Constraining the Stellar Mass Function from the Deficiency of Tidal
  Disruption Flares in the Nuclei of Massive Galaxies
  The rate of tidal disruption flares (TDFs) per mass of the disrupting black
hole encodes information on the present-day mass function (PDMF) of stars in
the clusters surrounding super massive black holes. We explore how the shape of
the TDF rate with black hole mass can constrain the PDMF, with only weak
dependence on black hole spin. We show that existing data can marginally
constrain the minimum and maximum masses of stars in the cluster, and the
high-mass end of the PDMF slope, as well as the overall TDF rate. With of order
100 TDFs expected to be identified with the Zwicky Transient Facility, the
overall rate can be highly constrained, but still with only marginal
constraints on the PDMF. However, if less than of order 10% of the TDFs
expected to be found by LSST over a decade (of order 1000 TDFs) are identified,
then precise and accurate estimates can be made for the minimum stellar mass
(within a factor of two) and the average slope of the high-mass PDMF (to within
~10%) in nuclear star clusters. This technique could be adapted in the future
to probe, in addition to the PDMF, the local black hole mass function and
possibly the massive black hole binary population.
