Approach to the separatrix with eccentric orbits

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.

38 pages, 11 figures

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Cited by in corpus (4)

• Post-adiabatic waveform-generation framework for asymmetric precessing binaries
• Peaking into the abyss: Characterizing the merger of equatorial-eccentric-geodesic plunges in rotating black holes
• Constants of motion in gravitational self-force theory
• Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane