Title:
Tidal Disruption Flares from Stars on Eccentric to Hyperbolic Orbits

Abstract:
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. 
The subsequent super-Eddington accretion of stellar debris falling onto 
the SMBH produces a characteristic flare lasting several months. 
It is theoretically expected that the bolometric light curve proportionally decays 
with the minus five third of time. However, some of the observed X-ray light curves 
deviate from such a standard decay rate, while some of them are overall 
in good agreement with it. Therefore, it is required to construct the theoretical model 
for explaining these light curve variations consistently. In this work, 
we revisit the mass fallback rates of tidal disruption of stars semi-analytically 
in terms of the debris binding energy and the period of the most tightly bound debris 
by taking account of the stellar internal structure, orbital eccentricity, penetration factor, 
and spread energy index (the power law index of the penetration factor 
shown in the debris spread energy). We find that these four factors make 
the mass fallback rate deviate from the standard decay rate. 
We confirm these results by performing three dimensional smoothed particle 
hydrodynamic simulations. We also discuss the extraordinary behavior of 
spread in debris energy for the eccentric TDEs with high penetration factor.