Spin effects in the phasing of gravitational waves from binaries on eccentric orbits

TL;DR

This paper calculates spin-orbit and spin-spin effects on gravitational wave phase evolution from eccentric binaries at 2PN order, revealing small residual eccentricities and complex precession patterns that impact waveform modeling.

Contribution

It introduces a divergence-free quasi-Keplerian parametrization for accurate 2PN calculations of spin effects in eccentric binary inspirals.

Findings

Residual eccentricity of 10^{-4} to 10^{-3} for supermassive black hole binaries in LISA band.

Spin-orbit precession causes complex eccentricity evolution patterns.

Results can improve gravitational wave parameter estimation accuracy.

Abstract

We compute here the spin-orbit and spin-spin couplings needed for an accurate computation of the phasing of gravitational waves emitted by comparable-mass binaries on eccentric orbits at the second post-Newtonian (PN) order. We use a quasi-Keplerian parametrization of the orbit free of divergencies in the zero eccentricity limit. We find that spin-spin couplings induce a residual eccentricity for coalescing binaries at 2PN, of the order of $10^{-4}$-$10^{-3}$ for supermassive black hole binaries in the LISA band. Spin-orbit precession also induces a non-trivial pattern in the evolution of the eccentricity, which could help to reduce the errors on the determination of the eccentricity and spins in a gravitational wave measurement.