Unified treatment of tidal disruption by Schwarzschild black holes

Abstract

Stars on orbits with pericenters sufficiently close to the supermassive black hole at the center of their host galaxy can be ripped apart by tidal stresses. Some of the resulting stellar debris becomes more tightly bound to the hole and can potentially produce an observable flare called a tidaldisruption event (TDE). We provide a self-consistent, unified treatment of TDEs by non-spinning (Schwarzschild) black holes, investigating several effects of general relativity including changes to the boundary in phase space that defines the loss-cone orbits on which stars are tidally disrupted or captured. TDE rates decrease rapidly at large black-hole masses due to direct stellar capture, but this effect is slightly countered by the widening of the loss cone due to the stronger tidal fields in general relativity. We provide a new mapping procedure that translates between Newtonian gravity and general relativity, allowing us to better compare predictions in both gravitational theories. Partial tidal disruptions in relativity will strip more material from the star and produce more tightly bound debris than in Newtonian gravity for a stellar orbit with the same angular momentum. However, for deep encounters leading to full disruption in both theories, the stronger tidal forces in relativity imply that the star is disrupted further from the black hole and that the debris is therefore less tightly bound, leading to a smaller peak fallback accretion rate. We also examine the capture of tidal debris by the horizon and the relativistic pericenter precession of tidal debris, finding that black holes of 10 6 solar masses and above generate tidal debris precessing by 10• or more per orbit.

Stellar tidal disruption events in general relativity

“…(32) and (33) at the points on each orbit experiencing the same threshold for tidal disruption (a gauge-invariant criterion), one finds that the tidal debris is slightly less tightly bound in GR. For the most massive Schwarzschild SMBH capable of fully disrupting a star without capture by the event horizon (for which relativistic effects will be most significant), the most tightly bound debris is ∼ 77% as tightly bound in GR as it is in Newtonian gravity [129]. If the TDE bolometric luminosity traced the fallback accretion rate as is sometimes assumed, this would imply slightly fainter TDEs in GR compared to Newtonian gravity.…”

Phenomenological aspects of black holes beyond general relativity

“…For M 10 7 M the tidal radius is very close to the Schwarzschild radius, therefore, tidal disruption events (TDE) happen in a region in which the Newtonian treatment is not sufficient and relativistic tidal forces must be taken into account [124], which is associated with the relativistic nature of the near-horizon orbits. Moreover, for M 10 8 M (this value for the order of magnitude takes into account the relevant relativistic features), tidal forces are not strong enough, so that main-sequence stars are able to reach the Schwarzschild radius while keeping their integrity [125,126].…”

Rates of Stellar Tidal Disruption

“…Calculating observable TDE rates in a fully self-consistent manner with the asymmetric, relativistic loss cones described above remains an open problem, but we can anticipate several qualitative features of the results. For Schwarzschild SMBHs, the tidal acceleration is stronger in GR than on Newtonian orbits with the same angular momentum L (Servin and Kesden 2017 Merritt [22] for 0 TD with an updated M relation. The colored curves show our relativistic corrections TD to this prediction.…”