Massive black hole binary eccentricity in rotating stellar systems

TL;DR

This study investigates how the eccentricity of massive black hole binaries evolves within rotating stellar systems, revealing that the degree of stellar co-rotation significantly influences whether the binary becomes more or less eccentric.

Contribution

It introduces a hybrid modeling approach combining numerical and analytical methods to analyze eccentricity evolution based on stellar rotation in cusps.

Findings

Counter-rotating stars increase binary eccentricity rapidly.

High co-rotation leads to binary circularization.

Hybrid model results agree qualitatively with N-body simulations.

Abstract

In this letter we study the eccentricity evolution of a massive black hole (MBH) binary (MBHB) embedded in a rotating stellar cusp. Following the observation that stars on counter-rotating (with respect to the MBHB) orbits extract angular momentum from the binary more efficiently then their co-rotating counterparts, the eccentricity evolution of the MBHB must depend on the degree of co-rotation (counter-rotation) of the surrounding stellar distribution. Using an hybrid scheme that couples numerical three-body scatterings to an analytical formalism for the cusp-binary interaction, we verify this hypothesis by evolving the MBHB in spherically symmetric cusps with different fractions F of co-rotating stars. Consistently with previous works, binaries in isotropic cusps (F=0.5) tend to increase their eccentricity, and when F approaches zero (counter-rotating cusps) the eccentricity rapidly increases to almost unity. Conversely, binaries in cusps with a significant degree of co-rotation (F>0.7) tend to become less and less eccentric, circularising quite quickly for F approaching unity. Direct N-body integrations performed to test the theory, corroborate the results of the hybrid scheme, at least at a qualitative level. We discuss quantitative differences, ascribing their origin to the oversimplified nature of the hybrid approach.