Kepler equation for inspiralling compact binaries

Abstract

Compact binaries consisting of neutron stars/black holes on eccentric orbit undergo a perturbed Keplerian motion. The perturbations are either of relativistic origin or are related to the spin, mass quadrupole, and magnetic dipole moments of the binary components. The post-Newtonian motion of such systems decouples into radial and angular parts. We present here for the first time the radial motion of such a binary encoded in a generalized Kepler equation, with the inclusion of all above-mentioned contributions, up to linear order in the perturbations. Together with suitably introduced parametrizations, the radial motion is solved completely.

First order post-Newtonian gravitational waveforms of binaries on eccentric orbits with Hansen coefficients

“…We note that the Kepler equation remains the same with the inclusion of the spin-orbit interaction (see ref. [21]) but it contains higher order contributions such as the spin-spin, quadrupole-monopole and magnetic dipole-dipole interactions [20] or the second post-Newtonian corrections [22]. For this reason we use an other parameterization which has only two eccentricities and the evolution of the azimuthal angle θ is similarly simple as Eq.…”

Eccentric motion of spinning compact binaries

“…For example, in [19], the circular-orbit motion has been solved with the help of a sequence of Lie transformations. In other publications, see [20], a Kepler equation for compact binaries with spin has been given; in [21] the GW forms of eccentric binaries with spin were worked out -the equations of motion of the entering spin orientation angles are given, but not solved there. In [22], tail-induced spin-orbit effects in the energy flux and the GW forms have been derived for circular orbits with arbitrary masses.…”

Post-Newtonian Approximations, Compact Binaries, and Strong-Field Tests of Gravity

“…If the body is a neutron star with a strong magnetic field, then the representing "particle" is endowed also with a magnetic type dipole moment. The speaker has demonstrated a generalized Kepler equation 55 where the orbital elements include contributions from the spin-spin, mass quadrupole and magnetic dipole interactions. The considered effects nicely fit in the standard Kepler form with the modified parameters of the orbit.…”