# Ready-to-use Fourier domain templates for compact binaries inspiraling along moderately eccentric orbits

## TL;DR

This paper develops accurate, ready-to-use Fourier domain gravitational wave templates for inspiraling compact binaries with moderate eccentricity, incorporating amplitude and phase corrections up to high post-Newtonian orders.

## Contribution

It introduces a novel analytic template family for eccentric binary inspirals, including amplitude and phase corrections up to 3PN order, with a prescription for periastron advance effects.

## Key findings

- Templates are accurate to 1PN amplitude order and 3PN phase order.
- Inclusion of eccentricity effects up to sixth order in phase evolution.
- Preliminary data analysis indicates these templates are essential for modeling eccentric binary coalescence.

## Abstract

We derive analytic expressions that provide Fourier domain gravitational wave (GW) response function for compact binaries inspiraling along moderately eccentric orbits. These expressions include amplitude corrections to the two GW polarization states that are accurate to the first post-Newtonian (PN) order. Additionally, our fully 3PN accurate GW phase evolution incorporates eccentricity effects up to sixth order at each PN order. Further, we develop a prescription to incorporate analytically the effects of 3PN accurate periastron advance in the GW phase evolution. This is how we provide a ready-to-use and efficient inspiral template family for compact binaries in moderately eccentric orbits. Preliminary GW data analysis explorations suggest that our template family should be required to construct analytic inspiral-merger-ringdown templates to model moderately eccentric compact binary coalescence.