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Astron. Astrophys. 350, 694-704 (1999)

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1. Introduction

For simplicity, traditional models of accretion disks ignore the self-gravity associated with the accreting material and consider the case where the disk is approximately Keplerian (e.g., see Pringle 1981). On the other hand, several studies have been carried out in order to investigate the effects related to the disk self-gravity. Studies of this type have addressed three different levels. The first stage is that where the disk self-gravity is incorporated in the study of the vertical structure of the disk. Here we may recall, among others, the pioneering work by Paczynski (1978) and the very recent analysis by Bardou et al. (1998). The second important level is that where one considers the effects of the disk self-gravity on waves and on transport processes in the disk. Here we may recall a number of interesting analyses, in particular the studies by Lin & Pringle (1987), by Adams et al. (1989), with the modified viscosity prescription proposed by Lin & Pringle (1990) (see also Andalib et al. 1997 and references therein). Recent hydrodynamical simulations (Laughlin & Bodenheimer 1994, Laughlin & Rózyczka 1996, Laughlin et al. 1997) have focused on one key aspect of the modeling of accretion disks. i.e. they have tried to assess whether the standard constant [FORMULA] viscosity prescription (Shakura & Sunyaev 1973) is justified in systems where non-axisymmetric instabilities driven by the disk self-gravity play a major role. The third level where the self-gravity of the disk can be considered is that where, because of the gravitational field contributed by the disk matter, the rotation itself of the accreting material is affected and is no longer kept to be Keplerian. In this direction very few attempts have been made (see, e.g., Bodo & Curir 1992).

The need for investigations where the self-gravity of the disk is properly taken into account, is further stimulated by recent accurate observations that point to significant deviations from Keplerian rotation in objects that are naturally interpreted as accretion disks (e.g., see Greenhill et al. 1996, Moran 1998) and by the finding that in some contexts, especially in the dynamics of protostellar disks, there are empirical indications that the amount of mass in the disk is large (see Hillenbrand et al. 1992, Drimmel 1996). From the theoretical point of view, to address the dynamics of a self-gravitating accretion disk is highly attractive especially because some global regulation aspects that are emerging as interesting and relevant from various lines of thought (see also Coppi 1980) should find a natural manifestation in systems where the long-range forces are bound to generate an inherently global behavior.

The basic framework for the construction of models of accretion disks is traditionally "asymmetric". While the momentum transport equations are generally replaced by a physically based prescription that bypasses our ignorance on the detailed mechanisms that are involved (Shakura & Sunyaev 1973; see also the recent modification proposed by Heyvaerts et al. 1996 and Bardou et al. 1998), the energy transport equations are usually kept in their ideal form, either following a detailed inclusion of the radiation transport across the disk (e.g., see Shakura & Sunyaev 1973; Bardou et al. 1998) or by invoking some ideal "equation of state" and by arguing that the energy dissipated by viscosity is partly redistributed in the disk (see Narayan & Yi 1994 and many following articles). In a situation where we lack strong empirical constraints (such as those that might be available in the laboratory) on the detailed mechanisms at the basis of the various transport processes involved, one might try to explore models where self-gravity, much like in galaxy disks, plays a major role at all the three levels mentioned above, taking the view that both momentum and energy transport equations should be handled heuristically. This is indeed the step taken in an earlier exploratory paper (Bertin 1997), where the viscosity prescription suggested by Shakura & Sunyaev (1973) is retained, and, on a similar footing, the energy transport equations are replaced by a physical condition of self-regulation, related to marginal Jeans stability, as suggested by the dynamics of galaxy disks (see Sect. 3).

In this paper we develop this latter point of view by describing the entire parameter space available for self-regulated accretion disks (Sects. 2 and 4), and by providing two non-trivial extensions of the model. The first extension is that of a "bimodal" disk, where full matching with an inner "standard" Keplerian accretion disk is obtained (see Sect. 5.1). The second extension is the construction of self-regulated accretion disks embedded in a spherical diffuse "halo", which may find application to the extended disk associated with AGN's. The analysis is further strengthened by a careful discussion of the vertical structure of the disk, in such a way that the transition from self-gravity dominated to non-gravitating disks is covered uniformly (Appendix A).

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© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999