On the impact of relativistic gravity on the rate of tidal disruption events

TL;DR

This paper analytically investigates how relativistic gravity influences the likelihood and distribution of tidal disruption events (TDEs) near supermassive black holes, highlighting the effects of black hole spin and mass on observable TDE rates.

Contribution

It provides a fully analytic analysis of stellar pericenter distributions in relativistic black hole metrics, quantifies the impact of spin and mass on TDE rates, and predicts a significant reduction in TDEs for high-mass SMBHs.

Findings

Relativistic effects cause a steep decline in stars with pericenter distances less than about 10 gravitational radii.

For maximally spinning SMBHs, the distribution of pericenter distances scales as r_p^{4/3}.

TDE rates are substantially reduced for SMBHs with masses above 10^7 solar masses.

Abstract

The tidal disruption of stars by supermassive black holes (SMBHs) probes relativistic gravity. In the coming decade, the number of observed tidal disruption events (TDEs) will grow by several orders of magnitude, allowing statistical inferences of the properties of the SMBH and stellar populations. Here we analyse the probability distribution functions of the pericentre distances of stars that encounter an SMBH in the Schwarzschild geometry, where the results are completely analytic, and the Kerr metric. From this analysis we calculate the number of observable TDEs, defined to be those that come within the tidal radius $r_{\rm t}$ but outside the direct capture radius (which is, in general, larger than the horizon radius). We find that relativistic effects result in a steep decline in the number of stars that have pericenter distances $r_{\rm p} \lesssim 10\,r_{\rm g}$, where $r_{\rm g} = GM/c^2$, and that for maximally spinning SMBHs the distribution function of $r_{\rm p}$ at such distances scales as $f_{\rm r_{\rm p}}\propto r_{\rm p}^{4/3}$, or in terms of $\beta \equiv r_{\rm t}/r_{\rm p}$ scales as $f_{\beta} \propto \beta^{-10/3}$. We find that spin has little effect on the TDE fraction until the very high-mass end, where instead of being identically zero the rate is small ($\lesssim 1\%$ of the expected rate in the absence of relativistic effects). Effectively independent of spin, if the progenitors of TDEs reflect the predominantly low-mass stellar population and thus have masses $\lesssim 1M_{\odot}$, we expect a substantial reduction in the rate of TDEs above $10^{7}M_{\odot}$.