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(gzipped) PostScript## Properties of self-gravitating -discs in AGN revisited## General scaling laws
^{1} DAEC et URA 173 du CNRS, Observatoire de Paris-Meudon,
Place Jules Janssen, F-92195 Meudon Cedex, France^{2} Université Paris 7 (Denis Diderot), 2 Place
Jussieu, F-75251 Paris Cedex 05, France
The radial structure of accretion discs in steady state is revisited in the framework of the -theory. The emphasis is mainly placed on the transition from the standard solution to the self-gravitating - and gravitationally unstable - solution. Disc properties are discussed for all accretion rates and central masses relevant to Active Galactic Nuclei; various values of the -parameter are considered. Calculations include realistic equation of state and opacities for a solar metallicity gas. We show that the disc structure is fully determined from a unique
equation and we propose a method to compute its solutions in the
-plane ( is the mass
density, and For accretion rates lower than /yr, the self-gravitating region is found approximately at the radius cm ( and being the accretion rate and the central mass respectively, in solar units). This law is however significantly modified by realistic opacities. For higher accretion rates, one finds cm. In addition to the standard solution, we report the discovery of two other solutions at a same radius, for accretion rates higher than /yr: the one is weakly self-gravitating and the radiative pressure is larger than (or of the same order of) the gas pressure, the other is strongly self-gravitating and the gas pressure dominates on the radiative pressure, but it is gravitationally unstable. This degeneracy is not due to opacities. We discuss the influence of self-gravitation on the thermal, viscous and gravitational instabilities in the -plane using classical criteria. We demonstrate in particular that the thermal instability is not sensitive to self-gravitation. In a first approximation, the gravitational instability occurs at a distance for accretion rates higher than about /yr, and for lower accretion rates. It is inferred that, as long as the -prescription holds, discs with should not be concerned with the thermal instability associated with the partial ionization of hydrogen. Finally, we deduce that the typical mass of the fragments which could form inside the gravitationally unstable disc increases with increasing accretion rate and it should not exceed ten solar masses for accretion rates lower than about 1 /yr, whatever the -parameter. The critical radii and
derived in this study are given as functions of
, and
Online publication: August 17, 1998 |