We model the effect of resonances between time-varying perturbative forces and the epicyclical motion of eccentric binaries in the gravitational wave (GW) driven regime. These induce secular drifts in the orbital elements, which are reflected in a dephasing of the binary’s GW signal, derived here systematically. The resulting dephasing prescriptions showcase a much richer phenomenology with respect to typically adopted models and are better able to model realistic environmental effects. The most important consequences are for gas embedded binaries, which we analyze in detail with a series of analytical calculations, numerical experiments, and a curated set of hydrodynamical simulations for equal masses. Even in these simplified tests, we find the surprising result that dephasing caused by epicyclical resonances dominate over expectations based on smoothed or orbit averaged gas drag models in GW signals that retain mild eccentricity in the detector band ($e>0.05$). We discuss how dissecting GW dephasing in its component Fourier modes can be used to probe the coupling of binaries with their surrounding environment in unprecedented detail.

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• Gravitational waves
• Accretion disk & black-hole plasma