The effect of dissipative corona on the structure and stability of cold optically thick accretion disks at high accretion rates
Ranjeev Misra\altaffilmark{1}
The vertical structure of optically thick accretion disks is investigated in the two-zone approximation. The disk is divided into an underlying disk and a corona, where the latter is defined as the upper surface layers for which the effective optical depth is unity. It is found that a significant part of the accretion flow (or dissipation rate) can take place in the corona if the scale height of the magnetic field is larger than that of the disk. The presence of such a dissipative corona leads to a modification in the topology of local disk solutions. For example, these solutions are found from local stability analysis to be both secularly and thermally stable, for accretion rates which are a factor $\approx$ four higher than those inferred from the stability of standard disk solutions. Thus, the applicability of optically thick disks with dissipative coronas are not as restrictive as disks without such coronas and can provide an attractive explanation for the origin of the soft spectral component observed in black hole X-ray binary systems.
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\shorttitle{Effect of Dissipative corona}
\shortauthors{R. Misra and R. E. Taam}


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\begin{document}

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\title{The effect of dissipative corona on the structure and stability of
cold optically thick accretion disks at high accretion rates}



\author{Ranjeev Misra\altaffilmark{1}} \and \author{Ronald E. Taam\altaffilmark{2}}


\altaffiltext{2}{Inter-University Center for Astronomy and Astrophysics,
Ghaneskhind Road, Pune, India; rmisra@iucaa.ernet.in}


\altaffiltext{2}{Department of Physics and Astronomy,
Northwestern University, 2131 Sheridan Road, Evanston,IL 60208;
taam@apollo.astro.nwu.edu}



\begin{abstract}

The vertical structure of optically thick accretion disks is investigated in
the two-zone approximation.  The disk is divided into an underlying
disk and a corona, where the latter is defined as the upper surface layers
for which the effective optical depth is unity.  It is found that
a significant part of the accretion flow (or dissipation rate)
can take place in the corona if the scale height of the magnetic field is larger 
than that of the disk. The presence of such a dissipative corona leads to a modification 
in the topology of local disk solutions. For example, 
these
solutions are found from local stability analysis to be both secularly and thermally stable,
for accretion rates which are a factor $\approx$ four higher than those inferred from
the stability of standard disk solutions.
Thus, the applicability of optically thick disks with dissipative coronas  are not 
as restrictive as disks without such coronas and can provide  
an attractive explanation for the origin of the soft spectral 
component observed in black hole X-ray binary systems.
\end{abstract}

\keywords{accretion, accretion disks-black hole physics -hydrodynamics}


\section{Introduction} \label{sec: I}

X-ray binary systems in which one star is believed to be a black hole 
are primarily, but not solely, observed in one of two long
term spectral states. In the so called soft state, the spectrum  of the system
consists of a soft black body-like component (kT $\approx 1$ keV), 
which often dominates the luminosity, and a hard
power-law tail with a photon index $\Gamma \approx 2.5$. 
In contrast, the hard spectral state can be described 
approximately as a harder power-law ($\Gamma \approx 1.7$) while 
the soft component is either weak or undetectable.  Although the existence 
of these spectral states has been known for a long time, there is no general
consensus for their origin.   In particular, several models have been proposed 
for the possible origin of the hard X-ray power-law. For example, the 
emission could arise from thermal Comptonization of soft photons in a hot
accretion disk (Shapiro, Lightman \& Eardley 1976; Esin, McClintock \& Narayan 1997) 
or from bulk Comptonization in
a converging flow (Laurent \& Titarchuk 2001). Other scenarios invoke a hot
low density Comptonizing coronal region sandwiching a cold accretion disk 
(Liang \& Price 1977; Haardt \& Maraschi 1993). Within the framework of 
these models, active time varying regions (or flares) on top of the disk 
may be responsible for the production of the hard X-ray spectrum (Poutanen 
\& Fabian 1999). In yet another model, the
hard X-rays may arise from a disk where the temperature is a rapidly varying
function of radius (Misra \& Melia 1996). Although these models are characterized
by different disk structure and geometry, they all attribute the low energy 
component of the soft state to  
emission from a cold 
accretion disk.
Thus, there seems to be a general consensus that, at least, during the
soft state, a cold accretion disk exists extending to nearly the innermost 
stable orbit in these systems.


In the standard theory of accretion disks pioneered by Shakura \& Sunyaev (1973), the 
turbulent viscosity
is parameterized as
\begin{equation} 
\tau_{r \phi} = \alpha P, 
\end{equation}
where $\tau_{r \phi}$ is the viscous torque, $P$ is the pressure and
$\alpha$ is the viscosity parameter. A cold optically thick disk with
such a viscosity prescription is known to be secularly and thermally
unstable 
if in the disk the ratio of the gas pressure to the total
pressure is less than $0.4$ (Lightman \& Eardley 1974; Shakura 
\& Sunyaev 1976). This occurs, for example  
at a radius, R, of $20 GM/c^2$ when the accretion rate is
\begin{equation}
{\dot M} > (10^{17} \hbox {g s}^{-1}) \alpha^{-1/8} ({M\over 10 M_\odot})^{7/8}
\end{equation}
which corresponds to luminosities greater than $5 \times 10^{36}$ ergs s$^{-1}$ for
a ten solar mass black hole.   
Although several X-ray binaries exceed this luminosity in the soft state, they
generally do not exhibit large amplitude temporal variations which are expected if  
the secular and thermal instabilities are indeed present (Taam \& Lin 1984). 
An exception to this statement is the microquasar GRS 1915+105 
(Mirabel \& Rodriguez 1999) where, indeed, 
large amplitude variations are often observed. It should be emphasized that
these predicted instabilities depend on the form of the viscosity prescription 
and occur when the viscosity and the temporal response of the viscosity is 
highly temperature sensitive (e.g., Honma, Matsumoto, \& Kato 1991). 

A promising mechanism for driving the turbulence responsible for angular 
momentum and energy transport is the action of the 
magneto-rotational 
instability (MRI) that is expected to take
place in such disks (Balbus \& Hawley 1991). In fact, recent 3D magneto hydrodynamic
(MHD) simulations have shown that the MRI can give rise to a turbulent
viscosity which leads to accretion flow in a Keplerian disk (Hawley, 
Balbus \& Stone 2001). 
The time averaged viscous torque in these simulations was found to be
proportional to the magnetic pressure which itself is locally proportional to
the disk pressure. 
Thus, the form of eqn (1), as a physical viscosity
prescription was justified. However, these simulations do not include
the effect of radiation and, hence, it is not clear whether this prescription
is valid when the disk is radiation pressure dominated. On the
other hand, there are no definite reasons to believe that it will be different.
In this framework, eqn (1) may well be valid only in a time averaged sense.
In this case, the characteristic timescale ($t_{ave}$)
over which the averaging needs to be performed 
can only be estimated after MHD simulations with radiation
and cooling are undertaken.
Any inferred temporal response of the disk using eqn (1) on timescales
shorter than $t_{ave}$ can be misleading.
Hence, the thermal instability inferred from the use of eqn (1) may not occur
if the thermal timescale is much shorter than $t_{ave}$.
However, the secular instability occurs on the viscous timescale which should be 
longer or at least comparable to $t_{ave}$. Thus, contrary to observations,
radiation pressure dominated disks are expected to be non steady, suffering from,
at least, the secular instability.

