Formation of dust clumps in the torus of active galactic nuclei

The putative dusty torus is a key ingredient of the unification scheme of active galactic nuclei (AGN), but its origin remains a mystery. Here we put forward a new physical model to explain how a large number of small dusty gas clumps form and they collectively appear as a geometrically thick dynamic dusty torus. The circumnuclear hot gas flows towards the central black hole (BH) and forms a rotating disk on sub-pc scales. A fraction of inflowing hot gas condenses to form small cold clumps due to thermal instabilities, when the accretion rate is sufficiently high. These cold dusty gas clumps are irradiated by the central accretion disk and re-radiate as dust emission mostly in the infrared. We propose that the dusty torus in AGN consists of such cold clumps vertically supported by the radiation force against gravity. For clumps with suitable column density, the vertical component of the BH gravity is in quasi-static equilibrium with the infrared radiation force together with the vertical component of the disk radiation force. Our model is robust in the sense that for any reasonable range of parameters concerning clump vertical dynamical equilibrium a torus exists. We further show that the hot gas in the rotating flow condenses to cold clumps only if its accretion rate is higher than about one percent of the Eddington rate. The radiation force is unable to lift the cold gas clumps up away from the mid-plane when the luminosity of the disk surrounding the BH is lower than 0.1 percent of the Eddington luminosity. These two features of our model may provide a physical explanation for the lack of evidence of dusty tori in low-luminosity AGNs.