Interaction of massive black hole binaries with their stellar environment: III. Scattering of bound stars

TL;DR

This paper develops a formalism to study how massive black hole binaries interact with their stellar environment, revealing how these interactions influence binary evolution, stellar cusp erosion, and hypervelocity star ejection.

Contribution

It introduces a new formalism for analyzing the dynamics of black hole binaries in stellar cusps and explores their orbital decay and stellar ejection processes.

Findings

Bound star scattering accelerates binary decay and increases eccentricity.

Binaries can reach the gravitational wave regime within a Hubble time.

Ejected hypervelocity stars can escape the Milky Way's gravitational potential.

Abstract

We develop a formalism for studying the dynamics of massive black hole binaries embedded in gravitationally-bound stellar cusps, and study the binary orbital decay by three-body interactions, the impact of stellar slingshots on the density profile of the inner cusp, and the properties of the ejected hypervelocity stars (HVSs). We find that the scattering of bound stars shrinks the binary orbit and increases its eccentricity more effectively than that of unbound ambient stars. Binaries with initial eccentricities e>0.3 and/or unequal-mass companions (M_2/M_1<0.1) can decay by three-body interactions to the gravitational wave emission regime in less than a Hubble time. The stellar cusp is significantly eroded, and cores as shallow as \rho\propto r^-0.7 may develop from a pre-existing singular isothermal density profile. A population of HVSs is ejected in the host galaxy halo, with a total mass ~M_2. We scale our results to the scattering of stars bound to Sgr A*, the massive black hole in the Galactic Center, by an inspiraling companion of intermediate mass. Depending on binary mass ratio, eccentricity, and initial slope of the stellar cusp, a core of radius ~0.1 pc typically forms in 1-10 Myr. On this timescale about 500-2500 HVSs are expelled with speeds sufficiently large to escape the gravitational potential of the Milky Way.