Relativistic accretion disc in tidal disruption events

Abstract

ABSTRACT We construct a time-dependent relativistic accretion model for tidal disruption events (TDEs) with an α-viscosity and the pressure dominated by gas pressure. We also include the mass fallback rate $\dot{M}_\mathrm{ f}$ for both full and partial disruption TDEs, and assume that the infalling debris forms a seed disc in time tc, which evolves due to the mass addition from the infalling debris and the mass-loss via accretion on to the black hole. Besides, we derive an explicit form for the disc height that depends on the angular momentum parameter in the disc. We show that the surface density of the disc increases at an initial time due to mass addition, and then decreases as the mass fallback rate decreases, which results in a decrease in the disc mass Md with a late-time evolution of Md ∝ t−1.05 and t−1.38 for full and partial disruption TDEs, respectively, where t is the time parameter. The bolometric luminosity L shows a rise and decline that follows a power law at late times given by L ∝ t−1.8 and t−2.3 for full and partial disruption TDEs, respectively. Our obtained luminosity declines faster than the luminosity inferred using $L \propto \dot{M}_\mathrm{ f}$. We also compute the light curves in various spectral bands.