Dependence of tidal disruption flares on stellar density profile and orbital properties

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. It is theoretically expected that the bolometric light curve decays with time as proportional to $t^{-5/3}$. However, some of the observed X-ray light curves deviate from the $t^{-5/3}$ decay rate, while some of them 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 semi-analytically by taking account of the stellar internal structure, orbital eccentricity and penetration factor. We find that the mass fallback rate is shallower than the standard $t^{-5/3}$ decay rate independently of the polytropic index, and the orbital eccentricity only changes the magnitude of the mass fallback rate. Furthermore, the penetration factor significantly can modify the magnitude and variation of mass fallback rate. We confirm these results by performing the computational hydrodynamic simulations. We also discuss the relevance of our model by comparing these results with the observed light curves.