We point out that these predictions of instability are based on simplifying assumptions 
on the vertical distribution of the energy dissipation rate in the disk. 
In particular, it is possible that the vertical disk structure is sufficiently 
complex that these instabilities may be suppressed. For example, the existence of
a corona in the upper layers of the disk could play a dynamically and energetically
important role in the accretion process. Such a dissipative corona (i.e., a corona
where a substantial fraction of the 
energy dissipated and/or accretion flow takes place) may be
able to stabilize the underlying disk (see Ionson \& Kuperus 1984; Svensson \& 
Zdziarski 1994; Chen 1995; Abramowicz, Chen, \& Taam 1995; Zycki, Collin-Souffrin, 
\& Czerny 1995). 
To compute the 
vertical structure of the disk, a knowledge of the energy 
dissipation rate as a function of height is required.
Due to the uncertainties involved the dissipation rate has been assumed, in 
the literature, to be proportional to the gas density 
(e.g., Ross \& Fabian 1996, Shimura \& Takahara 1995). With this assumption, 
the dissipation in the low density upper layers of the disk is negligible
compared to its contributions in the midplane. However, the dissipation rate is proportional to the magnetic pressure for the MRI induced viscosity, and 
numerical simulations show that the magnetic pressure scale height is larger than
the disk scale height (Hawley, Balbus \& Stone 2001). 
In such a description, a low density but highly magnetized
dissipative corona can form 
which may act to stabilize the disk. 

In this work, we investigate the conditions under
which a dynamically important dissipative corona exists and study the
effect of such a corona on the stability of the disk. 
A simplified approach is adopted
where the disk is divided into two distinct regions: the underlying
disk and the corona. Here, the corona is explicitly defined as the upper
layer of the disk where the effective optical depth is unity. Thus
the definition of a corona here differs from 
previous works where an optically thin distinct region above an optically
thick  disk is referred to as the corona.
In this approach, the disk
structure equations are reduced to simple algebraic relations in terms
of average quantities of the disk and corona. Such an analysis, while giving 
qualitative results, is more suitable for comparison with the standard vertically
integrated disk solutions and stability analysis. 

In the next section, the disk and corona structure equations are formulated and the 
assumptions underlying our analysis are presented.  The 
solutions of these equations are described in \S 3, and the stability of the disk is
analyzed in \S 4.  Finally, we summarize our work and discuss its implications in 
the last section. 

\section{Disk Structure Equations} \label{sec: II}

The disk and overlying corona structures are cast into algebraic form 
in a development similar to standard thin disk theory.  In contrast to 
the standard theory, the effect of the corona on the disk and vice versa
are explicitly taken into account. The following approximate equations describe  
the vertically averaged quantities of the disk and corona. Throughout this paper,
quantities with D (C) subscript denote the disk (corona).

Hydrostatic equilibrium for the disk gives,

\begin{equation}
{P_D -P_C \over H_D} = {GM m_p\over R^3} n_D H_D
\end{equation}
while for the corona it is given by,

\begin{equation}
{P_C \over H_C} = {GM m_p\over R^3} n_C (H_C+H_D)
\end{equation}
where $P$ is the total pressure, $R$ is the radius, $H$ is the height,
$n$ is the number density and $M$ is the mass of the black hole.
The total pressure consists of contributions from gas, radiation and magnetic pressures.
In the above, we have assumed that the disk and corona are geometrically thin 
(i.e., $H << R$). 
Thus for the disk, 
\begin{equation}
P_D = P_{DR}+P_{DG}+P_{DB} = 2 n_D k T_D + 4 \sigma T_D^{4}/3c +P_{DB}
\end{equation}
and similarly for the corona,
\begin{equation}
P_C = P_{CR}+P_{CG}+P_{CB} = 2 n_C k T_C + 4 \sigma T_C^{4}/3c +P_{CB}
\end{equation}
where $T$ is the temperature and 
$P_{DB}$ 
($P_{CB}$) 
is the magnetic pressure in the disk (corona). 
For simplicity, the gas is assumed to be composed of pure hydrogen. 
It can be seen that the effect of the corona on the underlying disk enters 
through eqn (3) in the matching pressure condition at the interface of 
the disk and corona. 

The viscous torque is assumed to be proportional to the magnetic pressure.
Hence the energy flux dissipated in the disk is,
\begin{equation}
F_{DG} = {3\over 2} \alpha_B P_{DB} H_D \Omega_K 
\end{equation}
while for the corona it is,
\begin{equation}
F_{CG} = {3\over 2} \alpha_B P_{CB} H_C \Omega_K 
\end{equation}
where $\Omega_K$ is the Keplerian angular velocity and the
constant of proportionality $\alpha_B$ is assumed to be same for
both the disk and the corona. For the disk, the dissipated flux is matched by the radiative flux,
\begin{equation}
F_{DR} = {4 \sigma  \over 3 \tau_D } (T_D^4 - T_C^4) = F_{DG}
\end{equation}
For the corona the entire flux energy generated in the disk is radiated away. Hence,
\begin{equation}
F_{CR} = {4 \sigma T_C^4 \over 3 \tau_C } = F_{CG}+F_{DG}
\end{equation}
By definition the effective optical depth in the corona is
unity,
\begin{equation}
\tau_{C*}^2 = \tau_C \times 1.8 \times 10^{-25} n_C^2 T_C^{-7/2} H_C = 1
\end{equation}
Note that since $\tau_{C*} = 1$, the corona is expected to be in approximate
thermal equilibrium (see for e.g. Ross \& Fabian 1996)
 which justifies eqn (10) and the expression for radiation pressure in
the corona, taken to be equal to $4 \sigma T_C^{4}/3c$. Essentially,
although the Compton y-parameter in the corona is large, the free-free absorption
is still dominant, making the radiation nearly thermal.

It is assumed here that the magnetic pressure in the disk is a
fraction of the gas and radiation pressure. Thus
\begin{equation}
P_{DB} = \beta_D (P_{DR} + P_{DG})
\end{equation}
where $\beta_D$ measures the fraction of the magnetic pressure to
its equipartition value in the disk. To take account of the possibility
that the scale height of the magnetic field could differ from that of the density,
the magnetic 
pressure
in the corona is assumed to be given by,
\begin{equation}
P_{CB} = P_{DB} [{(P_{CR}+P_{CG}) \over (P_{DR}+P_{DG})}]^\gamma
\end{equation}
Note that if the exponent $\gamma = 1$, the ratio of the
magnetic pressure to its equipartition value is the same in the disk
as well as in the corona. At the other extreme if $\gamma = 0$,
the magnetic field is the same for the disk and the corona which
corresponds to the limit where the magnetic scale height is
much larger than that of the disk. This implies that the 
magnetic field in the corona exceeds its equipartition value
(Hawley, Balbus \& Stone 2001).

The disk and corona structure can now be solved based on 
eqns (3-13) for various values of the total optical depth
$\tau_T = \tau_D + \tau_C$ for a given 
mass of the black hole $M$, the distance $R$ from the black hole, the proportionality
constant $\alpha_B$, disk equipartition fraction $\beta_D$ and
the exponent $\gamma$.  For each solution the accretion rates
in the disk and corona can be inferred from

\begin{equation}
F_{DG} = {3\over 8 \pi} {G M \dot M_D \over R^3}
\end{equation}

\begin{equation}
F_{CG} = {3\over 8 \pi} {G M \dot M_C \over R^3}
\end{equation}
where the boundary effects have been neglected. If a zero-torque
boundary condition in the last stable orbit is enforced then the
accretion rates would be a factor $1/J$ larger than the ones inferred
using Eqns (14) and (15), where $J = 1-(6GM/c^2R)^{1/2}$ for a black hole 
described in terms of a Schwarzschild metric.

