2020ApJ...900....3P

We study the mass fallback rate of tidally disrupted stars on marginally bound and unbound orbits around a supermassive black hole (SMBH) by performing three-dimensional smoothed particle hydrodynamic simulations with three key parameters. The star is modeled by a polytrope with two different indexes (n = 1.5 and 3). The stellar orbital properties are characterized by five orbital eccentricities ranging from e = 0.98 to 1.02, and five different penetration factors ranging from β = 1 to 3, where β represents the ratio of the tidal disruption to pericenter distance radii. We derive analytic formulae for the mass fallback rate as a function of the stellar density profile, orbital eccentricity, and penetration factor. Moreover, two critical eccentricities to classify tidal disruption events (TDEs) into five different types: eccentric (e< e_crit,1), marginally eccentric (e_crit,1≲e< 1), purely parabolic (e = 1), marginally hyperbolic (1< e< e_crit,2), and hyperbolic (e≳e_crit,2) TDEs, are reevaluated as e_crit,1=1-2q^–1/3β^k–1 and e_crit,2=1+2q^–1/3β^k–1, where q is the ratio of the SMBH to stellar masses and 0 < k <= 2. We find the asymptotic slope of the mass fallback rate varies with the TDE type. The asymptotic slope approaches -5/3 for the parabolic TDEs, is steeper for the marginally eccentric TDEs, and is flatter for the marginally hyperbolic TDEs. For the marginally eccentric TDEs, the peak of mass fallback rates can be about one order of magnitude larger than the parabolic TDE case. For marginally hyperbolic TDEs, the mass fallback rates can be much lower than the Eddington accretion rate, which can lead to the formation of a radiatively inefficient accretion flow, while hyperbolic TDEs lead to failed TDEs. Marginally unbound TDEs could be an origin of a very low-density gas disk around a dormant SMBH.