The geometrically thin disk models we have been discussing so far have been explored most extensively. However, there are good reasons to believe that accretion flows in AGNS may not always (if ever!) adopt such a simple geometry. In this section we discuss the alternatives and point out, where we can, the main observational and theoretical difficulties. However, it should be borne in mind that much more theoretical work needs to be done to enable these models to be compared with observations. In many cases the models have not yet received the theoretical attention necessary to enable them to address some of the main observational issues discussed in this review.
5.1. Thick Disks
At both low and high accretion rates, it is possible for internal pressure to become just as important as gravity and rotation. The vertical thickness can then become comparable to the radius, which will result in a thick disk. Such disks can resemble tori and/or quasi-spherical accretion flows. At high accretion rates, the outward radiation flux saturates near the Eddington limit (Begelman & Meier 1982), and radiation pressure becomes very important and might support a thick disk geometry. Most of the models of radiation pressure-supported thick disks assume that away from the innermost regions, the flow is in hydrostatic equilibrium on an orbital timescale. This necessarily requires that the flow have a low viscosity parameter , which is simply the ratio of the orbital time to the infall time for geometrically thick flows. Exceedingly low viscosities are also required in order that the flow be optically thick (see, e.g., Rees 1984). Models of radiation-supported thick disks or tori have been constructed by Paczynski & Wiita (1980), Jaroszynski, Abramowicz & Paczynski (1980), and Abramowicz, Calvani, & Nobili (1980). The geometry of such models is determined by their surface distribution of specific angular momentum, which is not known a priori and is presumably determined by the "viscous" angular momentum transport. In addition to the viscosity constraints, such models in their simplest (nonaccreting!) forms may be subject to global hydrodynamical instabilities (Papaloizou & Pringle 1984), which produce strong spiral waves in the flow (Hawley 1991). Accretion through the disk may, however, reduce the effects of these instabilities (Blaes 1987; Gat & Livio 1992; Dwarkadus & Balbus 1996).
There have been very few predictions of the observed properties of radiation-supported thick disks. Madau (1988) has modeled the emerging SED, which has a strong dependence on viewing angle. This is because most of the luminosity originates in the central funnel region, which is shadowed by the outer torus-shaped disk for large viewing angles. Observers who can view the funnel see a spectrum that extends up to the soft X-rays, whereas observers who view the disk more edge-on see a much cooler spectrum. High inclination angles may be required to make the models compatible with observed UV/soft X-ray flux ratios in Seyfert 1 galaxies (Walter & Fink 1993). This may be incompatible with the unified model and low inclination angles inferred from Fe K lines, but it should be pointed out that thin disk models have not succeeded in explaining the soft X-ray excess in a self-consistent fashion either. In addition, the optical/UV SED for thick disks suffers the same problem as in thin disks in being bluer than observed. On the other hand, scattering in the funnel provides a way of producing polarization parallel to the radio axis (Coleman & Shields 1990; Kartje & Königl 1991). In addition, because heat diffuses in all directions, not just vertically, all elements of the photosphere are thermally coupled together, and optical and UV radiation might therefore be expected to exhibit correlated variability with no lags (see the discussion by Szuskiewicz, Malkan & Abramowicz 1996), as observed.