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

TL;DR

This paper proposes a method to constrain the stellar mass function in galactic nuclei by analyzing the rate of tidal disruption flares, with potential for precise measurements using upcoming transient surveys.

Contribution

It introduces a novel approach to infer the stellar mass function from TDF rates, demonstrating how future data can tightly constrain stellar and black hole populations.

Findings

Existing data can marginally constrain the PDMF parameters.

With ~100 TDFs, the overall rate can be well constrained.

Detection of fewer than 10% of expected TDFs allows precise PDMF estimates.

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 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.