Exploring the origin of stars on bound and unbound orbits causing tidal
  disruption events
  Tidal disruption events (TDEs) probe properties of supermassive black holes
(SMBHs), their accretion disks, and the surrounding nuclear stellar cluster.
Light curves of TDEs are related to orbital properties of stars falling SMBHs.
We study the origin, density, and velocity distributions of bound and unbound
stars in the nuclear star cluster, which are causing TDEs as a function of
their orbital eccentricity $e$ and energy $E$. These quantities determine near
the SMBH the ratio of the orbit's pericenter to tidal disruption radii (denoted
as penetration factor, $\beta$). We develop an analytical model for the density
and velocity distribution of such stars in the cluster, which agrees well with
N-body experiments. Our model extends classical models of angular momentum
diffusion in the loss cone. We also derive an analytical model for three
characteristic eccentricities in the loss cone: the minimum and maximum value
for given $\beta$, respectively, and $e_{\rm lcb}$, which represents the
orbital eccentricity defining the boundary between empty and full loss cone
regimes. With N-body experiments, we show that stars causing TDEs are
distributed between these eccentricity limits on the $e-\beta$ plane. Moreover,
we find most of the bound stars between $e_{\rm lcb}$ and $e=1$ (i.e., the full
loss cone regime), whereas the remaining bound stars are originating from the
empty loss cone regime. This is consistent with the loss cone theory. We
propose that the $e-\beta$ distribution of stars in a star cluster or galactic
nucleus can be a good tool to diagnose whether the stars can cause TDEs.
