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We have modeled the evaporation of dusty molecular clouds exposed to the strong ionizing continuum of an Active Galactic Nucleus. This is important to unified models of AGN which include a torus of dusty molecular clouds within a parsec or so of the active nucleus.
Deep within an evaporating cloud, where the UV/soft X-ray optical depth is high, the gas is mostly molecular and is close to thermal equilibrium at $\simeq 10^3\, {\rm K}$. This molecular core is surrounded by a layer of partially ionized atomic gas at $\sim 10^4 {\rm K}$. At some radius the ionization parameter in the cloud reaches the critical value where it can no longer maintain this $\sim 10^4 {\rm K}$ equilibrium. At this point the cloud makes the transition to a fully ionized, X-ray heated wind. The dust grains are carried along with this wind until they are destroyed by sputtering.
We model the wind as a spherically symmetric, steady state, trans-sonic flow with zero pressure at infinity. We take into account the effects of dust opacity including radiation force. We find evaporation lifetimes $ t_{\rm evap} \simeq 1.2\times 10^5 (F/10^7 {\rm ergs\, cm^{-2} \, s^{-1}})^{0.19} (M/0.1 M_\odot)^{0.40} {\rm yr} , $ Where $F$ is the ionizing flux incident on the cloud and $M$ is the mass of the cloud. This is comparable to the drift time-scale due to loss of orbital energy from inelastic cloud-cloud collisions in the torus but is longer than the typical orbital time-scale. Therefore, clouds on eccentric orbits will approach the active nucleus much closer than the inner edge of the torus set by cloud evaporation.
The cloud itself is primarily pressurized by radiation pressure and therefore has an ionization structure independent of cloud parameters. We calculate the set of emission lines produced by evaporating clouds and discuss their use as diagnostics of the torus.
