Circularization of Tidally Disrupted Stars around Spinning Supermassive
  Black Holes
  We study the circularization of tidally disrupted stars on bound orbits
around spinning supermassive black holes by performing three-dimensional
smoothed particle hydrodynamic simulations with Post-Newtonian corrections. Our
simulations reveal that debris circularization depends sensitively on the
efficiency of radiative cooling. There are two stages in debris circularization
if radiative cooling is inefficient: first, the stellar debris streams
self-intersect due to relativistic apsidal precession; shocks at the
intersection points thermalize orbital energy and the debris forms a
geometrically thick, ring-like structure around the black hole. The ring
rapidly spreads via viscous diffusion, leading to the formation of a
geometrically thick accretion disk. In contrast, if radiative cooling is
efficient, the stellar debris circularizes due to self-intersection shocks and
forms a geometrically thin ring-like structure. In this case, the dissipated
energy can be emitted during debris circularization as a precursor to the
subsequent tidal disruption flare. The possible radiated energy is up to
~2*10^{52} erg for a 1 Msun star orbiting a 10^6 Msun black hole. We also find
that a retrograde (prograde) black hole spin causes the shock-induced
circularization timescale to be shorter (longer) than that of a non-spinning
black hole in both cooling cases. The circularization timescale is remarkably
long in the radiatively efficient cooling case, and is also sensitive to black
hole spin. Specifically, Lense-Thirring torques cause dynamically important
nodal precession, which significantly delays debris circularization. On the
other hand, nodal precession is too slow to produce observable signatures in
the radiatively inefficient case. We also discuss the relationship between our
simulations and the parabolic TDEs that are characteristic of most stellar
tidal disruptions.
