Tidal Disruptions of Main Sequence Stars -- V. The Varieties of
  Disruptions
  Tidal disruption events (TDEs), events in which a star passes very close to a
supermassive black hole, are generally imagined as leading either to the star's
complete disruption or to its passage directly into the black hole. In the
former case it is widely believed that in all cases the bound portion of the
debris quickly "circularizes" due to relativistic apsidal precession, i.e.,
forms a compact accretion disk, and emits a flare of standardized lightcurve
and spectrum. We show here that TDEs are more diverse and can be grouped into
several distinct categories on the basis of stellar pericenter distance $r_p$;
we calculate the relative frequency of these categories. In particular, because
rapid circularization requires $r_p \lesssim 10r_g$ ($r_g \equiv GM_{\rm
BH}/c^2$), it can happen in only a minority of total disruptions, $\lesssim
1/4$ when the black hole has mass $M_{\rm BH} = 10^6 M_\odot$. For larger
pericenter distances, $10 < r_p/r_g < 27$ (for $M_{\rm BH}=10^6M_\odot$), main
sequence stars are completely disrupted, but the bound debris orbits are highly
eccentric and possess semimajor axes $\sim 100\times$ the scale of the expected
compact disk. Partial disruptions with fractional mass-loss $\gtrsim 10\%$
should occur with a rate similar to that of total disruptions; for fractional
mass-loss $\gtrsim 50\%$, the rate is $\approx 1/3$ as large. Partial
disruptions -- which must precede total disruptions when the stars' angular
momenta evolve in the "empty loss-cone" regime -- change the orbital energy by
factors $\gtrsim O(1)$. Remnants of partial disruptions are in general far from
thermal equilibrium. Depending on the orbital energy of the remnant and
conditions within the stellar cluster surrounding the SMBH, it may return after
hundreds or thousands of years and be fully disrupted, or it may rejoin the
stellar cluster.
