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.
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.