Sharpening the dark matter signature in gravitational waveforms. II. Numerical simulations

Future gravitational wave observatories can probe dark matter by detecting the dephasing in the waveform of binary black hole mergers induced by dark matter overdensities. Such a detection hinges on the accurate modeling of the dynamical friction, induced by dark matter on the secondary compact object in intermediate and extreme mass ratio inspirals. In this paper, we introduce nbodyimri, a new publicly available code designed for simulating binary systems within cold dark matter spikes. Leveraging higher particle counts and finer time steps, we validate the applicability of the standard dynamical friction formalism and provide an accurate determination of the maximum impact parameter of particles which can effectively scatter with a compact object, across various mass ratios. We also show that in addition to feedback due to dynamical friction, the dark matter also evolves through a stirring effect driven by the time-dependent potential of the binary. We introduce a simple semianalytical scheme to account for this effect and demonstrate that including stirring tends to slow the rate of dark matter depletion and therefore enhances the impact of dark matter on the dynamics of the binary.