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Viscous evolution of an accretion disk in a binary system 
Galina V. Lipunova y and Nikolai I. Shakura
Sternberg Astronomical Institute, Moscow State University, Universitetskii pr. 13,
Moscow, 119899 Russia (galja@sai.msu.ru)
Abstract. A new analytical solution describing a time-dependent disk in a binary
system at outburst, which has a xed tidally-truncated outer radius, is applied to
1975 X-ray nova burst of A0620-00. The X-ray ux of a multicolor (black-body)
-disk decays quasi-exponentially with time. Modeling the X-ray and the optical
light curves of A0620-00, we can estimate  and obtain `distance{mass of compact
object' relation.
Keywords: accretion disk, close binaries, X-ray novae, A0620-00 (=V616 Mon)
We consider the basic viscous diusion equation (e.g., Lipunova and
Shakura, 2000) as applied to accretion disks. This equation shows that
the time behaviour of a disk depends on the relation between kinematic
coeфcient of turbulent viscosity , column density of a disk , and
radius r.
If  is a function of radius alone, the basic dierential equation of
diusion type is linear. This case was considered by Weizsacker (1948),
Lust (1952), Lynden-Bell and Pringle (1974).
The general case, when  is a power{law function of  and r, was
considered by Filipov (1984; 1988), Lyubarskii and Shakura (1987).
We adopt the  /  l r m relation and pioneer in considering a con-
ned accretion disk. We assume specic outer boundary conditions for
a disk in a binary system (Lipunova and Shakura, 2000) and obtain a
new solution. The standard -model of the viscosity is assumed.
The bolometric luminosity is found to vary with time as a power low
with an index of 5=2, if Thomson scattering dominates the opacity,
and 10=3, if free-free and free-bound transitions do.
Assuming the spectrum to be a multi-color black body one, the X-
ray luminosity is obtained to vary as exp ( t 5=6 ). This is quite close to
the exponential behaviour.
To illustrate how the parameters of the disk can be obtained, we
model the 1975 burst of A0620-00 (Fig. 1). We used the X-ray data in
the 3{6 keV band of Ariel-5 (Kaluzienski et al. 1977) and the data in
B and V optical bands (Kuulkers 1998, and references therein).
 The work is partially supported by the RFBR grant 00{02{17164, the program
`Universitety Rossii' (grant 5559), and NTP `Astronomia' grant 1.4.4.1 (Russia)
y GVL is thankful to Instituto de Astrosica de Andalucia for supporting her
visit to Granada. She is also supported by ISSEP.
c
2000 Kluwer Academic Publishers. Printed in the Netherlands.
allbook.tex; 15/11/2000; 21:23; p.211

212 G.V. Lipunova and N.I.Shakura
Figure 1. A multitude of models is restricted to the following values of parameters:
mx = MBH=M = 525, B V (27th day after peak) = 0:170:26. We checked the
values of : 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6. d is the distance to the
source. The right upper panel displays the corresponding values of to (see Lipunova
and Shakura, 2000) if we set t to be the time after the peak of the outburst, MJD
42638.4 = 13/08/1975.
We see that the model is consistent with the idea of a black hole
in this binary and with the distance estimates available in literature
(Barret et al., 1996; Chen et al., 1997). We choose the models with
E(B V)=0.39 (Wu et al., 1976). From Kuulkers (1998) we have
B V (27 d)= 0.24 (10%), then BH mass lies in the range 9{14 M .
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