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

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 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). 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 107 M ⊙.

The Luminosity Function of Tidal Disruption Flares for the ZTF-I Survey

“…Therefore, the average Hills mass should be lower, yielding a more consistent, lower luminosity. The above result agrees with the recent calculation of Coughlin & Nixon (2022), which indicates a rate suppression for BHs with M BH > 10 7 M e , given a predominantly low-mass stellar population.…”

Live to Die Another Day: The Rebrightening of AT 2018fyk as a Repeating Partial Tidal Disruption Event

“…The tidal radius is also highly relativistic, suggesting that-even for partial TDEs-disk formation will be prompt, which is consistent with the observed properties of AT 2018fyk (e.g., the presence of low-ionization Fe II lines in the optical spectrum, the persistent X-ray brightness at UV/optical peak, the thermal X-ray spectrum at early times, and its short-timescale variability in the X-ray; Wevers et al 2019Wevers et al , 2021. These arguments suggest that the star that initially fueled the outburst from AT 2018fyk by virtue of producing an observable flare was partially disrupted (most TDEs will result in unobservable direct captures for the high black hole mass; see also Coughlin & Nixon 2022). Typically, tidally disrupted stars are on approximately parabolic orbits (e.g., Merritt 2013), which begs the question of how a partial TDE could yield a rebrightening because, as noted by Cufari et al (2022a), tidal dissipation within the partially disrupted star yields a minimum orbital period of a few × 10 3 yr for a 10 7.7 M e SMBH (see their Equation (1)).…”

“…For a 10 7.7 M e SMBH, at most (for maximal spin), 5% of stars with masses and radii comparable to those of the Sun (or smaller) will enter within the tidal radius, be destroyed completely, and not swallowed whole (Kesden 2012;Ryu et al 2020;Coughlin & Nixon 2022). The tidal radius is also highly relativistic, suggesting that-even for partial TDEs-disk formation will be prompt, which is consistent with the observed properties of AT 2018fyk (e.g., the presence of low-ionization Fe II lines in the optical spectrum, the persistent X-ray brightness at UV/optical peak, the thermal X-ray spectrum at early times, and its short-timescale variability in the X-ray; Wevers et al 2019Wevers et al , 2021.…”

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

“…Recent investigations by, e.g., Beloborodov et al (1992), Kesden (2012), , Servin &Kesden (2017), andStone et al (2019) highlighted the fact that the direct capture radius can influence the TDE rate in a way that depends on black hole spin (on which the direct capture radius depends, as well as the projection of the angular momentum of the incoming star on the spin axis of the SMBH; see Equation (24) of Coughlin & Nixon 2022a), providing the possibility of constraining this parameter by using the precise variation of the TDE rate at the high-mass end of the SMBH mass function. However, there are additional factors that modify the direct capture condition that are related to, e.g., the population of tidally destroyed stars (D'Orazio et al 2019), andNixon (2022a) pointed out that if the stellar mass function is dominated by low-mass stars, the cutoff in the TDE mass function should be closer to 10 7 M e rather than the oftenquoted value of ∼10 8 M e (e.g., Hills 1975). Modeling of observed TDEs suggests that essentially all are consistent with low-mass stars and SMBH masses 10 7 M e (Nicholl et al 2022).…”