TY - JOUR

T1 - On the Impact of Relativistic Gravity on the Rate of Tidal Disruption Events

AU - Coughlin, Eric R.

AU - Nixon, C. J.

N1 - Funding Information:
We thank the referee for a useful and constructive report. E.R.C. acknowledges support from the National Science Foundation through grant AST-2006684, and a Ralph E. Powe Junior Faculty Enhancement Award through the Oakridge Associated Universities. C.J.N. acknowledges support from the Science and Technology Facilities Council [grant No. ST/W000857/1].
Publisher Copyright:
© 2022. The Author(s). Published by the American Astronomical Society.

PY - 2022/9/1

Y1 - 2022/9/1

N2 - 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 r 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 p ≲ 10 r g, where r g = GM/c 2, and that for maximally spinning SMBHs the distribution function of r p at such distances scales as f r p ∝ r p 4 / 3 , or in terms of β ≡ r t/r p scales as f β ∝ 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).

AB - 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 r 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 p ≲ 10 r g, where r g = GM/c 2, and that for maximally spinning SMBHs the distribution function of r p at such distances scales as f r p ∝ r p 4 / 3 , or in terms of β ≡ r t/r p scales as f β ∝ 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).

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U2 - 10.3847/1538-4357/ac85b3

DO - 10.3847/1538-4357/ac85b3

M3 - Article

AN - SCOPUS:85137406310

SN - 0004-637X

VL - 936

JO - Astrophysical Journal

JF - Astrophysical Journal

IS - 1

M1 - 70

ER -