ABSTRACT
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 $\mathcal {O}(100)$ 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 ${\lesssim } 10 {{\ \rm per\ cent}}$ of the TDFs expected to be found by LSST over a decade ($\mathcal {O}(10^3)$ TDFs) are identified, then precise and accurate estimates can be made for the minimum stellar mass (within a factor of 2) and the average slope of the high-mass PDMF (to within $\mathcal {O}(10{{\ \rm per\ cent}})$) 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.
Tidal disruption events by a massive black hole binary