The impact of Post-Newtonian effects on massive black hole binary evolution at $\sim 1000\,R_{sch}$ separations

TL;DR

This study investigates how Post-Newtonian corrections, including gravitational wave emission, influence the energy dynamics of supermassive black hole binaries at around 1000 Schwarzschild radii during stellar interactions.

Contribution

It demonstrates that Post-Newtonian terms are essential for accurately modeling SMBH binary evolution at these separations, beyond Newtonian approximations.

Findings

Newtonian models are insufficient for SMBH binary energy evolution at these scales.

Post-Newtonian corrections significantly affect the binary's orbital energy during stellar interactions.

Including GW emission and PN terms is crucial for realistic SMBH binary evolution simulations.

Abstract

Aims: We study the impact of Post-Newtonian correction terms on the energetic interaction between a gravitational wave (GW)-emitting supermassive black hole (SMBH) binary system and incoming stars via three-body scattering experiments. Methods: We use the AR-chain code to simulate with high accuracy the interactions between stars and an SMBH binary at separations of$\sim 1000\,R_{sch}$. For all of the interactions, we investigate in detail the energy balance of the three-body systems, using both Newtonian and Post-Newtonian expressions for the SMBH binary orbital energy, taking into account the GW emission by the binary. Results: We find that at these separations, purely Newtonian treatment of the binary orbital energy is insufficient to properly account for the SMBH binary orbital evolution. Instead, along with GW emission, even terms in the PN-corrections must be included in order to describe the energy change of the binary during the stellar interaction.es, 2