Gravitational waves from binaries on unbound orbits

TL;DR

This paper introduces a generalized parametrization for describing both bound and unbound binary orbits in general relativity, providing detailed 1PN gravitational waveforms including higher multipole moments and eccentricity effects.

Contribution

It presents a new true anomaly-type parametrization for unbound and bound orbits, with explicit 1PN gravitational waveforms for unbound binaries including higher multipole moments.

Findings

Explicit 1PN gravitational waveforms for unbound orbits

Inclusion of higher multipole moments beyond quadrupole

Analysis of eccentricity effects on waveforms

Abstract

A generalized true anomaly-type parametrization, convenient to describe both bound and open orbits of a two-body system in general relativity is introduced. A complete description of the time evolution of both the radial and of the angular equations of a binary system taking into account the first order post-newtonian (1PN) is given. The gravitational radiation field emitted by the system is computed in the 1PN approximation including higher multipole moments beyond the standard quadrupole term. The gravitational waveforms in the time domain are explicitly given up to the 1PN order for unbound orbits, but the results are also illustrated on binaries on elliptic orbits with special attention given to the effects of eccentricity.