Mem. S.A.It. Vol. 76, 150 � SAIt 2005 c Memorie della Infrared emission from the dusty veil around AGN Thomas Beckert Max-Planck-Institut f¨ ur Radioastronomie, Auf dem H¨ ugel 69, 53121 Bonn, Germany e- mail: tbeckert@mpifr-bonn.mpg.de Abstract. We discuss consequences of the concept of a clumpy and dusty torus around AGN. Cloud-cloud collisions lead to an e ff ective viscosity and a geometrically thick ac- cretion disk, which has the required properties of a torus. A quantitative comparison of radiative transfer calculations for dust re-emission from the torus with NIR images, long- baseline visibilities and spectral energy distributions for the torus in the Seyfert nucleus of NGC 1068 is presented. Key words. AGN – torus – infrared – NGC 1068 1. Introduction: Dusty tori in the from these tori. Nenkova et al. (2002) realized unified model of AGN that the clumpiness might be important for the appearance of the tori and developed an ap- The unified model of AGN, which emerged proximative and statistical scheme which ac- from the interpretation spectropolarimetry of counts for the clumpiness in radiative transfer NGC 1068 (Miller & Antonucci 1983), ex- calculations of the thermal infrared emission plains the di ff erence between type 1 and type 2 from clouds, which are individually optically AGN with aspect-angle-dependent obscuration thick τ V > 40. This approach resolved some by a dusty torus or thick disk. In the simplest of the problems with earlier radiative transfer unification scheme all Seyfert 2 nuclei harbor a calculations. In this paper we summarize the Seyfert 1 core, so that the ratio of type 1s to 2s, model of a dynamical equilibrium of quasi- which varies between 1:4 (Maiolino & Rieke stable dusty clouds in the gravitational poten- 1995) and to 1:1 (Lacy t al. 2004) measures the tial of an galactic nucleus described in Vollmer thickness of the torus. The torus should there- et al. (2004) and Beckert & Duschl (2004). fore have a half opening ratio H / R ∼ 1. Krolik & Begelman (1988) argued that 2. Cloud distribution and their these tori must consist of a large number of properties in the torus individual dusty clouds. The clumpiness was not included in the following radiative trans- The equilibrium model of cold, dusty clouds fer calculations (e.g., Pier & Krolik 1992; is distinctively di ff erent from the multi-phase Granato & Danese 1994) of dust re-emission medium in the general ISM of a galaxy (Vollmer et al. 2004), in so far, as the clouds Send o ff print requests to : T. Beckert are quasi-stable and experience frequent cloud- Correspondence to : Auf dem H¨ ugel 69, 53121 cloud collisions. These collisions are the domi- Bonn, Germany
Thomas Beckert: Infrared emission from the dusty veil around AGN 151 nant process for the creation and destruction of 16 clouds. The mass and size of the largest clouds in the torus is limited by the shear in the grav- 12 itational potential of the galactic nucleus and 8 the internal pressure support against their own gravity. Their size and mass is given by the 4 shear limit and the Jeans limit for a given in- 0 Z ternal sound speed c s . In a model for the distri- bution of clouds (Beckert & Duschl 2004) we -4 decouple the the vertical and radial structure as -8 is usually done for geometrically thin accretion -12 disks, despite the thickness of the torus. The important parameter of the torus in ra- -16 diative transfer calculations is the vertical opti- -16 -12 -8 -4 0 4 8 12 16 X cal depth for intercepting a cloud � Fig. 1. Meridional cut through the probability d z l − 1 τ = coll , (1) density distribution of finding a dusty cloud in the torus. The distribution leaves room for an where l coll is the mean free path of clouds in the outflow along the polar axis. The spatial scale torus. We expect that clouds accumulate at the is in units of the dust sublimation radius. The shear limit when they experience increasing mean number of clouds along a line of sight to tidal forces while being accreted to the center. the center drops below 1 for angels larger that 40 ◦ from the midplane ( Z = 0). The upper limit to the cloud size corresponds to a lower limit of the torus surface density τ M ( R ) c s also a dimensionless collision frequency τ ∼ Σ ≥ (2) √ . ω c / Ω , this implies that cloud-cloud collisions R 2 v φ 8 are frequent in a torus. For anisotropic velocity Here M ( R ) is the total enclosed mass at radius dispersions of clouds Goldreich & Tremaine R and v φ is the Keplerian circular velocity at (1978) derived a su ffi cient approximation for that radius. the e ff ective viscosity For the distribution of clouds in the torus σ 2 τ we assume hydrostatic equilibrium for the ver- ν = (3) 1 + τ 2 Ω tical stratification. In Beckert & Duschl (2004) we used a modified isothermal distribution for angular momentum redistribution. The re- function of cloud velocities in an external po- quired anisotropy can be determined self- tential, which includes a cut-o ff scale height consistently for thin accretion disks and we use x H at which the density drops to zero. This this limit also for the torus. leaves room for a wide polar outflow cavity. Like in ordinary accretion disks, the e ff ec- The cut-o ff height is larger than the pressure tive viscosity from Eq. (3) allows mass to be scale height H in all models. An example for accreted towards the black hole. For the spe- the case of NGC 1068 is shown in Fig. 1. The cial case of a dusty torus attention must be paid radial structure is derived from a stationary ac- to the proper inner boundary condition for the cretion scenario. conservation law of angular momentum of the cloud distribution. The inner boundary will be at the sublimation radius for dust ( R ∼ 1 pc), 3. Cloud collisions and accretion where neither torque nor shear will vanish. In addition the torque at the inner boundary is The optical depth τ defined in Eq. (1) has to most likely not well described by the viscosity be τ ∼ 1 for obscuration of the AGN for (Eq. 3). line of sights through the torus. Because τ is
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