Effect of the density profile of a star on the bolometric light curve in tidal disruption events

Tidal disruption events (TDEs) provide evidence for quiescent supermassive black holes (SMBHs) in the centers of inactive galaxies. TDEs occur when a star on a parabolic orbit approaches close enough to a SMBH to be disrupted by the tidal force of the SMBH. The subsequent super-Eddington accretion of stellar debris falling back to the SMBH produces a characteristic flare lasting several months. The theoretically expected bolometric light curve decays with time as proportional to $t^{-5/3}$. However, the light curves observed in most of the optical-UV TDEs deviate from the $t^{-5/3}$ decay rate especially at early time, while the light curves of some soft-X-ray TDEs are overall in good agreement with the $t^{-5/3}$ law. Therefore, it is required to construct the theoretical model for explaining these light curve variations consistently. In this paper, we revisit the mass fallback rates analytically and semi-analytically by taking account of the structure of the star, which is simply modeled by the polytrope. We find the relation between a polytropic index and the power law index of the mass fallback rate. We also discuss whether and how the decay curves, which we derived, fit the observed ones.