The maximum mass of a black hole which can tidally disrupt a star: measuring black hole spins with tidal disruption events

Abstract

The tidal acceleration experienced by an object at the event horizon of a black hole decreases as one over the square of the black hole's mass. As such there is a maximum mass at which a black hole can tidally disrupt an object outside of its event horizon and potentially produce observable emission. This maximum mass is known as the ``Hills mass'', and in full general relativity is a function of both the black hole's spin $a_{\bullet }$ and the inclination angle of the incoming object's orbit with respect to the black hole's spin axis $\psi$. In this paper we demonstrate that the Hills mass can be represented by a simple analytical function of $a_{\bullet }$ and $\psi$, the first general solution of this problem. This general solution is found by utilising the symmetries of a class of critical Kerr metric orbits known as the innermost bound spherical orbits. Interestingly, at fixed black hole spin the maximum Hills mass can lie at incoming orbital inclinations outside of the black hole's equatorial plane $\psi \ne \pi /2$. When compared to previous results in the literature this effect can lead to an increase in the maximum Hills mass (at fixed spin) by as much as a factor of $\sqrt{11/5}\simeq 1.48$ for a maximally rotating black hole. We then demonstrate how Bayesian inference, coupled with an estimate of the mass of a black hole in a tidal disruption event, can be used to place conservative constraints on that black hole's spin. We provide a publicly available code tidalspin which computes these spin distributions.

V2: Typographical errors corrected in equations C1 and C6. No results changed. With thanks to Bence Kocsis. V1: 16 pages + appendices, 15 figures. Version accepted for publication in MNRAS. Code for computing spin posteriors available at https://github.com/andymummeryastro/tidalspin

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Cited by in corpus (10)

• Demographics of Tidal Disruption Events with L-Galaxies: I. Volumetric TDE rates and the abundance of Nuclear Star Clusters
• An Extremely Luminous Flare Recorded from a Supermassive Black Hole
• Evidence for a steeper SMBH-Bulge mass relationship extended to low masses using TDE host galaxies
• Toward Black Hole Stars: supermassive black hole growth in nuclear clusters via stellar-object and gas accretion
• Wind-mediated Eddington-limited emission in a $10^4{M}_{\odot }$ Black Hole Tidal Disruption Event
• Roche limit and stellar disruption in the Simpson--Visser spacetime
• Partial tidal disruption of White Dwarfs in off-equatorial orbits around Kerr black holes
• AT2024lhc and AT2024kmq in the landscape of featureless tidal disruption events
• Discovery of a Featureless Tidal Disruption Event at z~1 with the Wide Field Survey Telescope
• Prospects for Measuring Black Hole Masses using TDEs with the Vera C. Rubin Observatory