\section{Results} \label{sec: III}

The topology of the local disk solutions in ($\dot M_T, \tau_T$) space
is shown in Fig. 1 for a given black hole mass, radius, $\alpha_B$, $\beta_D$ and for
various values of $\gamma$.
Here $\dot M_T$ is the total accretion rate (i.e., the sum
of the mass flow rate through the corona and the disk). In Figures 2 (a-f), the ratios
of structural parameters of the disk and corona are shown as a function of $\dot M_T$.
For reference the well known topology
of the solutions for the standard accretion disk theory for the same set of parameters
is also shown in Fig. 1 (dashed line). 
For small accretion rates ($\dot M < 10^{17}$ g s$^{-1}$), the
disk solutions are gas pressure dominated and $\dot M_T$  increases with
$\tau_T$, while for higher accretion rates, the disk is radiation pressure 
dominated and $\dot M_T$
decreases with $\tau_T$. Here the solutions have been terminated 
when the disk becomes optically thin and the assumption that the radiation is in
thermal equilibrium breaks down. Note that the solutions for disks with dissipative coronas
require one more parameter ($\gamma$) than the standard disk model, which characterizes
the variation of the scale height of the magnetic field as compared to the disk scale height.
The set of solutions for $\gamma = 1$, has not been shown since they are similar
to the standard disk ones.

For small accretion rates  $\dot M_T < 10^{17}$ g s$^{-1}$,
the coronal accretion rate is much smaller than within the disk (except for the case when 
$\gamma = 0$)
and hence the effect of the corona on the underlying disk is minimal. The solutions are
similar to models of the standard disk. At high $\dot M_T$, the solutions are different
than the standard ones. In particular, the accretion rate at which the slope
of 
$\dot M_T$ 
vs $\tau_T$ changes sign, is higher. For $\gamma = 0$,
this slope at high accretion rates is steeper than that for standard disk solutions.
Fig 2 (b) shows that for low values of $\gamma < 0.25$, $\dot M_C \approx \dot M_D$,
and hence it for these values of $\gamma$ that a dissipative corona can exist.
 Figures (3) and (4) show how the solutions change
when $\beta_D$ and the radius is varied. 
In particular, the critical mass accretion rate above which the slope of $\dot M_T$
vs $\tau$ changes sign increases with decreasing values of $\beta_D$ and increasing 
radius $R$.
Varying $\alpha_B$, has a similar effect as 
changing $\beta_D$. 

Simple analytical expressions for the disk structure can be obtained for the
standard disk model when either the disk is radiation or gas pressure dominated. For
disks with dissipative corona the situation is more complex. Several different limits and their
combination can be considered. For example, the disk could be radiation or gas 
pressure dominated while the corresponding corona could be gas or radiation pressure dominated.
Figs. 2 (e) and 2 (f) show that, in general, all four 
possible combinations are realizable. Moreover,
to obtain analytical expressions, one has to assume 
that either the accretion rate through the
corona or the disk dominates over the other. While it is possible to present such analytical 
expressions, they are not generally valid for
the most interesting solutions (typically at high accretion rates).
Thus, only the numerical solutions to
the disk structure equations have been presented. 

In this work, the emergent spectra from such disks have not been computed, since
a detailed radiative transfer calculation in the vertical direction would be required.
The corona is, by definition, marginally optically thick (i.e. 
$\tau_{C*} = 1$),
and hence the radiation is expected to be nearly in thermal equilibrium. The  
emergent spectrum should be a black body (with flux proportional to the total dissipation)
diluted by the effect of Comptonization in the uppermost layers of the corona where the
Compton y-parameter is of order unity (Ross \& Fabian 1996). Thus,
the total spectrum from the disk
should be close to the multi-color disk spectrum which is often used for fitting the soft 
spectral component of black hole X-ray binary systems.  

\section{Stability of disks with dissipative coronas} \label{sec: IV}

In the standard accretion disk theory, radiation pressure dominated disks are
known to be both secularly and thermally unstable. The secular instability criterion
depends on the topology of solutions in ($\dot M$, $\tau$) space,
where if $\dot M$ is inversely proportional to $\tau$, the disk would be locally unstable.
Thus, whether disks with dissipative coronas are secularly stable or not,
can be directly inferred from Fig. 1.
For $\gamma < 0.5$, which correspond to nearly the same equipartition fraction for the disk
and corona, the accretion rate at which the disk is 
locally unstable (Fig 1, curves 1) is nearly same as that for the standard disk theory.
On the other hand, when $\gamma = 0$ (Fig. 1, curve 3),
a secularly stable disk can exist for $\dot M < 4 \times 10^{17}$ g s$^{-1}$
which is $\approx 4$ higher than what is expected for the standard disk solution (eqn 1).
Moreover, for $\gamma = 0$, in the unstable branch, the dependence of $\dot M_T$ on
$\tau_T$ is steeper and for a
given accretion rate the steady state optical depth is larger
than that predicted by the standard theory. This means that
the secular instability would 
occur 
on a longer time-scale and the global
evolution of such disks could be significantly different than the scenario
predicted by time dependent numerical simulations of standard disks (Taam \&
Lin 1984). Thus disks
with dissipative coronas, with low values of $\gamma$ 
(i.e., when the scale height  of the magnetic field is
sufficiently large compared to the disk scale height) 
may be secularly stable for higher accretion rates than standard disks.
  
While the secular instability occurs on the viscous timescale, the thermal instability
occurs on the much shorter thermal timescale. As discussed in \S 1,
a thermal stability analysis using the viscosity law (eqn. 1) is valid only when
the averaging timescale of the viscous law is shorter than the thermal timescale. Thus, 
the thermal
stability analysis presented here 
may not be directly applicable to 
disks with dissipative coronas. Given this caveat, 
for the total disk to be thermally stable, both 
the underlying disk
and the corona must be stable individually. The thermal stability criterion for the disk is,
\begin{equation}
\xi_{DR} > \xi_{DG}
\end{equation}
where,
\begin{equation}
\xi_{DG} = {d \;\hbox {log} F_{DG} \over d \;\hbox {log} T_D} \Big {|}_{\tau_T}
\end{equation}
and
\begin{equation}
\xi_{DR} = {d \;\hbox {log} F_{DR} \over d \;\hbox {log} T_D} \Big {|}_{\tau_T}
\end{equation}
Here, the derivatives are taken while maintaining the total optical depth, $\tau_T$, 
to be constant.
Since the thermal timescale of the corona is much smaller
than 
in
the disk, it is assumed here that the corona is in thermal
equilibrium during the perturbation. The stability criterion for the corona is,
\begin{equation}
\xi_{CR} > \xi_{CG}
\end{equation}
where,
\begin{equation}
\xi_{CG} = {d \;\hbox {log} F_{CG} \over d \;\hbox {log} T_C} \Big {|}_{P_D}
\end{equation}
and
\begin{equation}
\xi_{CR} = {d \;\hbox {log} F_{CR} \over d \;\hbox {log} T_C} \Big {|}_{P_D}
\end{equation}
Here, the derivatives are taken with the underlying disk pressure, $P_D$, held  
constant since the thermal timescale of the disk is much larger than that of the corona.
These logarithmic derivatives are numerically computed and shown in Figs. 5 (a) and (b).
For $\gamma = 0$, Fig 5 (a) shows that $\xi_{CR}$ (solid line) is always greater than
$\xi_{CG}$ (dashed line). 
Hence the corona is thermally stable even when it is radiation
pressure dominated (Fig. 2 f). The underlying disk becomes unstable when 
radiation pressure dominates and hence $\xi_{DR}$ is less than $\xi_{DG}$ (Fig. 5 b)
for $\dot M_T > 4 \times 10^{17}$ g s$^{-1}$. 
Thus, disks with dissipative
coronas with low values of $\gamma$, are both thermally and secularly stable for accretion
rates less than about $ 
4 \times 
10^{17}$ g s$^{-1}$  (for parameter values used in Fig 1) 
corresponding to a luminosity of 
$\approx 2 \times 10^{37}$ ergs/sec or $0.01$ times the Eddington
Luminosity for a 10 solar mass black hole. 

