## 1. IntroductionAccretion discs play an important role in astrophysics. Whenever material with some angular momentum falls towards a central object a disc is generally formed. The basic philosophy behind the disc accretion model is the
following: The matter first forms a disk shaped annular structure
around the accreting object at the circularization radii appropriate
to the specific angular momentum of the incoming matter. The thickness
of the disc The disc is basically a 2D structure and all thermodynamic
quantities vary with the cylindrical radial coordinate
and Viscous energy dissipation removes angular momentum and generates
heat. Under certain conditions it is possible that the heat generated
in the process cannot be removed by the radiation and as a consequence
the gas does not cool and cannot be accreted. The gas then moves away
from the z=0 plane and no disc structure forms. Such a possibility can
be seen from the following example. Consider a constant temperature
disc, namely but not
. Next assume the standard assumption
that the heating is proportional to the gas pressure The structure of discs in the vertical direction must allow for the viscous energy released in each volume element. If the disc is in thermal equilibrium, the energy balance dictates an constraint which the hydrostatic equilibrium equation must satisfy. It is this condition which affects so dramatically the structure of the disc in the vertical direction. Shaviv & Wehrse (1986,SW) integrated the vertical structure equations including the radiation field and encountered numerical problems in convergence. They solved the problem by assuming an artificial cutoff in the viscous energy dissipation and in this way were able to obtain disc models and continuum spectra of classical nova disc with high accretion rate. Later Adam et al. (1987) showed how the problem encountered by SW is actually a thermal instability which leads to the formation of corona above the disc. Czerny & King 1989a,b expanded the idea of SW (1986) and considered optically thin layer above an optically thick disc. They confirmed the results of SW and showed that viscous dissipation in the outer atmospheres of unilluminated accretion disc produces hot corona and thermally driven winds. Czerny & King 1989a also obtained a critical accretion rate above which a full hydrostatic equilibrium does not exist. The limiting accretion rate corresponds to where is the critical accretion rate which leads to the Eddington luminosity and is the viscosity constant. Here we treat the optically thick regime and show that the flow starts already in the optically thick region. Dumont et al. (1991) (here after DCKL) discussed the structure of
optically thin accretion disc. In particular, they investigated in
detail the effects NLTE has on the vertically integrated structure
equations. DCKL obtained the energy balance of the disc from equating
the cooling to the required energy dissipation for a given accretion
rate. The basic equations used by DCKL are the vertical height
averaged equations, namely they assumed a height where is the speed of sound and a surface density which is given by where is the total accretion rate and the kinematic viscosity is given by Thus, the first difference between the present treatment and that of DCKL is that DCKL considered averaged equations while here we use the local equation. The second difference is in the energy balance. Given the cooling expressed in terms of the vertical averaged equations, DCKL equate the averaged cooling to the required energy loss for a given accretion rate and thus obtain that: where is the vertically averaged number density of hydrogen nuclei and the vertically averaged cooling rate. The advantage of this approach is that in this way the details of the dissipation mechanism and in particular the assumption expressed in Eq. 3 disappears from the equations. In short, DCKL investigated the radial structure while we here explore the vertical structure. The present work is a further investigation of the instability in the thermal balance of the vertical structure of the disc for low systems. We show that it determines the fate of the entire disc structure. © European Southern Observatory (ESO) 1999 Online publication: March 18, 1999 |