Sharpening the dark matter signature in gravitational waveforms. I. Accretion and eccentricity evolution

Dark matter overdensities around black holes can alter the dynamical evolution of a companion object orbiting around it, and cause a dephasing of the gravitational waveform. Here, we present a refined calculation of the coevolution of the binary and the dark matter distribution, taking into account the accretion of dark matter particles on the companion black hole, and generalizing previous quasicircular calculations to the general case of eccentric orbits. These calculations are validated by dedicated $N$-body simulations. We show that accretion can lead to a large dephasing, and therefore cannot be neglected in general. We also demonstrate that dark matter spikes tend to circularize eccentric orbits faster than previously thought.