\section{Summary and Discussion} \label{sec: V}

In this study we have investigated the vertical disk structure in the two zone
approximation where 
the disk is divided into a disk and an overlying corona.  
In contrast
to previous studies, the corona is defined as
the upper regions of the disk with an effective optical depth of unity. 
It is
shown that if the scale height of the magnetic field
in the disk is larger than the density scale height, a dissipative corona can form where
significant accretion flow (and hence significant dissipation) takes place. The
topology of such disk solutions differs from that of the standard disk
solutions. For the case when the magnetic scale height is much greater than
the disk scale height (i.e. when the magnetic field is constant in the vertical
direction corresponding to $\gamma = 0$), the disk is both thermally and
secularly stable for accretion rates less than $\dot M = 4 \times 10^{17}$ g s$^{-1}$ (
for a ten solar mass black hole and $R = 20 GM/c^2$)
as compared to $\dot M = 10^{17}$ g s$^{-1}$ for 
the standard disk. Although this accretion rate is nearly independent  of the
viscosity parameterization, $\dot M \propto \beta^{0.2}$ (Fig. 3), 
it is possible that it may be  higher if either  a) the
magnetic field in the corona is larger than that in the disk (i.e. $\gamma < 0$) or
b) if a significant amount of the energy dissipated in the disk is transported
non-radiatively to the corona. We 
defer
such detailed and perhaps more speculative
studies for a future work.
Thus, disks with dissipative coronas 
may provide a more attractive explanation for the source of the high luminosity soft spectral
component observed in black hole X-ray binary systems. 

The two zone approximation employed in this study, simplifies the disk equations to algebraic
form and provides qualitative insight into the existence and effect of dissipative coronas.
Clearly, there is a need to confirm these results and to obtain quantitative solutions by  
constructing models based on calculations of the vertical radiative transfer differential 
equations.  The simple analysis undertaken here
points not only to the possible existence of dissipative coronas but also provides a 
description of qualitative different boundary conditions required for the solution  
of the radiative
transfer equations. The complete radiative transfer analysis will also yield theoretical
emergent spectra from such disks which can then be compared with observations of black hole 
X-ray binary systems.
Such meaningful comparisons with observations would provide a test for the hypothesis 
that
the soft X-ray emission originates from disks with dissipative coronas

\acknowledgements


We thank the referee for the detailed comments which has significantly improved 
the manuscript.  
R.M. gratefully acknowledges support from  the Lindheimer Fellowship at 
Northwestern University. 

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\bibitem[] {}Ross, R. R. \&  Fabian, A. C. 1996, \mnras, 281, 637

\bibitem[]{}Shakura, N. I., \& Sunyaev, R.A. 1973, \aap, 24, 337

\bibitem[]{}Shakura, N. I., \& Sunyaev, R.A. 1976, \mnras, 175, 613

\bibitem[] {}Shapiro, S. L., Lightman A. P. \& Eardley, D. M. 1976, \apj, 204, 187

\bibitem[] {}Shimura, T. \& Takahara, F. 1995, \apj, 445, 780

\bibitem[] {}Svensson, R., \& Zdziarski, A. 1994, \apj, 436, 599

\bibitem[] {} Taam, R. E. \& Lin, D. C. N. 1984, \apj, 287, 761

\bibitem[] {}Zycki, P. T., Collin-Souffrin, S., \& Czerny, B. 1995, \mnras, 277, 70
\end{thebibliography}

\input psbox.tex

\begin{figure*}[h]
\hspace{-1.5cm}
{\mbox{\psboxto(17cm;20cm){f1.eps}}}
\caption{ Total accretion rate ($\dot M_T = \dot M_C + \dot M_D$) versus
total optical depth ($\tau_T$). Curve 1: $\gamma = 0.5$.  Curve 2: 
$\gamma = 0.25$.  Curve 3: $\gamma = 0$. Dashed
line is for the standard accretion disk solutions. The solutions have
been terminated when the effective optical depth of the disk becomes
inconsistently less than unity.  }
\end{figure*}

\begin{figure*}[h]
\hspace{-1.5cm}
{\mbox{\psboxto(17cm;20cm){f2.eps}}}
\caption{Variation of various  ratios with accretion rate. Parameters
and curve numbers ( corresponding to different values of $\gamma$) are same
as in Fig 1. Note that in general $\tau_D >> \tau_C$ and for $\gamma < 0.25$
the coronal accretion rate is always comparable to the disk accretion rate.}
\end{figure*}


\begin{figure*}[h]
\hspace{-1.5cm}
{\mbox{\psboxto(17cm;20cm){f3.eps}}}
\caption{Total accretion rate ($\dot M_T = \dot M_C + \dot M_D$) versus
total optical depth ($\tau_T$). Curve 1: $\beta_D = 0.25$.  Curve 2: 
$\beta_D = 0.1$.  Curve 3: $\beta_D = 0.05$. }
\end{figure*}

\begin{figure*}[h]
\hspace{-1.5cm}
{\mbox{\psboxto(17cm;20cm){f4.eps}}}
\caption{ Total accretion rate ($\dot M_T = \dot M_C + \dot M_D$) versus
total optical depth ($\tau_T$). Curve 1: $R = 40 GM/c^2$.  Curve 2: 
$R = 20 GM/c^2$.  Curve 3: $R = 10 GM/c^2$.}
\end{figure*}

\begin{figure*}[h]
\hspace{-1.5cm}
{\mbox{\psboxto(17cm;20cm){f5.eps}}}
\caption{ (a) $\xi_{CG}$ (dashed line) and $\xi_{CR}$ (solid line)  versus accretion rate for $\gamma = 0$
(curve 3 of Figure 1). The corona is thermally stable. (b) 
 $\xi_{DG}$ (dashed line) and $\xi_{DR}$ (solid line) versus accretion rate for $\gamma = 0$
(curve 3 of Figure 1). The disk is thermally stable for accretion rate
less $4 \times 10^{17}$ g/sec.}
\end{figure*}


