Massive black hole binary eccentricity in rotating stellar systems

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 than their corotating counterparts, the eccentricity evolution of the MBHB must depend on the degree of corotation (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 fractionsof corotating stars. Consistent with previous works, binaries in isotropic cusps () tend to increase their eccentricity, and whenapproaches zero (counter-rotating cusps) the eccentricity rapidly increases to almost unity. Conversely, binaries in cusps with a significant degree of corotation () tend to become less and less eccentric, circularizing quite quickly forapproaching unity. DirectN-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. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.