According to unified schemes of Active Galactic Nuclei (AGN), the central engine is surrounded by dusty, optically thick clouds in a toroidal structure. We have recently developed a formalism that for the first time takes proper account of the clumpy nature of the AGN torus. We now provide a detailed report of our findings in a two-paper series. Here we present our general formalism for radiative transfer in clumpy media and construct its building blocks for the AGN problem -- the source functions of individual dusty clouds heated by the AGN radiation field. We show that a fundamental difference from smooth density distributions is that in a clumpy medium, a large range of dust temperatures coexist at the same distance from the radiation central source. This distinct property explains the low dust temperatures found close to the nucleus of NGC1068 in 10 \mic interferometric observations. We find that irrespective of the overall geometry, a clumpy dust distribution shows only moderate variation in its spectral energy distribution, and the 10\mic\ absorption feature is never deep. Furthermore, the X-ray attenuating column density is widely scattered around the column density that characterizes the IR emission. All of these properties are characteristic of AGN observations. The assembly of clouds into AGN tori and comparison with observations is presented in the companion paper.Comment: To appear in ApJ September 20, 200

Unified schemes of active galactic nuclei (AGN) require an obscuring dusty torus around the central engine. The compact sizes (only a few pc) determined in recent high-resolution observations require that the obscuring matter be clumpy and located inside the region where the black-hole gravity dominates over the galactic bulge. This location is in line with the scenario depicting the torus as the region of the clumpy wind coming off the accretion disk in which the clouds are dusty and optically thick. We study here the outflow scenario within the framework of hydromagnetic disk winds, incorporating the cloud properties determined from detailed modeling of the IR emission from clumpy tori. We find that torus clouds were likely detected in recent water maser observations of NGC 3079. In the wind scenario, the AGN main dynamic channel for release of accreted mass seems to be switching at low luminosities from torus outflow to radio jets. The torus disappears when the bolometric luminosity decreases below about \E{42} erg/sec because the accretion onto the central black hole can no longer sustain the required cloud outflow rate. This disappearance seems to have been observed in both LINERs and radio galaxies. With further luminosity decrease, suppression of cloud outflow spreads radially inward from the disk's dusty, molecular region into its atomic, ionized zone, resulting in disappearance of the broad emission line region at lower luminosities, yet to be determined.Comment: ApJ Letters, to be publishe

Unified schemes of active galactic nuclei (AGN) require an obscuring dusty torus around the central source, giving rise to Seyfert 1 line spectrum for pole-on viewing and Seyfert 2 characteristics in edge-on sources. Although the observed IR is in broad agreement with this scheme, the behavior of the 10 micron silicate feature and the width of the far-IR emission peak remained serious problems in all previous modeling efforts. We show that these problems find a natural explanation if the dust is contained in about 5-10 clouds along radial rays through the torus. The spectral energy distributions (SED) of both type 1 and type 2 sources are properly reproduced from different viewpoints of the same object if the visual optical depth of each cloud is larger than about 60 and the clouds' mean free path increases roughly in proportion to radial distance.Comment: 11 pages, submitted to ApJ Letter

Dust infrared emission possesses scaling properties that yield powerful results with farreaching observational consequences. Scaling was first noticed by Rowan-Robinson for spherical shells and is shown here to be a general property of dust emission in arbitrary geometries. Overall luminosity is never an input parameter of the radiative transfer problem; spectral shape is the only relevant property of the heating radiation when the inner boundary of the dusty region is controlled by dust sublimation. Similarly, the absolute scales of densities and distances are irrelevant; the geometry enters only through angles, relative thicknesses and aspect ratios, and the actual magnitudes of densities and distances enter only through one independent parameter, the overall optical depth. That is, as long as the overall optical depth stays the same, the system dimensions can be scaled up or down by an arbitrary factor without any effect on the radiative transfer problem. Dust properties enter only through dimensionless, normalized distributions that describe the spatial variation of density and the wavelength dependence of scattering and absorption efficiencies. Scaling enables a systematic approach to modelling and classification of IR spectra. We develop a new, fully scale-free method for solving radiative transfer, present exact numerical results, and derive approximate analytical solutions for spherical geometry, covering the entire range of parameter space relevant to observations. For a given type of grains, the spectral energy distribution (SED) is primarily controlled by the profile of the spatial dust distribution and the optical depth — each density profile produces a family of solutions, with position within the family determined by optical depth. From the model SEDs presented here, the density distribution and optical depth can be observationally determined for various sources. Scaling implies tight correlations among the SEDs of various members of the same class of sources such as young stellar objects, late-type stars, etc. In particular, all members of the same class occupy common, well-defined regions in colour-colour diagrams. The observational data corroborate the existence of these correlations.

We present a new diagnostic diagram for mid-infrared spectra of infrared galaxies based on the equivalent width of the 6.2 micron PAH emission feature and the strength of the 9.7 micron silicate feature. Based on the position in this diagram we classify galaxies into 9 classes ranging from continuum-dominated AGN hot dust spectra and PAH-dominated starburst spectra to absorption-dominated spectra of deeply obscured galactic nuclei. We find that galaxies are systematically distributed along two distinct branches: one of AGN and starburst-dominated spectra and one of deeply obscured nuclei and starburst-dominated spectra. The separation into two branches likely reflects a fundamental difference in the dust geometry in the two sets of sources: clumpy versus non-clumpy obscuration. Spectra of ULIRGs are found along the full length of both branches, reflecting the diverse nature of the ULIRG family.