\end{document}











psbox.tex
%
%       %%%%%%%    %%%%%        %%%%%%    %%%%%   %     %
%       %      %  %             %     %  %     %   %   %
%       %      %  %             %     %  %     %    % %
%       %%%%%%%    %%%%%        %%%%%%   %     %     %
%       %               %       %     %  %     %    % %
%       %               %       %     %  %     %   %   %
%       %         %%%%%%        %%%%%%    %%%%%   %     %
%
%       By Jean Orloff
%
% WHAT IS IT:
% psbox is a set of machine-independent TeX macros to
% 1) allow (Encapsulated) PostScript figure inclusion in all versions
%    of TeX (Plain, LaTeX) on all machines using a PostScript printer
% 2) facilitate the communication (e-mail, ftp, ...) of all the files
%    (text, macros, figs) needed to reproduce a TeX document by grouping
%    them together into a single, TeXable file.
%
% History:
%  1.34  \readfilename=final fix for all filename scans; try \psforptips
%  1.33: corrects \psnewinput for LaTeX (still fails if fname=a{b}c)
%  1.32: corrects \psfordvialw and adds .TEX to PSBOXALL(!)
%  1.31: adds \psfordvialw(?)
%  1.30: adds \splitfile & \joinfiles for multi-file management
%  1.24: fix error handling & add \psonlyboxes
%  1.22: makes \drawingBox \global for use in Phyzzx
%  1.21: accepts %%BoundingBox: (atend)
%  1.20: tries to add \psfordvitps for the TeXPS package.
%  1.10: adds \psforoztex, error handling...
%2345678 1 2345678 2 2345678 3 2345678 4 2345678 5 2345678 6 2345678 7 23456789
%
% Checking version no to avoid multiple loadings
\def\temp{1.34}%
\let\tempp=\relax
\expandafter\ifx\csname psboxversion\endcsname\relax
  \message{PSBOX(\temp) loading}%
\else
    \ifdim\temp cm>\psboxversion cm
      \message{PSBOX(\temp) loading}%
    \else
      \message{PSBOX(\psboxversion) is already loaded: I won't load
        PSBOX(\temp)!}%
      \let\temp=\psboxversion
      \let\tempp=\endinput
    \fi
\fi
\tempp
\let\psboxversion=\temp
\catcode`\@=11
% Every macro likes a little privacy...
%
%Trying to tame the variety of \special commands for Postscript: the
%  universal internal command \PSspeci@l##1##2 takes ##1 to be the
%  filename and ##2 to be the integer scale factor*1000 (as for usual
%   TeX \scale commands)
%
\def\psfortextures{%     For TeXtures on the Macintosh
%-----------------
\def\PSspeci@l##1##2{%
\special{illustration ##1\space scaled ##2}%
}}%
\def\psfordvitops{%      For the DVItoPS converter on IBM mainframes
%----------------
\def\PSspeci@l##1##2{%
\special{dvitops: import ##1\space \the\drawingwd \the\drawinght}%
}}%
\def\psfordvips{%      For DVIPS converter on VAX, UNIX and PC's
%--------------
\def\PSspeci@l##1##2{%
%    \special{/@scaleunit 1000 def}% never read dox without trying!
\d@my=0.1bp \d@mx=\drawingwd \divide\d@mx by\d@my% BUG! for large \drawingwd
\special{PSfile=##1\space llx=\psllx\space lly=\pslly\space%
urx=\psurx\space ury=\psury\space rwi=\number\d@mx
}}}%
\def\psforoztex{%        For the OzTeX shareware on the Macintosh
%--------------
\def\PSspeci@l##1##2{%
\special{##1 \space
      ##2 1000 div dup scale
      \number-\psllx\space \number-\pslly\space translate
}}}%
\def\psfordvitps{%       From the UNIX TeXPS package, vers.>3.12
%---------------
% Convert a dimension into the number \psn@sp (in scaled points)
\def\psdimt@n@sp##1{\d@mx=##1\relax\edef\psn@sp{\number\d@mx}}
\def\PSspeci@l##1##2{%
% psfig.psr contains the def of "startTexFig": if you can locate it
% and include the correct pathname, it should work
\special{dvitps: Include0 "psfig.psr"}% contains def of "startTexFig"
\psdimt@n@sp{\drawingwd}
\special{dvitps: Literal "\psn@sp\space"}
\psdimt@n@sp{\drawinght}
\special{dvitps: Literal "\psn@sp\space"}
\psdimt@n@sp{\psllx bp}
\special{dvitps: Literal "\psn@sp\space"}
\psdimt@n@sp{\pslly bp}
\special{dvitps: Literal "\psn@sp\space"}
\psdimt@n@sp{\psurx bp}
\special{dvitps: Literal "\psn@sp\space"}
\psdimt@n@sp{\psury bp}
\special{dvitps: Literal "\psn@sp\space startTexFig\space"}
\special{dvitps: Include1 "##1"}
\special{dvitps: Literal "endTexFig\space"}
}}%
\def\psfordvialw{%   Try for dvialw, a UNIX public domain
%---------------
\def\PSspeci@l##1##2{
\special{language "PostScript",
position = "bottom left",
literal "  \psllx\space \pslly\space translate
  ##2 1000 div dup scale
  -\psllx\space -\pslly\space translate",
include "##1"}
}}%
\def\psforptips{%   For MS-DOS; LUOMA@brandeis.bitnet
%---------------
\def\PSspeci@l##1##2{{
\d@mx=\psurx bp
\advance \d@mx by -\psllx bp
\divide \d@mx by 1000\multiply\d@mx by \xscale
\incm{\d@mx}
\let\tmpx\dimincm
\d@my=\psury bp
\advance \d@my by -\pslly bp
\divide \d@my by 1000\multiply\d@my by \xscale
\incm{\d@my}
\let\tmpy\dimincm
\d@mx=-\psllx bp
\divide \d@mx by 1000\multiply\d@mx by \xscale
\d@my=-\pslly bp
\divide \d@my by 1000\multiply\d@my by \xscale
\at(\d@mx;\d@my){\special{ps:##1 x=\tmpx, y=\tmpy}}
}}}%
\def\psonlyboxes{%     Draft-like behaviour if none of the others works
%---------------
\def\PSspeci@l##1##2{%
\at(0cm;0cm){\boxit{\vbox to\drawinght
  {\vss\hbox to\drawingwd{\at(0cm;0cm){\hbox{({\tt##1})}}\hss}}}}
}}%
\def\psloc@lerr#1{%
\let\savedPSspeci@l=\PSspeci@l%
\def\PSspeci@l##1##2{%
\at(0cm;0cm){\boxit{\vbox to\drawinght
  {\vss\hbox to\drawingwd{\at(0cm;0cm){\hbox{({\tt##1}) #1}}\hss}}}}
\let\PSspeci@l=\savedPSspeci@l% restore normal output for other figs!
}}%
%\def\psfor...  add your own!
%
% Some common defs
%
\newread\pst@mpin
\newdimen\drawinght\newdimen\drawingwd
\newdimen\psxoffset\newdimen\psyoffset
\newbox\drawingBox
\newcount\xscale \newcount\yscale \newdimen\pscm\pscm=1cm
\newdimen\d@mx \newdimen\d@my
\newdimen\pswdincr \newdimen\pshtincr
\let\ps@nnotation=\relax
{\catcode`\|=0 |catcode`|\=12 |catcode`|%=12 |catcode`~=12
|catcode`#=12 |catcode`*=14
|xdef|backslashother{\}*
|xdef|percentother{%}*
|xdef|tildeother{~}*
|xdef|sharpother{#}*
}%
% useful to display special chars in \tt; fails for \,#,%
\def\R@moveMeaningHeader#1:->{}%
\def\uncatcode#1{%
\edef#1{\expandafter\R@moveMeaningHeader\meaning#1}}%
%
\def\execute#1{#1}% NOT stupid: cs in #1 are then identified BEFORE execution
\def\psm@keother#1{\catcode`#112\relax}% borrowed from latex
\def\executeinspecs#1{%
\execute{\begingroup\let\do\psm@keother\dospecials\catcode`\^^M=9#1\endgroup}}%
\def\@mpty{}%
% \if\matchin#1#2<=> \iftrue if #1 contains #2, <=>\iffalse otherwise:
% \if\matchexpin: idem, but #1 & #2 are first fully expanded (no \if
% inside!)
% \tmpa & \tmpb contain what's before and after the occurence of #2
\def\matchexpin#1#2{
  \fi%
%\message{(#1>#2)}
  \edef\tmpb{{#2}}%
  \expandafter\makem@tchtmp\tmpb%
  \edef\tmpa{#1}\edef\tmpb{#2}%
  \expandafter\expandafter\expandafter\m@tchtmp\expandafter\tmpa\tmpb\endm@tch%
  \if\match%
}%
\def\matchin#1#2{%
  \fi%
  \makem@tchtmp{#2}%
  \m@tchtmp#1#2\endm@tch%
  \if\match%
}%
\def\makem@tchtmp#1{\def\m@tchtmp##1#1##2\endm@tch{%
  \def\tmpa{##1}\def\tmpb{##2}\let\m@tchtmp=\relax%
  \ifx\tmpb\@mpty\def\match{YN}%
  \else\def\match{YY}\fi%
}}%
% converts any dimen in cm, with 1E-4 cm precision
\def\incm#1{{\psxoffset=1cm\d@my=#1
 \d@mx=\d@my
  \divide\d@mx by \psxoffset
  \xdef\dimincm{\number\d@mx.}
  \advance\d@my by -\number\d@mx cm
  \multiply\d@my by 100
 \d@mx=\d@my
  \divide\d@mx by \psxoffset
  \edef\dimincm{\dimincm\number\d@mx}
  \advance\d@my by -\number\d@mx cm
  \multiply\d@my by 100
 \d@mx=\d@my
  \divide\d@mx by \psxoffset
  \xdef\dimincm{\dimincm\number\d@mx}
}}%
%
