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Astron. Astrophys. 337, 625-649 (1998)

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Properties of self-gravitating [FORMULA]-discs in AGN revisited

General scaling laws

Jean-Marc Huré 1, 2

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

Received 24 September 1997 / Accepted 17 June 1998


The radial structure of accretion discs in steady state is revisited in the framework of the [FORMULA]-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 [FORMULA]-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 [FORMULA]-plane ([FORMULA] is the mass density, and T is the midplane temperature). To specify the location of the self-gravitating region relative to the black hole, a close comparison with the standard disc is performed. We establish that self-gravitation plays a role inside the gas pressure dominated region for accretion rates lower than about [FORMULA] [FORMULA]/yr. For higher accretion rates, the radiative pressure dominated region is self-gravitating.

For accretion rates lower than [FORMULA] [FORMULA]/yr, the self-gravitating region is found approximately at the radius [FORMULA] cm ([FORMULA] and [FORMULA] 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 [FORMULA] cm.

In addition to the standard solution, we report the discovery of two other solutions at a same radius, for accretion rates higher than [FORMULA] [FORMULA]/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 [FORMULA]-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 [FORMULA] for accretion rates higher than about [FORMULA] [FORMULA]/yr, and [FORMULA] for lower accretion rates. It is inferred that, as long as the [FORMULA]-prescription holds, discs with [FORMULA] 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 [FORMULA]/yr, whatever the [FORMULA]-parameter.

The critical radii [FORMULA] and [FORMULA] derived in this study are given as functions of [FORMULA], [FORMULA] and M in the appendix in the form of data sets and cover at best the following ranges: [FORMULA], [FORMULA], all central masses.

Key words: accretion, accretion disks – instabilities – galaxies: active – galaxies: nuclei

Send offprint requests to: J.M. Huré (hure@obspm.fr)

© European Southern Observatory (ESO) 1998

Online publication: August 17, 1998