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.
@article{arxiv.2412.04249,
title = {Approach to the separatrix with eccentric orbits},
author = {Guillaume Lhost and Geoffrey Compère},
journal= {arXiv preprint arXiv:2412.04249},
year = {2025}
}