5. SURFACE PHYSICS AND RADIO EMISSION

It is fortunate that large column densities of material (equation 3) are expected close to the active nucleus, for there is an enormous radiation pressure on dusty gas directly exposed to a quasar's UV flux. The opacity of a single grain is / m 2 x 10⁴ (0.1 µ/a) cm² g^-1. If the grains are coupled by collisions or Lorentz forces to gas, then with a Galactic gas to dust ratio, the total opacity is _gr 200 cm² g^-1 (roughly the cross section to mass ratio of an interstellar cloud with A_v ~ 1). This is nearly 10³ times larger than the Thomson opacity _T = 0.4 cm² g^-1 which defines the Eddington limit, so radiation pressure will tend to expel unshielded dusty gas from all but the outer edges of the host galaxy. In the absence of forces other than radiation pressure and gravity, at radius r_pc gas in which dust survives will reach a terminal velocity

(5)

where _gr = 10² ₂ cm² g^-1. The innermost radius at which dust can survive (section 6) defines a characteristic velocity v,sub>max ~ 210⁴ L₄₆^1/4 ₂^1/2 km s^-1.

The component of this radiation force normal to the disk surface, which must be balanced by vertical pressure gradients in a quasi-static situation, would destroy in a dynamical time any warp in a disk with < 50r_pc^-1 cos . Since this is generally less than _sg (equation 3), warps can survive. The tangential force along the disk surface cannot be balanced, so the surface layers will be ablated. The radiation force acts primarily only on a thin layer of column density ~ _gr^-1. Large-scale Kelvin-Helmholtz instabilities might couple the motion of that layer to underlying material, but the resulting shocks would destroy the dust in the surface layers and thus reduce the rate of ablation. With and without coupling, we find that the ablation timescale is considerably longer than the inferred inflow timescales (see section 4), so the disk is likely to survive. The fate of the dust in the surface layers is less clear. The dust can be destroyed by sputtering if it develops a high speed v relative to the surrounding gas. Collisional coupling maintains (v)² ~ p_rad / _gas (proportional to the ionization parameter) small enough near the disk that grains can survive. But since accelerated dust must pass through shocks to follow a warped surface, it may well be destroyed long before it and its associated gas reach the terminal speed (5).

The column density of a Stromgren length is _s = 0.05 T₄ g cm^-1, where is the ratio of ionizing radiation pressure to gas pressure, and 10⁴ T₄ K is the temperature of the photoionized gas. Plausible transition-zone disks have 10^0±2 at all radii. Except in the outskirts of the galaxy _sg >> _c, so only a thin surface layer will be photoionized. If dust survives in this layer (as is especially likely in the low-density outer regions of the galaxy) resonance line emission from this layer will be converted into infrared photons, while other emission lines will be heavily reddened. If dust is destroyed (as is likely in the inner regions), the surface may contribute to (and perhaps dominate!) the emission line flux from the AGN (Collin-Souffrin 1987).

Free-free emission from the photoionized surface layers of the warped disk with electron density n_e will be optically thin at frequencies > 10¹⁰ (n_e / 10⁵ cm^-3)^1/2 Hz, so radio frequency free-free emission will come predominantly from the outer parts of the disk, while free-free at millimeter wavelengths could have a comparable contribution from the inner parsecs. It is easy to show that the free-free luminosity density L(ff) (the optically thin free-free emissivity, integrated over the photoionized volume), is simply related to the infrared luminosity re-radiated by the underlying (and/or cospatial, if dust survives in the photoionized surface) gas:

(6)

where g(, T) is the Gaunt factor. The resulting free-free luminosities are comparable to those of the flat-spectrum components observed in quasars by Antonucci and Barvainis (1988), and also to the level of the radio detections in most PG quasars (Kellermanm reported in Sanders et al. 1989).