Rates of Stellar Tidal Disruption as Probes of the Supermassive Black
  Hole Mass Function
  Rates of stellar tidal disruption events (TDEs) by supermassive black holes
(SMBHs) due to two-body relaxation are calculated using a large galaxy sample
(N=146) in order to explore the sensitivity of the TDE rates to observational
uncertainties, such as the parametrization of galaxy light profiles and the
stellar mass function. The largest uncertainty arises due to the poorly
constrained occupation fraction of SMBHs in low-mass galaxies, which otherwise
dominate the total TDE rate. The detection rate of TDE flares by optical
surveys is calculated as a function of SMBH mass and other observables for
several physically-motivated models of TDE emission. We also quantify the
fraction of galaxies that produce deeply penetrating disruption events. If the
majority of the detected events are characterized by super-Eddington
luminosities (such as disk winds, or synchrotron radiation from an off-axis
relativistic jet), then the measured SMBH mass distribution will tightly
constrain the low-end SMBH occupation fraction. If Eddington-limited emission
channels dominate, however, then the occupation fraction sensitivity is much
less pronounced in a flux-limited survey (although still present in a
volume-complete event sample). The SMBH mass distribution of the current sample
of TDEs, though highly inhomogeneous and encumbered by selection effects,
already suggests that Eddington-limited emission channels dominate. Even our
most conservative rate estimates appear to be in tension with much lower
observationally inferred TDE rates, and we discuss several possible resolutions
to this discrepancy.