%  \ReadPSize{PSfilename} reads the dimensions of a PostScript drawing
%      and stores it in \drawinght(wd)
\newif\ifNotB@undingBox
\newhelp\PShelp{Proceed: you'll have a 5cm square blank box instead of
your graphics (Jean Orloff).}%
\def\s@tsize#1 #2 #3 #4\@ndsize{
  \def\psllx{#1}\def\pslly{#2}%
  \def\psurx{#3}\def\psury{#4}%  needed by a crazyness of dvips!
  \ifx\psurx\@mpty\NotB@undingBoxtrue% this is not a valid one!
  \else
    \drawinght=#4bp\advance\drawinght by-#2bp
    \drawingwd=#3bp\advance\drawingwd by-#1bp
%  !Units related by crazy factors as bp/pt=72.27/72 should be BANNED!
  \fi
  }%
\def\sc@nBBline#1:#2\@ndBBline{\edef\p@rameter{#1}\edef\v@lue{#2}}%
\def\g@bblefirstblank#1#2:{\ifx#1 \else#1\fi#2}%
{\catcode`\%=12
\xdef\B@undingBox{%%BoundingBox}}%
%% is not a true comment in PostScript, even if % is!
\def\ReadPSize#1{
 \readfilename#1\relax
 \let\PSfilename=\lastreadfilename
 \openin\pst@mpin=#1\relax
 \ifeof\pst@mpin \errhelp=\PShelp
   \errmessage{I haven't found your postscript file (\PSfilename)}%
   \psloc@lerr{was not found}%
   \s@tsize 0 0 142 142\@ndsize
   \closein\pst@mpin
 \else
% each entry in \GlobalInputList should be unique
   \if\matchexpin{\GlobalInputList}{, \lastreadfilename}%
   \else\xdef\GlobalInputList{\GlobalInputList, \lastreadfilename}%
     \immediate\write\psbj@inaux{\lastreadfilename,}%
   \fi%
   \loop
     \executeinspecs{\catcode`\ =10\global\read\pst@mpin to\n@xtline}%
     \ifeof\pst@mpin
       \errhelp=\PShelp
       \errmessage{(\PSfilename) is not an Encapsulated PostScript File:
           I could not find any \B@undingBox: line.}%
       \edef\v@lue{0 0 142 142:}%
       \psloc@lerr{is not an EPSFile}%
       \NotB@undingBoxfalse
     \else
       \expandafter\sc@nBBline\n@xtline:\@ndBBline
       \ifx\p@rameter\B@undingBox\NotB@undingBoxfalse
         \edef\t@mp{%
           \expandafter\g@bblefirstblank\v@lue\space\space\space}%
         \expandafter\s@tsize\t@mp\@ndsize
       \else\NotB@undingBoxtrue
       \fi
     \fi
   \ifNotB@undingBox\repeat
   \closein\pst@mpin
 \fi
\message{#1}%
}%
%
% \psboxto(xdim;ydim){psfilename}: you specify the dimensions and
%    TeX uniformly scales to fit the largest one. If xdim=0pt, the
%    scale is fully determined by ydim and vice versa.
%    Notice: psboxes are a real vboxes; couldn't take hbox otherwise all
%    indentation and all cr's would be interpreted as spaces (hugh!).
%
\def\psboxto(#1;#2)#3{\vbox{
   \ReadPSize{#3}%
   \divide\drawingwd by 1000
   \divide\drawinght by 1000
   \d@mx=#1
   \ifdim\d@mx=0pt\xscale=1000
         \else \xscale=\d@mx \divide \xscale by \drawingwd\fi
   \d@my=#2
   \ifdim\d@my=0pt\yscale=1000
         \else \yscale=\d@my \divide \yscale by \drawinght\fi
   \ifnum\yscale=1000
         \else\ifnum\xscale=1000\xscale=\yscale
                    \else\ifnum\yscale<\xscale\xscale=\yscale\fi
              \fi
   \fi
   \divide\pswdincr by 1000 \multiply\pswdincr by \xscale
   \divide\pshtincr by 1000 \multiply\pshtincr by \xscale
   \divide\psxoffset by1000 \multiply\psxoffset by\xscale
   \divide\psyoffset by1000 \multiply\psyoffset by\xscale
   \global\divide\pscm by 1000
   \global\multiply\pscm by\xscale
   \multiply\drawingwd by\xscale \multiply\drawinght by\xscale
   \ifdim\d@mx=0pt\d@mx=\drawingwd\fi
   \ifdim\d@my=0pt\d@my=\drawinght\fi
   \message{scaled \the\xscale}%
 \hbox to\d@mx{\hss\vbox to\d@my{\vss
   \global\setbox\drawingBox=\hbox to 0pt{\kern\psxoffset\vbox to 0pt{
      \kern-\psyoffset
      \PSspeci@l{\PSfilename}{\the\xscale}%
      \vss}\hss\ps@nnotation}%
   \advance\pswdincr by \drawingwd
   \advance\pshtincr by \drawinght
   \global\wd\drawingBox=\the\pswdincr
   \global\ht\drawingBox=\the\pshtincr
   \baselineskip=0pt
   \copy\drawingBox
 \vss}\hss}%
  \global\psxoffset=0pt
  \global\psyoffset=0pt
  \global\pswdincr=0pt
  \global\pshtincr=0pt % These are local to one figure
  \global\pscm=1cm %should not be necessary
  \global\drawingwd=\drawingwd
  \global\drawinght=\drawinght
}}%
%
% \psboxscaled{scalefactor*1000}{PSfilename} allows to bypass the
%   rounding errors of TeX integer divisions for situations where the
%   TeX box should fit the original BoundingBox with a precision better
%   than 1/1000.
%
\def\psboxscaled#1#2{\vbox{
  \ReadPSize{#2}%
  \xscale=#1
  \message{scaled \the\xscale}%
  \advance\drawingwd by\pswdincr\advance\drawinght by\pshtincr
  \divide\pswdincr by 1000 \multiply\pswdincr by \xscale
  \divide\pshtincr by 1000 \multiply\pshtincr by \xscale
  \divide\psxoffset by1000 \multiply\psxoffset by\xscale
  \divide\psyoffset by1000 \multiply\psyoffset by\xscale
  \divide\drawingwd by1000 \multiply\drawingwd by\xscale
  \divide\drawinght by1000 \multiply\drawinght by\xscale
  \global\divide\pscm by 1000
  \global\multiply\pscm by\xscale
  \global\setbox\drawingBox=\hbox to 0pt{\kern\psxoffset\vbox to 0pt{
     \kern-\psyoffset
     \PSspeci@l{\PSfilename}{\the\xscale}%
     \vss}\hss\ps@nnotation}%
  \advance\pswdincr by \drawingwd
  \advance\pshtincr by \drawinght
  \global\wd\drawingBox=\the\pswdincr
  \global\ht\drawingBox=\the\pshtincr
  \baselineskip=0pt
  \copy\drawingBox
  \global\psxoffset=0pt
  \global\psyoffset=0pt
  \global\pswdincr=0pt
  \global\pshtincr=0pt % These are local to one figure
  \global\pscm=1cm
  \global\drawingwd=\drawingwd
  \global\drawinght=\drawinght
}}%
%
%  \psbox{PSfilename} makes a TeX box having the minimal size to
%      enclose the picture
\def\psbox#1{\psboxscaled{1000}{#1}}%
%------------------------------------------------------
%  \joinfiles file1, file2, ...n \into joinedfilename .
%     makes one file out of many
%  \splitfile joinedfilename
%     the opposite
\newif\ifn@teof\n@teoftrue
\newif\ifc@ntrolline
\newif\ifmatch
\newread\j@insplitin
\newwrite\j@insplitout
\newwrite\psbj@inaux
\immediate\openout\psbj@inaux=psbjoin.aux
\immediate\write\psbj@inaux{\string\joinfiles}%
\immediate\write\psbj@inaux{\jobname,}%
%
% INPUT REDEFINITION
%
% works if #1 is a single character
\def\toother#1{\ifcat\relax#1\else\expandafter%
  \toother@ux\meaning#1\endtoother@ux\fi}%
\def\toother@ux#1 #2#3\endtoother@ux{\def\tmp{#3}%
  \ifx\tmp\@mpty\def\tmp{#2}\let\next=\relax%
  \else\def\next{\toother@ux#2#3\endtoother@ux}\fi%
\next}%
%
% \readfilename defs:
%
\let\readfilenamehook=\relax
\def\re@d{\expandafter\re@daux}% spares typing 10 \expandafter's...
\def\re@daux{\futurelet\nextchar\stopre@dtest}%
\def\re@dnext{\xdef\lastreadfilename{\lastreadfilename\nextchar}%
  \afterassignment\re@d\let\nextchar}%
\def\stopre@d{\egroup\readfilenamehook}%
\def\stopre@dtest{%
  \ifcat\nextchar\relax\let\nextread\stopre@d
  \else
    \ifcat\nextchar\space\def\nextread{%
      \afterassignment\stopre@d\chardef\nextchar=`}%
    \else\let\nextread=\re@dnext
      \toother\nextchar
      \edef\nextchar{\tmp}%
    \fi
  \fi\nextread}%
\def\readfilename{\vbox\bgroup%
  \let\\=\backslashother \let\%=\percentother \let\~=\tildeother
  \let\#=\sharpother \xdef\lastreadfilename{}%
  \re@d}%
%
% redefines \input using \readfilename
%
\xdef\GlobalInputList{\jobname}%
\def\psnewinput{%
  \def\readfilenamehook{% each entry in \GlobalInputList should be unique
    \if\matchexpin{\GlobalInputList}{, \lastreadfilename}%
    \else\xdef\GlobalInputList{\GlobalInputList, \lastreadfilename}%
      \immediate\write\psbj@inaux{\lastreadfilename,}%
    \fi%
    \ps@ldinput\lastreadfilename\relax%
    \let\readfilenamehook=\relax%
  }\readfilename%
}%
\expandafter\ifx\csname @@input\endcsname\relax    % then Plain
  \immediate\let\ps@ldinput=\input\def\input{\psnewinput}%
\else
  \immediate\let\ps@ldinput=\@@input
  \def\@@input{\psnewinput}%
\fi%
%
\def\nowarnopenout{%
 \def\warnopenout##1##2{%
   \readfilename##2\relax
   \message{\lastreadfilename}%
   \immediate\openout##1=\lastreadfilename\relax}}%
\def\warnopenout#1#2{%
 \readfilename#2\relax
 \def\t@mp{TrashMe,psbjoin.aux,psbjoint.tex,}\uncatcode\t@mp
 \if\matchexpin{\t@mp}{\lastreadfilename,}%
 \else
   \immediate\openin\pst@mpin=\lastreadfilename\relax
   \ifeof\pst@mpin
     \else
     \errhelp{If the content of this file is so precious to you, abort (ie
press x or e) and rename it before retrying.}%
     \errmessage{I'm just about to replace your file named \lastreadfilename}%
   \fi
   \immediate\closein\pst@mpin
 \fi
 \message{\lastreadfilename}%
 \immediate\openout#1=\lastreadfilename\relax}%
% % will have an unusual catcode below; use * instead
%\vbox
{\catcode`\%=12\catcode`\*=14
\gdef\splitfile#1{*
 \readfilename#1\relax
 \immediate\openin\j@insplitin=\lastreadfilename\relax
 \ifeof\j@insplitin
   \message{! I couldn't find and split \lastreadfilename!}*
 \else
   \immediate\openout\j@insplitout=TrashMe
   \message{< Splitting \lastreadfilename\space into}*
   \loop
     \ifeof\j@insplitin
       \immediate\closein\j@insplitin\n@teoffalse
     \else
       \n@teoftrue
       \executeinspecs{\global\read\j@insplitin to\spl@tinline\expandafter
         \ch@ckbeginnewfile\spl@tinline%Beginning-Of-File-Named:%\endcheck}*
       \ifc@ntrolline
       \else
         \toks0=\expandafter{\spl@tinline}*
         \immediate\write\j@insplitout{\the\toks0}*
       \fi
     \fi
   \ifn@teof\repeat
   \immediate\closeout\j@insplitout
 \fi\message{>}*
}*
\gdef\ch@ckbeginnewfile#1%Beginning-Of-File-Named:#2%#3\endcheck{*
 \def\t@mp{#1}*
 \ifx\@mpty\t@mp
   \def\t@mp{#3}*
   \ifx\@mpty\t@mp
     \global\c@ntrollinefalse
   \else
     \immediate\closeout\j@insplitout
     \warnopenout\j@insplitout{#2}*
     \global\c@ntrollinetrue
   \fi
 \else
   \global\c@ntrollinefalse
 \fi}*
\gdef\joinfiles#1\into#2{*
 \message{< Joining following files into}*
 \warnopenout\j@insplitout{#2}*
 \message{:}*
 {*
 \edef\w@##1{\immediate\write\j@insplitout{##1}}*
\w@{% This collection of files was produced with CERN psbox package}*
\w@{% To decompose and tex it:}*
\w@{%-save this with a filename CONTAINING ONLY LETTERS and a .TEX}*
\w@{% extension (say, JOINTFIL.TEX), in some uncrowded directory;}*
\w@{%-make sure you can \string\input\space psbox.tex (version>=1.3);}*
\w@{%  (else ftp cs.nyu.edu(=128.122.140.24):pub/TeX/psbox/, then get}*
\w@{%  and tex the file psboxall.tex; more info in psbREAD.ME)}*
\w@{%-tex JOINTFIL.TEX using Plain, or LaTeX, or whatever is needed by}*
\w@{%  the first file in the joining (after splitting JOINTFIL.TEX into}*
\w@{%  it's constituents, TeX will try to process it as it stands).}*
\w@{\string\input\space psbox.tex}*
\w@{\string\splitfile{\string\jobname}}*
\w@{\string\let\string\autojoin=\string\relax}*
}*
 \expandafter\tre@tfilelist#1, \endtre@t
 \immediate\closeout\j@insplitout
 \message{>}*
}*
\gdef\tre@tfilelist#1, #2\endtre@t{*
 \readfilename#1\relax
 \ifx\@mpty\lastreadfilename
 \else
   \immediate\openin\j@insplitin=\lastreadfilename\relax
   \ifeof\j@insplitin
     \errmessage{I couldn't find file \lastreadfilename}*
   \else
     \message{\lastreadfilename}*
     \immediate\write\j@insplitout{%Beginning-Of-File-Named:\lastreadfilename}*
     \executeinspecs{\global\read\j@insplitin to\oldj@ininline}*
     \loop
       \ifeof\j@insplitin\immediate\closein\j@insplitin\n@teoffalse
       \else\n@teoftrue
         \executeinspecs{\global\read\j@insplitin to\j@ininline}*
         \toks0=\expandafter{\oldj@ininline}*
         \let\oldj@ininline=\j@ininline
         \immediate\write\j@insplitout{\the\toks0}*
       \fi
     \ifn@teof
     \repeat
   \immediate\closein\j@insplitin
   \fi
   \tre@tfilelist#2, \endtre@t
 \fi}*
}%
% To be put at the end of a file, for making a tar-like file containing
%   everything it used.
\def\autojoin{%
 \immediate\write\psbj@inaux{\string\into{psbjoint.tex}}%
 \immediate\closeout\psbj@inaux
 \expandafter\joinfiles\GlobalInputList\into{psbjoint.tex}%
}%
%----------------------------------------------------------------
%  Annotations & Captions etc...
%
%
% \centinsert{anybox} is just a centered \midinsert, but is included as
%    people barely use the original inserts from TeX.
%
\def\centinsert#1{\midinsert\line{\hss#1\hss}\endinsert}%
\def\psannotate#1#2{\vbox{%
  \def\ps@nnotation{#2\global\let\ps@nnotation=\relax}#1}}%
\def\pscaption#1#2{\vbox{%
   \setbox\drawingBox=#1
   \copy\drawingBox
   \vskip\baselineskip
   \vbox{\hsize=\wd\drawingBox\setbox0=\hbox{#2}%
     \ifdim\wd0>\hsize
       \noindent\unhbox0\tolerance=5000
    \else\centerline{\box0}%
    \fi
}}}%
% for compatibility with older versions, but \psfig is a bad name!
%\def\psfig#1#2#3{\pscaption{\psannotate{#1}{#2}}{#3}}
%\def\psfigurebox#1#2#3{\pscaption{\psannotate{\psbox{#1}}{#2}}{#3}}
%
% \at(#1;#2)#3 puts #3 at #1-higher and #2-right of the current
%    position without moving it (to be used in annotations).
\def\at(#1;#2)#3{\setbox0=\hbox{#3}\ht0=0pt\dp0=0pt
  \rlap{\kern#1\vbox to0pt{\kern-#2\box0\vss}}}%
%
% \gridfill(ht;wd) makes a 1cm*1cm grid of ht by wd whose lower-left
%   corner is the current point
\newdimen\gridht \newdimen\gridwd
\def\gridfill(#1;#2){%
  \setbox0=\hbox to 1\pscm
  {\vrule height1\pscm width.4pt\leaders\hrule\hfill}%
  \gridht=#1
  \divide\gridht by \ht0
  \multiply\gridht by \ht0
  \gridwd=#2
  \divide\gridwd by \wd0
  \multiply\gridwd by \wd0
  \advance \gridwd by \wd0
  \vbox to \gridht{\leaders\hbox to\gridwd{\leaders\box0\hfill}\vfill}}%
%
% Useful to measure where to put annotations
\def\fillinggrid{\at(0cm;0cm){\vbox{%
  \gridfill(\drawinght;\drawingwd)}}}%
%
% \textleftof\anybox: Sample text\endtext
%   inserts "Sample text" on the left of \anybox ie \vbox, \psbox.
%   \textrightof is the symmetric (not documented, too uggly)
% Welcome any suggestion about clean wraparound macros from
%   TeXhackers reading this
%
\def\textleftof#1:{%
  \setbox1=#1
  \setbox0=\vbox\bgroup
    \advance\hsize by -\wd1 \advance\hsize by -2em}%
\def\textrightof#1:{%
  \setbox0=#1
  \setbox1=\vbox\bgroup
    \advance\hsize by -\wd0 \advance\hsize by -2em}%
\def\endtext{%
  \egroup
  \hbox to \hsize{\valign{\vfil##\vfil\cr%
\box0\cr%
\noalign{\hss}\box1\cr}}}%
%
% \frameit{\thick}{\skip}{\anybox}
%    draws with thickness \thick a box around \anybox, leaving \skip of
%    blank around it. eg \frameit{0.5pt}{1pt}{\hbox{hello}}
% \boxit{\anybox} is a shortcut.
\def\frameit#1#2#3{\hbox{\vrule width#1\vbox{%
  \hrule height#1\vskip#2\hbox{\hskip#2\vbox{#3}\hskip#2}%
        \vskip#2\hrule height#1}\vrule width#1}}%
\def\boxit#1{\frameit{0.4pt}{0pt}{#1}}%
%
%
\catcode`\@=12 % cs containing @ are unreachable
%
% CUSTOMIZE YOUR DEFAULT DRIVER:
%    Uncomment the line corresponding to your TeX system:
%\psfortextures%     For TeXtures on the Macintosh
%\psforoztex   %     For OzTeX shareware on the Macintosh
%\psfordvitops %     For the DVItoPS converter for TeX on IBM mainframes
 \psfordvips   %     For DVIPS converter on VAX and UNIX
%\psfordvitps  %     For dvitps from TeXPS package under UNIX
%\psfordvialw  %     For dvialw, UNIX public domain
%\psonlyboxes  %     Blank Boxes (when all else fails).

