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.
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.
