Dynamics of accretion and winds in tidal disruption events

Abstract

We have constructed self-similar models of a time-dependent accretion disk in both sub and super-Eddington phases with wind outflows for tidal disruption events (TDEs). The physical input parameters are the black hole (BH) mass $M_{\bullet}$, specific orbital energy $E$ and angular momentum $J$, star mass $M_{\star}$ and radius $R_{\star}$. We consider the sub-Eddington phase to be total pressure (model A1) and gas pressure (model A2) dominated. In contrast, the super-Eddington phase is dominated by radiation pressure (model B) with Thomson opacity. We derive the viscosity prescribed by the stress tensor, $Π_{rϕ}\propto Σ_d^b r^d$ where $Σ_d$ is the surface density of the disk, $r$ is the radius and $b$ and $d$ are constants. The specific choice of radiative or $α$ viscosity is motivated, and its parameters are decided by the expected disk luminosity and evolution time scale being in the observed range. The disk evolves due to mass loss by accretion onto the black hole and outflowing wind, and mass gain by fallback of the debris; this results in an increasing outer radius. We have simulated the luminosity profile for both sub and super-Eddington disks. As an illustrative example, we fit our models to the observations in X-ray, UV, and Optical of four TDE events and deduce the physical parameters above.