# Eccentric Gravitational Wave Bursts in the Post-Newtonian Formalism

## TL;DR

This paper develops a detailed post-Newtonian framework to model eccentric gravitational wave bursts, enhancing detection strategies for highly eccentric binaries in gravitational wave astronomy.

## Contribution

It introduces a generic post-Newtonian formalism for constructing time-frequency priors for eccentric GW bursts, including a third post-Newtonian order model, the most accurate analytic model to date.

## Key findings

- Provides a new formalism for eccentric GW burst modeling
- Generates a third post-Newtonian order burst model
- Enhances detection strategies for eccentric binaries

## Abstract

The detection of GW150914 by ground based gravitational wave observatories has brought about a new era in astrophysics. At optimal sensitivity, these observatories are expected to detect several events each year, with one or two of these occurring with non-negligible eccentricity. Such eccentric binaries will emit bursts of gravitational radiation during every pericenter passage, where orbital velocities can reach greater than ten percent the speed of light. As a result, such binaries may prove to be powerful probes of extreme gravitational physics and astrophysics. A promising method of achieving detection of such binaries is through power stacking, where the power in each burst is added up in time-frequency space. This detection strategy requires a theoretical prior of where the bursts will occur in time and frequency so that one knows where to search for successive bursts. We here present a generic post-Newtonian formalism for constructing such time-frequency model priors at generic post-Newtonian order. We apply our formalism to generate a burst model at third post-Newtonian order, making it potentially the most accurate, fully analytic model to date.