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

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