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The rate of tidal disruption flares (TDFs) per mass of the disrupting blackhole encodes information on the present-day mass function (PDMF) of stars inthe clusters surrounding super massive black holes. We explore how the shape ofthe TDF rate with black hole mass can constrain the PDMF, with only weakdependence on black hole spin. We show that existing data can marginallyconstrain the minimum and maximum masses of stars in the cluster, and thehigh-mass end of the PDMF slope, as well as the overall TDF rate. With of order100 TDFs expected to be identified with the Zwicky Transient Facility, theoverall rate can be highly constrained, but still with only marginalconstraints on the PDMF. However, if less than of order 10% of the TDFsexpected 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 futureto probe, in addition to the PDMF, the local black hole mass function andpossibly the massive black hole binary population.

Constraining the Stellar Mass Function from the Deficiency of Tidal Disruption Flares in the Nuclei of Massive Galaxies