  The disruption of stars by supermassive black holes has been linked to more
than a dozen flares in the cores of galaxies out to redshift $z \sim 0.4$.
Modeling these flares properly requires a prediction of the rate of mass return
to the black hole after a disruption. Through hydrodynamical simulation, we
show that aside from the full disruption of a solar mass star at the exact
limit where the star is destroyed, the common assumptions used to estimate
$\dot{M}(t)$, the rate of mass return to the black hole, are largely invalid.
While the analytical approximation to tidal disruption predicts that the
least-centrally concentrated stars and the deepest encounters should have more
quickly-peaked flares, we find that the most-centrally concentrated stars have
the quickest-peaking flares, and the trend between the time of peak and the
impact parameter for deeply-penetrating encounters reverses beyond the critical
distance at which the star is completely destroyed. We also show that the
most-centrally concentrated stars produced a characteristic drop in
$\dot{M}(t)$ shortly after peak when a star is only partially disrupted, with
the power law index $n$ being as extreme as -4 in the months immediately
following the peak of a flare. Additionally, we find that $n$ asymptotes to
$\simeq -2.2$ for both low- and high-mass stars for approximately half of all
stellar disruptions. Both of these results are significantly steeper than the
typically assumed $n = -5/3$. As these precipitous decay rates are only seen
for events in which a stellar core survives the disruption, they can be used to
determine if an observed tidal disruption flare produced a surviving remnant.
These results should be taken into consideration when flares arising from tidal
disruptions are modeled.
  [abridged]
