the corona may be either uniform or non-uniform (take the powerlaw for
non-uniform distribution); and the electron energy distribut on in the corona may take
either thermal form or non-thermal form (powerlaw).
Our simulation results can be summarized as following: 1) for a given electron
temperature, the scattered photon spectrum in the high energy band is determined by
the optical depth of the corona (FIGURE 1.a); 2) the shape of scattered photon spectrum
in the low energy band is related to the geometrical size of the corona (FIGURE 1.b); 3)
for the same properties of disk and corona, the ratio betweenthe flux of soft component
and that of the hard component is related to the inclination angle of the accretion disk
(FIGURE 1.c); 4) the high energy portions of the spectra are ve y different for different
electron energy distributions in the corona, even though the low energy portions are quite
similar (FIGURE 1.d).
Based on our simulation results, we have built up two different table models for ther-
mal and powerlaw electron energy distributions respectively. The table models consist
of the following parameters: temperature of the inner boundary of the accretion disk
(Tin), thermal electron temperature (KT ) or the electron powerlaw index (Γe) , size of the
corona (Size), scattering optical depth of the corona (τ), inclination angle of the accretion
disk, and normalization parameter (KBB) which is added by theXSPEC automatically.
APPLICATION TO XTE J2012+381
The two models are applied to model the BeppoSAX broad-band data on the black
hole candidate XTE J2012+381. FIGURE 2 shows the modeling results withdiskbb+
powerlaw model in XSPEC and the results with our table models. During the rising
phase of the outburst, the powerlaw component was very strong (Sun et al., 2001)(FIG-
URE 2(a)). For the BeppoSAX observation during the rising phase we have analyzed,
the observed spectrum can be fitted reasonably well usingdiskbb+ powerlaw model
with photon index around 2.4 (FIGURE 2(b)). When fitting withour table model for
the thermal electron case, the fit to the high energy data above 10 keV is not acceptable
(FIGURE 2(c)) and thus the thermal model is rejected. However, when fitting with our
table model for the powerlaw electron distribution, the result is comparable to the that
with the diskbb+ powerlaw model. The powerlaw index for electron energy distribu-
tion is around 4, the size of corona is around several tens of gravitational radius and the
inclination angle of the disk is around 60 degrees (FIGURE 2(d)).
FIGURE 3 shows the results of inner disk radius inferred withd fferent models. When
modeling withdiskbb+ powerlaw model anddiskbb+ compT T model, the inner disk
radius inferred directly from the normalization ofdiskbb model are very small compared
to the results obtained with our table model. The results after the radiative transfer
correction (see Zhang et al. 2001 for detail) are consistentwith the results of our table
model reasonably well.
FIGURE 1. X-ray photon spectra for the spherical corona with different physical properties of
the accretion disk and the corona. Panel (a) and panel (b) show the photon spectra for the thermal
electron energy distribution with a temperature of 40 keV. Panel (a) is for a corona with different
optical depths but with the same size. Panel (b) is for a corona with different sizes but with the
same optical depth. Panel (c) shows the different photon spectra with different inclination angles
when the electron energy distribution has the powerlaw form. Panel (d) shows the comparison
of the photon spectra between thermal and powerlaw electronenergy distributions in the corona.
CONCLUSION AND DISCUSSION
According to our simulation results and data analysis, the X-ray spectral shape in the low
energy band might be related to the size of corona and the electron energy distribution
may be inferred from the spectral shape in the high energy band. Two powerful table
models have been built up based on our simulation results andthe physical parameters
can be obtained directly when modeling the data with these tabl models.
According to the fitting results with our table models, the elctron energy distribution
in the corona of XTE J2012+381 during the rising phase seems to have a powerlaw form
rather than the thermal form and the size of the corona is justseveral tens of gravitational
radii and the inclination angle of the disk is around 60 degres.
The reason that the size of the corona may be determined from the X-ray data is
because in our model the seed photons for the inverse Comptonscattering come from
the disk, whose temperature is a function of the distance from the central black hole. The
relatively small size of the corona indicates that most of the hard X-ray photons come
from the region very close to the black hole.
Another interesting result is that the spectral fitting is quite sensitive to the disk
