Power spectrum of gravitational waves from unbound compact binaries

TL;DR

This paper derives an analytic energy spectrum formula for gravitational waves emitted by unbound compact binaries on hyperbolic orbits, relevant for future gravitational wave detectors, and confirms its consistency with known limiting cases.

Contribution

It provides a new analytic expression for the gravitational wave energy spectrum from hyperbolic encounters, extending previous work to a broader range of eccentricities.

Findings

Analytic formula agrees with known parabolic and high-eccentricity limits.

The spectrum covers a wide frequency range relevant for detectors like LISA and LIGO.

The work enhances understanding of gravitational wave signals from unbound systems.

Abstract

Unbound interacting compact binaries emit gravitational radiation in a wide frequency range. Since short burst-like signals are expected in future detectors, such as LISA or advanced LIGO, it is interesting to study their energy spectrum and the position of the frequency peak. Here we derive them for a system of massive objects interacting on hyperbolic orbits within the quadrupole approximation, following the work of Capozziello et al. In particular, we focus on the derivation of an analytic formula for the energy spectrum of the emitted waves. Within numerical approximation our formula is in agreement with the two known limiting cases: for the eccentricity {\epsilon} = 1, the parabolic case, whose spectrum was computed by Berry and Gair, and the large {\epsilon} limit with the formula given by Turner.