On the Impact of Relativistic Gravity on the Rate of Tidal Disruption Events

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 analyze the probability distribution functions of the pericenter 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 rt 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 rp ≲ 10 rg, where rg = GM/c2, and that for maximally spinning SMBHs the distribution function of rp at such distances scales as ${f}_{{{\rm{r}}}_{{\rm{p}}}}\propto {r}_{{\rm{p}}}^{4/3}$, or in terms of β ≡ rt/rp scales as fβ ∝ β−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 (≲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 ≲1M⊙, we expect a substantial reduction in the rate of TDEs above 107M⊙.