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 ≈ 200) 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 disc 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.