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

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. Spinorbit precession also induces a nontrivial 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. DOI: https://doi.org/10.1103/PhysRevD.81.124001 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-41690 Accepted Version Originally published at: Klein, A; Jetzer, P (2010). Spin effects in the phasing of gravitational waves from binaries on eccentric orbits. Physical Review D, 81(12):124001. DOI: https://doi.org/10.1103/PhysRevD.81.124001 ar X iv :1 00 5. 20 46 v1 [ gr -q c] 1 2 M ay 2 01 0 Spin effects in the phasing of gravitational waves from binaries on eccentric orbits Antoine Klein∗ and Philippe Jetzer Institut für Theoretische Physik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich (Dated: May 13, 2010) 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 10-10 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.