Advective accretion disc-corona model with fallback for tidal disruption events

Abstract

Tidal disruption events (TDEs) show a correlation between the UV to X-ray spectral index and the Eddington ratio, with non-thermal X-ray emission at the low Eddington ratio. We consider the corona surrounding the accretion disc as a non-thermal X-ray source. We construct a time-dependent and non-relativistic advective accretion disc-corona model for TDEs. The infalling debris is assumed to form a seed disc in time $t_c$, that evolves due to the mass gain from the infalling debris at the constant outer radius with a mass fallback rate $\dot{M}_{\rm fb}$ and the mass loss through accretion onto the black hole. The viscous stress in our model depends on gas ($P_g$) and total ($P_t$) pressures as $\tau_{r\phi} \propto P_g^{1-\mu} P_t^{\mu}$, where $\mu$ is a constant. We find that the mass accretion rate $\dot{M}_a$ evolves from Eddington to sub-Eddington accretion with a late-time evolution close to $t^{-5/3}$, where $t$ is the time. We find that the bolometric disc luminosity follows a late-time evolution close to $t^{-5/3}$. The ratio of total X-ray luminosity from corona to bolometric disc luminosity increases with $\mu$ and increases at late times for $\mu \neq 1$. We obtain the X-ray blackbody temperature of the disc that agrees with the temperature from X-ray observations ($\sim~10^5~{\rm K}$). We find the radiative efficiency of the disc increases with time and decreases for a disc when the corona is included. We have neglected the outflow, and our model is more applicable for near-to-sub-Eddington accretion and when $\dot{M}_{\rm fb}$ is sub-Eddington.