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

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6. Discussion

In this paper we have developed a framework for the construction of a class of self-gravitating accretion disks, independently of the specific conditions characterizing the astrophysical systems where the accretion disk paradigm applies. In principle, we might even speculate that the above framework could be the starting point to describe some stages of the formation of protogalactic disks (e.g. see Fall & Efstathiou 1980) or the establishment of some regular extended HI disks in elliptical galaxies (see Morganti et al. 1997). In practice, our class of models appears to be best applicable to two categories of astrophysical objects, i.e. to Active Galactic Nuclei and to protostellar disks. Concrete applications, which will require a detailed consideration of the available observational constraints, are beyond the scope of the present paper. Still we would like to make a few comments that should illustrate why the models appear to be promising for the above categories of objects.

Recently, from radio maser emission, it has been possible to obtain accurate measurements of the rotation of the disk in the central parts of a few Active Galactic Nuclei; these include NGC 4258, NGC 1068, Circinus, NGC 4945, NGC 3079, and NGC 1386 (see Moran, 1998). These measurements have shown that, although in some cases (as for NGC 4258, see Miyoshi et al. 1995) the rotation curve is Keplerian to a high degree of approximation, there may be significant deviations from the [FORMULA] profile. For example, in NGC 1068 the rotation velocity at distances [FORMULA] pc from the "center" turns out to decline as [FORMULA] (see Greenhill et al. 1996; Kumar 1999). The general conclusion is that rather extended disks, which may contain large amounts of mass, are present; indeed one possible reason for the deviation from the Keplerian decline has been identified in the influence of the gravitational field contributed by the accretion disk itself. At the same time, the application of "standard" accretion disk models to some of these objects has led to finding values of the Q parameter well below unity (for NGC 1068, see Kumar 1999). All these are clues that show that a model where the role of the disk self-gravity is fully incorporated is called for. Note that if we adopt the numbers suggested by the data for NGC 1068 we would find [FORMULA] pc and [FORMULA]; then, it is curious to find that a self-regulated disk with these characteristics would have, for [FORMULA], a gradient of the rotation curve at [FORMULA] pc compatible with [FORMULA].

On a completely different mass scale, if we refer to the case of protostellar disks, typically quoted parameters are [FORMULA] and [FORMULA] (Hartmann et al. 1998). Under these circumstances we find [FORMULA] AU and [FORMULA]. Interestingly, protostellar disks have been observed to extend out to a radius from [FORMULA] AU to [FORMULA] AU (Dutrey et al. 1996; McCaughrean & O'Dell 1996). As for the case of AGN's, a check on the values of the temperatures anticipated on the basis of the effective thermal speeds predicted by the self-regulated models shows that the numbers fall reasonably within the range suggested by the observations.

Finally, it is interesting to note that studies of the spherical, inviscid collapse of a molecular cloud, imagined to eventually generate a system composed of a protostar and a circumstellar disk, lead to mass accretion rates [FORMULA] (Hunter 1977, Shu 1977), curiously analogous to those of our completely different accretion scenario. This coincidence may offer interesting clues for modeling the entire process where a cloud, starting out in an initially spherical collapse, ends up in a protostellar accretion disk.

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© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999