2. DUST AND WARPS

Most previous discussions of dust and gas in the host galaxy of an active nucleus have concentrated on spherically symmetrical distributions of dust (Rees et al. 1969, Bollea & Cavaliere 1976, Barvainis 1987 - the latter also considered conical sectors, or have concentrated on their effects on emission line clouds: Davidson & Netzer 1979, MacAlpine 1985 and references therein). A few have considered disk-like distributions (Begelman, McKee & Shields 1983, Begelman 1985, Shlosman & Begelman 1988), but have assumed the disks were planar and relatively thin, so that they intercepted only a small fraction ( 1%) of the luminosity of the central accretion disk. Neither of these distributions is very likely. The gas and dust most probably lie in what could crudely be described as a heavily warped (and probably clumpy) disk. Beyond about a kiloparsec radius, the orbital time t_orb 10⁸ (r / 3 kpc) yr is so long that gas captured or disturbed by a recent interaction with another galaxy will not have had time to settle into the preferred plane of the host galaxy's potential in a quasar lifetime (~ 10⁸ yr). Since quasars seem commonly to be involved in interactions or mergers (Hutchings 1983, MacKenty & Stockton 1984), large warps and streamers are to be expected. The warped disk of NGC 5128 (Centurus A) is a famous example. Moving inwards, warps on kiloparsec scales can be produced by counter rotating bars (Vietri 1986), by continuing infall of gas (Ostriker & Binney 1989), and by Kelvin-Helmholtz instability as the disk rotates through a pressure-supported corona (Gunn 1979) Though such warps are difficult to detect in external galaxies which are not nearly edge-on, let alone in quasars, the gas at ~ 3 kpc in our own Galaxy is tilted by about 15° with respect to the plane defined at larger radii (Vietri 1986), and most well-studied Seyfert galaxies have strong kiloparsec-scale bars (Adams 1977).

The same warp-inducing processes can operate on scales of parsecs. The molecular torus extending from 2-8 pc from our Galactic center is tilted by ~ 15° (in the opposite direction from the 3 kpc warp!) with respect to the plane defined by the stars. The parsec-scale dust torus in NGC 1068 (Antonucci & Miller 1985) has its axis at right angles to the kiloparsec-scale disk of gas and stars (Wilson & Ulvestad 1982), and the axes of similar tori inferred to exist in other Seyferts make random angles to the minor axes of the disks of their host galaxies (Unger et al. 1987, Haniff et al. 1988).

We conclude that warps are common and substantial enough to allow the nuclear continuum to illuminate the dust and gas on scales from 1-10⁴ parsecs. The broad-line region (BLR) will be obscured by this dust over a range of viewing angles comparable to the covering factor of the dust disk. Except in the case that the narrow line gas is cospatial with the dusty disk in a symmetrical warp, it is difficult to prevent the narrow line region from being visible from some viewing angles when the BLR is obscured. This occurs for a fraction of sky of order the covering factor of the dust disk extending beyond the NLR: typically ~ 0.05-0.1. Since molecular clouds are larger than the 0.1-1 pc scale of the BLR, the same fraction of quasars with obscured broad line regions would be expected even if the dust were in clouds at high latitudes rather than in a disk. These objects would appear as ``quasar-2's'' (by analogy to Seyfert 2's). Such objects have been rare in optical surveys, but appear common in infrared-selected samples (Sanders et al. 1988b). In radio samples they may masquerade as narrow line radio galaxies (Scheuer 1987, Barthel 1989).

We now examine the state of dust in a warped disk illuminated by the central accretion disk of a quasar, and its possible relevance to the infrared and submillimeter spectra of quasars. We postpone to section 5 a discussion of the vertical structure of an illuminated disk, and the expected optical and radio emission therefrom.

The equilibrium temperature T_g of dust grains of characteristic radius a 20 Å at distance r from a radiation source of luminosity density L (erg s^-1 Hz^-1) is determined implicitly by

(1)

where Q_abs () is the absorption efficiency (cross section in units of a²), at frequency . Graphite grains with a ~ 0.1 µm are transparent to X-rays with h > 0.4 keV and for 0.1 keV < h < 0.28 keV (K-edge of Carbon), so Q_abs() a at those energies. At wavelengths < 2 a where the grain is not transparent Q_abs 1. At longer wavelengths > 2 a the grain becomes a weakly coupled antenna, Q_abs (2 a / ) f() where f() depends on the dielectric tensor and shape of the grains (fits for various grain compositions and shapes, and discussion of the Mie scattering range can be found in Martin 1978, Draine & Lee 1984, Wright 1987, and references therein). Observations of galactic dust indicate that outside resonances f() ^1-, with 1 2 (Whittet 1988).

In quasars, most of the energy from the central source is emitted at frequencies for which Q_abs () 1, and reradiated at wavelengths > 2 a. Hence if we ignore heating and cooling of grains by collisions with atoms (generally weak), the temperature of directly illuminated grains is given approximately by

(2)

where < Q_abs(T) > is the Planck-averaged absorption efficiency (cf. Draine 1981), < Q_abs(T) > T_g. Crudely, therefore, T_g [L / (r² a)]^1/(4+). At a given distance from the source, the smallest grains in thermal equilibrium (~ 30 Å) will be about a factor of 2 hotter than the largest grains commonly considered (~ 0.3 µm).

The heat capacity of grains with a 20 Å is so low that their temperature fluctuates, being significantly affected by the absorption of a single UV photon. Grains deeper in the dusty disk will not be exposed directly to UV radiation from the central source, but to longer-wavelength re-emission from shielding gas and dust. This shielded dust will have a temperature nearly independent of a, and slightly lower (by a factor ~ (T_re / 2500 K)^1/(4+)) than that of the directly illuminated grains of temperature T_re.

The emission from dust at temperature T_g at long wavelengths scales as ²⁺ T_g, peaks very sharply at h ~ (3 + )kT_g ( ~ 30 T₂^-1 µm, where T_g = 100 T₂ K) and declines exponentially at higher frequencies. Except for the small grains of fluctuating temperature, which can contribute high frequency emission from regions where the equilibrium temperature is low, most emission at frequency v will come from the radius where the equilibrium dust temperature T_g ~ h / (3 + ) k, i.e., from a radius r L^{1/2 -(4+)/2}, and the flux of radiation at that frequency will (for an isotropic central source) be proportional to the fraction of the sky at the central source covered by dust at the appropriate radii. This radius-frequency scaling can cause curious effects. At frequencies where is large (e.g., 1 < < 7 µm, where 1.7 - Whittet 1988), the temperature is nearly independent of radius, enhancing the probability of having a large warp at an appropriate radius, and hence a large sky covering factor and a large ~ 3 µm flux (see figure 2). This may be the cause of the ``3-5 µm bumps'' commonly observed in AGN (Edelson & Malkan 1986).