On the equal-mass limit of precessing black-hole binaries

Abstract

We analyze the inspiral dynamics of equal-mass precessing black-hole binaries using multi-timescale techniques. The orbit-averaged post-Newtonian evolutionary equations admit two constants of motion in the equal-mass limit, namely the magnitude of the total spin $S$ and the effective spin $ξ$. This feature makes the entire dynamics qualitatively different compared to the generic unequal-mass case, where only $ξ$ is constant while the variable $S$ parametrizes the precession dynamics. For fixed individual masses and spin magnitudes, an equal-mass black-hole inspiral is uniquely characterized by the two parameters $(S,ξ)$: these two numbers completely determine the entire evolution under the effect of radiation reaction. In particular, for equal-mass binaries we find that (i) the black-hole binary spin morphology is constant throughout the inspiral, and that (ii) the precessional motion of the two black-hole spins about the total spin takes place on a longer timescale than the precession of the total spin and the orbital plane about the total angular momentum.

13 pages, 1 figure, accepted for publication in CQG