Approach to the separatrix with eccentric orbits

TL;DR

This paper derives an analytic solution for the late-time behavior of eccentric binary inspirals near the separatrix, using self-force coefficients and the Lambert W function, advancing modeling capabilities in gravitational wave physics.

Contribution

It introduces a novel analytic approach to describe inspiral trajectories near the separatrix, incorporating the Lambert W function and self-force coefficients.

Findings

Analytic late-time solution for eccentric inspirals near the separatrix.

Identification of Lambert W function as key in modeling approach.

Enhanced understanding of inspiral dynamics in gravitational wave sources.

Abstract

Eccentric binary compact mergers are prime targets of current and future gravitational wave observatories. In the small mass ratio expansion, post-adiabatic inspirals have been modeled up to the separatrix, where first-principle modeling currently ends. In this paper, we derive the analytic late time solution to the adiabatic inspiral in terms of self-force coefficients at the separatrix. We identify the role of the Lambert $W_{-1}$ function as a key mathematical ingredient in the approach to the separatrix.