The Luminosity Function of Tidal Disruption Events from Fallback-powered Emission: Implications for the Black Hole Mass Function

Abstract

Tidal disruption events (TDEs), in which a star is destroyed by the gravitational field of a supermassive black hole (SMBH), are being observed at a high rate owing to the advanced state of survey science. One of the properties of TDEs that is measured with increasing statistical reliability is the TDE luminosity function, d N ̇ TDE / dL , which is the TDE rate per luminosity (i.e., how many TDEs are within a given luminosity range). Here we show that if the luminous emission from a TDE is directly coupled to the rate of return of tidally destroyed debris to the SMBH, then the TDE luminosity function is in good agreement with observations and scales as ∝L −2.5 for high luminosities, provided that the SMBH mass function dN • / dM • —the number of SMBHs (N •) per SMBH mass (M •)—is approximately flat in the mass range over which we observe TDEs. We also show that there is a cutoff in the luminosity function at low luminosities that is a result of direct captures, and this cutoff has been tentatively observed. If dN • / dM • is flat, which is in agreement with some observational campaigns, these results suggest that the fallback rate feeds the accretion rate in TDEs. Contrarily, if dN • / d log M • is flat, which has been found theoretically and is suggested by other observational investigations, then the emission from TDEs is likely powered by another mechanism. Future observations and more TDE statistics, provided by the Rubin Observatory/LSST, will provide additional evidence as to the reality of this tension.

Tidal Disruption Events through the Lens of the Cooling Envelope Model

“…After reaching peak luminosity, some TDE light curves decay roughly as L ∝ t −5/3 (e.g., Gezari et al 2006;Hung et al 2017), consistent with the predicted mass fallback rate for complete disruptions (Phinney 1989;Guillochon & Ramirez-Ruiz 2013). This has motivated semiphenomenological lightcurve models like MOSFiT, which assume that the radiated luminosity scales with the fallback rate (e.g., Guillochon et al 2018;Mockler et al 2019;Nicholl et al 2020;Coughlin & Nicholl 2023). However, the postmaximum decay is sometimes better fit as an exponential (e.g., Holoien et al 2016b;Blagorodnova et al 2017) or may even exhibit a flattening or secondary peaks (e.g., Leloudas et al 2016;van Velzen et al 2019;Wevers et al 2019).…”

Ultradeep Cover: An Exotic and Jetted Tidal Disruption Event Candidate Disguised as a Gamma-Ray Burst

“…and theoretical (e.g.,Hopkins et al 2007;Merloni & Heinz 2008;Shankar et al 2009;Volonteri & Begelman 2010) works find a flat distribution in the log of the black hole mass and hence a diverging number of black holes with small masses. The steep power-law decline of the observed TDE luminosity function (e.g., van Velzen 2018;Lin et al 2022;Charalampopoulos et al 2023;Guolo et al 2023;Yao et al 2023) is consistent with the former (i.e., a flat distribution in M • ) if TDEs are powered by fallback accretion(Coughlin & Nicholl 2023).While the precise rate of ultradeep TDEs is difficult to constrain without a better understanding of the SMBH mass function, it is clear from Table1that they are, in general, rare. It is therefore not surprising, and indeed broadly consistent with this model, that of the (large) number of GRBs that have been observed to date, GRB 191019A appears almost unique.…”