Gravitational wave energy spectrum of a parabolic encounter

TL;DR

This paper derives an analytic gravitational wave energy spectrum for parabolic encounters, highlighting the importance of periapse distance over eccentricity, with implications for detecting signals from black hole interactions.

Contribution

It provides a new analytic expression for gravitational wave spectra from parabolic orbits, extending previous eccentric orbit models and comparing weak and strong-field results.

Findings

Peak energy spectrum depends mainly on periapse distance.

Weak-field approximation is accurate within 10% for certain orbital parameters.

Results are applicable to modeling gravitational wave bursts detectable by LISA.

Abstract

We derive an analytic expression for the energy spectrum of gravitational waves from a parabolic Keplerian binary by taking the limit of the Peters and Matthews spectrum for eccentric orbits. This demonstrates that the location of the peak of the energy spectrum depends primarily on the orbital periapse rather than the eccentricity. We compare this weak-field result to strong-field calculations and find it is reasonably accurate (~10%) provided that the azimuthal and radial orbital frequencies do not differ by more than ~10%. For equatorial orbits in the Kerr spacetime, this corresponds to periapse radii of rp > 20M. These results can be used to model radiation bursts from compact objects on highly eccentric orbits about massive black holes in the local Universe, which could be detected by LISA.