FIGURE 2. Panel (a) shows the ASM light curve of the black hole candidate XTE J2012+381
during its burst in 1998 and the dotted lines in the plot indicate the times of BeppoSAX
observations we have analyzed. The first observation is in the rising phase in which the hard
component is relatively strong and the other two observations are in the soft state in which the
hard component is very weak. Panel (b) shows the modeling result for the first observation with
diskbb+ powerlaw model. The best fit parameters are:Tin = 0.77±0.002 keV, KBB = 887±
10.0, Γ = 2.4±0.03, and the Chi-Squared is 1368 with 553 degrees of freedom. Panel (c) shows
the modeling result with our table model for thermal electron distribution in the corona. The best
fit parameters are:Tin = 0.6±0.02 keV, KT = 52±6.2 keV,Size = 19±1.7Rg, τ = 0.6±0.06,
and the Chi-Squared is 3109 with 548 degrees of freedom. Panel (d) shows the modeling result
with our table model for powerlaw electron distribution in the corona. The best fit parameters
are:Tin = 0.76±0.002keV, Γe = 4, Size = 49±6.2Rg, τ = 0.09±0.003, θ = 590±3.60, and
the Chi-Squared is 1564 with 552 degrees of freedom.
inclination angle. This is because the observed flux from thedisk depends strongly upon
the inclination angle, while the hard X-ray flux is almost isotropic, especially for the
case of spherical corona. Unfortunately the inclination angle and the geometrical factor
(opaqueness of the corona) may be coupled together in the spectral fitting if the quality
of the data is not good enough. If the inclination angle of thesystem is determined
independently, e.g., with optical photometry observations r radio measurements of jets,
the shape of the corona may be constrained reliably with X-ray spectral fitting.
Determining the value of the inner disk radius is very important in understanding the
FIGURE 3. Inner disk radius (R2in ∝ KBB) in-
ferred with different models. These three data
points correspond to the three observations
indicated in FIGURE 2(a). When modeling
with diskbb+ powerlaw model anddiskbb+
compTT model, the results inferred directly
from the soft component are quite small com-
pared to the results inferred from our table
model and the results after the radiative trans-
fer correction.
physics of the accretion disk and the black hole angular momentum (Zhang, Cui and
Chen 1997). The normalization parameter inferred with our table model, which is pro-
portional to the square of the inner disk radius (Makishima et l., 1986), is significantly
different from that determined with the simplediskbb+ powerlaw or diskbb+compTT
model without radiative transfer correction. This is because the corona, though optically
thin in most cases, scatters some of the photons emitted fromthe disk and make the
observed soft component different significantly from the original disk emission.
Therefore modeling broad-band X-ray continuum spectra with physically consistent
and accurate models provides a powerful tool in determiningthe properties of accretion
disks and coronae in black hole X-ray binaries. However suchstudies require high
quality and broad-band data, which may be provided by BeppoSAX, Chandra and
XMM currently. Future data from Integral, Swift and especially the Constellation X-
ray missions will provide significant breakthroughs in thisfield.
Currently, we have not included non-uniform corona and other geometry in our
table models. The general relativistic effects and Dopplereffects (Zhang, et al., these
proceedings) are also not taken into account in our table model currently. All of these
will be our future work.
Acknowledgments: Mr. Yongzhong Chen is acknowledged for his initial work on
this project during his visit to UAH in 1999-2000. We thank Drs. Lev Titarchuk, Wei
Cui and Yuxin Feng for interesting discussions. This work was supported in part by
NASA Marshall Space Flight Center under contract NCC8-200 and by NASA Long
Term Space Astrophysics Program under grants NAG5-7927 andNAG5-8523.
REFERENCES
1. Makishima et al., ApJ 308, 635, (1986)
2. Mitsuda et al., PASJ, 36, 741, (1984),
3. Sun, X. J, et al., to be submitted to ApJ, 2001
4. Sunyaev, R. A., & Titarchuk, L. G., 1980, A&A, 86, 121
5. Titarchuk, L., 1994, ApJ, 434, 570
6. Zhang, S. N., Cui, Wei, and Chen, Wan, 1997, ApJ, L155
7. Zhang, S. N.,et al. , 1997, Invited Review of the 4th Compton Symposium Proceedings, AIP Confer-
ence Series, 410, 141, eds Charles D. Dermer, Mark S. Strickman, James D. Kurfess.
8. Zhang, S. Nan, et al., to be submitted to ApJ, 2001
9. Zhang, Xiaoling, Zhang, S. Nan, & Yao, Yangsen, these proceedings


Studying the accretion disks in black hole X-ray binaries with Monte-Carlo simulations

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Studying the accretion disks in black hole X-ray binaries with Monte-Carlo simulations

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