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

Abstract

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 co-evolution 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 quasi-circular 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.

Comments: 20 pages, 14 figures + appendices. Companion paper to "Sharpening the dark matter signature in gravitational waveforms II: Numerical simulations with the NbodyIMRI code" (arXiv:2402.13762). v3: Minor updates to match version published in PRD