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We study the rates of tidal disruption of stars by intermediate-mass tosupermassive black holes on bound to unbound orbits by using high-accuracydirect N-body experiments. The approaching stars from the star cluster to theblack hole can take three types of orbit: eccentric, parabolic, and hyperbolicorbits. Since the mass fallback rate shows a different variability depending onthese orbital types, we can classify tidal disruption events (TDEs) into threemain categories: eccentric, parabolic, and hyperbolic TDEs. Respective TDEs arecharacterized by two critical values of the orbital eccentricity: the lowercritical eccentricity is the one below which the stars on eccentric orbitscause the finite, intense accretion, and the higher critical eccentricity abovewhich the stars on hyperbolic orbits cause no accretion. Moreover, we find thatthe parabolic TDEs are divided into three subclasses: precisely parabolic,marginally eccentric, and marginally hyperbolic TDEs. We analytically derivethat the mass fallback rate of the marginally eccentric TDEs can be flatter andslightly higher than the standard fallback rate proportional to $t^{-5/3}$,whereas it can be flatter and lower for the marginally hyperbolic TDEs. Weconfirm by N-body experiments that only few eccentric, precisely parabolic, andhyperbolic TDEs can occur in a spherical stellar system with a singleintermediate-mass to supermassive black hole. A substantial fraction of thestars approaching to the black hole would cause the marginally eccentric ormarginally hyperbolic TDEs.

Classification of Tidal Disruption Events Based on Stellar Orbital Properties