Eccentric-orbit EMRI gravitational wave energy fluxes to 7PN order

TL;DR

This paper provides high-precision calculations of gravitational wave energy fluxes from eccentric extreme-mass-ratio binaries up to 7PN order, confirming previous results and extending them with new analytic and numeric terms.

Contribution

It introduces new high-order PN terms for eccentric EMRI energy fluxes, confirms existing coefficients, and develops improved methods for modeling hereditary terms at high eccentricities.

Findings

Confirmed all coefficients up to 3PN order

Derived new analytic and numeric terms between 3.5PN and 7PN

Developed a model for eccentricity singular functions that improves fit at high eccentricity

Abstract

We present new results through 7PN order on the energy flux from eccentric extreme-mass-ratio binaries. The black hole perturbation calculations are made at very high accuracy (200 decimal places) using a Mathematica code based on the Mano-Suzuki-Takasugi (MST) analytic function expansion formalism. All published coefficients in the expansion through 3PN order are confirmed and new analytic and numeric terms are found to high order in $e^2$ at orders between 3.5PN and 7PN. We also show original work in finding (nearly) arbitrarily accurate expansions for hereditary terms at 1.5PN, 2.5PN, and 3PN orders. We fit to a model where at each PN order an eccentricity singular function is factored out, improving substantially the fit even as $e \to 1$.