Tidal Disruptions of Stars by Supermassive and Intermediate-mass Black Hole Binaries: The Effects of the First-order Post-Newtonian Cross Terms

Abstract In the vicinity of galactic nuclei, stars orbiting supermassive black hole (SMBH) binaries can undergo tidal disruption events (TDEs) due to the Lidov–Kozai mechanism and three-body interactions. While numerical simulations have incorporated post-Newtonian (PN) corrections up to 2.5PN order, they have not accounted for the 1PN cross-term effects among the three bodies. In this study, we employ N -body simulations to investigate the impact of the 1PN cross terms on the orbits of stars around an intermediate-mass black hole (IMBH) perturbed by an outer SMBH. Our findings indicate that while the 1PN cross terms do not substantially affect the fractions of stellar outcomes, they can cause considerable variations in the orbits of stars around IMBH–SMBH binaries. Specifically, we find that the inclusion of the 1PN cross terms can lead to more concentrated distributions of semimajor axes. Furthermore, we observe heavy tails in the distributions of temporal shifts in TDEs when these cross terms are included, with the maximum change reaching about 10 6 yr, approaching the maximum integration time of this study. This investigation underscores the critical importance of incorporating the 1PN cross terms to ensure accuracy in comprehensive simulations of multibody systems in galactic nuclei. Notably, for stars partially disrupted by an SMBH binary, omitting these cross terms could result in erroneous predictions.