astro-ph0203332.extracted_bib
\begin{thebibliography}{}

\bibitem[] {}Abramowicz, M. A., Chen, X., \& Taam, R. E. 1995, \apj, 452, 379

\bibitem[] {}Balbus, S. A., \& Hawley, J. F. 1991, \apj, 376, 214 

\bibitem[] {}Chen, X. 1995, \apj, 448, 803
 
\bibitem[] {}Esin, McClintock, J.E., \& Narayan, R., 1997, \apj, 489, 865

\bibitem[] {}Haardt, F. \& Maraschi, L. 1993, \apj, 413, 507

\bibitem[] {}Hawley, J. F., Balbus, S. A. \& Stone, J. M. 2001, \apj, 554, L49

\bibitem[] {}Honma, F., Matsumoto, R., \& Kato, S. 1991, \pasj, 43, 147

\bibitem[] {}Ionson, J. A., \& Kuperus, M. 1984, \apj, 284, 389 

\bibitem[] {}Laurent, P. \& Titarchuk, L. 2001, \apj, 562, L67

\bibitem[] {}Liang, E. P., \& Price, R.H. 1977, \apj, 218, 247

\bibitem[] {}Lightman, A. P., \& Eardley, D. M. 1974, \apj, 187, L1

\bibitem[] {}Mirabel, I. F., \& Rodriguez, L. F. 1999, \araa, 37, 409

\bibitem[] {}Misra, R., \& Melia, F. 1996, \apj, 467, 405

\bibitem[] {}Poutanen, J. \& Fabian, A.C. 1999, \mnras, 306, L31

\bibitem[] {}Ross, R. R. \&  Fabian, A. C. 1996, \mnras, 281, 637

\bibitem[]{}Shakura, N. I., \& Sunyaev, R.A. 1973, \aap, 24, 337

\bibitem[]{}Shakura, N. I., \& Sunyaev, R.A. 1976, \mnras, 175, 613

\bibitem[] {}Shapiro, S. L., Lightman A. P. \& Eardley, D. M. 1976, \apj, 204, 187

\bibitem[] {}Shimura, T. \& Takahara, F. 1995, \apj, 445, 780

\bibitem[] {}Svensson, R., \& Zdziarski, A. 1994, \apj, 436, 599

\bibitem[] {} Taam, R. E. \& Lin, D. C. N. 1984, \apj, 287, 761

\bibitem[] {}Zycki, P. T., Collin-Souffrin, S., \& Czerny, B. 1995, \mnras, 277, 70
\end{thebibliography}