4. TRANSITION DISK

Between r ~ 1 kpc and the black hole's accretion disk proper (r 10³ GM_h / c² ~ 0.03 M₈ pc for a black hole of mass M_h = 10⁸ M₈ M) lies the transition disk. Unlike the accretion disk, this disk will be heated primarily by external radiation rather than by the local release of gravitational binding energy. Beyond r ~ 20 ₂^-2 M₈ pc the stars in the galaxy, of velocity dispersion 10² ₂ km s^-1 determine the potential. A photoionized or molecular disk will be self-gravitating and Jeans unstable if its column density exceeds

(3)

where h is the scale height of the disk and T = 10³ T₃ K the gas temperature. If this gas flows in on a timescale t_in to supply the black hole with an accretion rate = M yr^-1, then ~ 1 r_pc^-1 v₃₀₀^-1 (t_in / t_orb)g cm^-2 where the orbital speed of the gas is 300 v₃₀₀ km s^-1 and t_orb is the orbital time of gas at radius r. Purely local viscosity results in enormous inflow times, and Begelman, Frank and Shlosman (papers in these proceedings, and references therein) have argued that the angular momentum transport is determined by self-gravitation and global bar instabilities, so that the mean column density always exceeds _sg. Dust in such a column has an enormous optical depth to UV photons: 10⁴ T₃^1/2 ₂ r_pc^-1. Provided the disk is warped (by any of the mechanisms described in section 2) or flared, infrared reradiation is inevitable. A disk warped through angle will intercept and reradiate a fraction ~ / 3 of the luminosity of the central source. For idealized dust of constant , if C = d(covering factor) / dln r r^q, then in the `inertial range' (kT_min << h< << kT_max) the superposition of dust emission from all radii produces a reradiated spectrum with L ^-s, where

(4)

Since substantial warps are to be expected on all scales, we expect in some average sense q 0 and hence s ~ 1. A diversity of bumps and wiggles is to be expected in individual objects, depending on the radii (and hence, via figure 1, wavelength) where their warps are most pronounced, the size and composition of their dust grains, and whether they are viewed from an angle where dust at a large radius absorbs re-emission from the interior. This seems in accord with the infrared spectral energy distributions of AGN: a great variety, with a median s ~ 1 (Sanders et al. 1989, 1988b). As discussed in section 2, the properties of more realistic galactic dust modify slightly the simple result of equation (4), and by flattening the T(r) relation introduces a propensity for 3-5 µm ``bumps'' (see figure 2).