Relativistic accretion disc in tidal disruption events

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 $\dot{M}_f$ for both full and partial disruption TDEs, and assume that the infalling debris forms a seed disc in time $t_c$, which evolves due to the mass addition from the infalling debris and the mass loss via accretion onto 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 $M_{\rm d}$ with a late-time evolution of $M_{\rm d} \propto t^{-1.05}$ and $M_{\rm d} \propto t^{-1.38}$ 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 $L \propto t^{-1.8}$ and $L \propto t^{-2.3}$ for full and partial disruption TDEs respectively. Our obtained luminosity declines faster than the luminosity inferred using $L \propto \dot{M}_f$. We also compute the light curves in various spectral bands.

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