Classification of Tidal Disruption Events Based on Stellar Orbital
  Properties
  We study the rates of tidal disruption of stars by intermediate-mass to
supermassive black holes on bound to unbound orbits by using high-accuracy
direct N-body experiments. The approaching stars from the star cluster to the
black hole can take three types of orbit: eccentric, parabolic, and hyperbolic
orbits. Since the mass fallback rate shows a different variability depending on
these orbital types, we can classify tidal disruption events (TDEs) into three
main categories: eccentric, parabolic, and hyperbolic TDEs. Respective TDEs are
characterized by two critical values of the orbital eccentricity: the lower
critical eccentricity is the one below which the stars on eccentric orbits
cause the finite, intense accretion, and the higher critical eccentricity above
which the stars on hyperbolic orbits cause no accretion. Moreover, we find that
the parabolic TDEs are divided into three subclasses: precisely parabolic,
marginally eccentric, and marginally hyperbolic TDEs. We analytically derive
that the mass fallback rate of the marginally eccentric TDEs can be flatter and
slightly higher than the standard fallback rate proportional to $t^{-5/3}$,
whereas it can be flatter and lower for the marginally hyperbolic TDEs. We
confirm by N-body experiments that only few eccentric, precisely parabolic, and
hyperbolic TDEs can occur in a spherical stellar system with a single
intermediate-mass to supermassive black hole. A substantial fraction of the
stars approaching to the black hole would cause the marginally eccentric or
marginally hyperbolic TDEs.
