On the survival of dark matter spikes: Stellar and compact-object perturbations

Abstract

Establishing realistic expectations for the dark matter (DM) distribution near a supermassive black hole (BH) is essential for assessing environmental imprints on gravitational wave (GW) signals. Using the Galactic Center as an observationally constrained case study, we investigate the evolution of DM density spikes under gravitational perturbations from the nuclear stellar and black hole populations surrounding the central BH. We find that scattering of DM particles by the nuclear star cluster depletes the DM distribution at radii $r \sim 10^{-1}~\mathrm{pc}$, far outside the region where the relevant GW signals are produced. At smaller radii, at $r \sim 10^{-3}~\mathrm{pc}$, the closest known stellar perturbers, S2 and S38, induce only negligible changes to the density profile. At still smaller radii, where no stellar perturbers are currently known, we assess the cumulative impact of past EMRIs by modelling successive mergers with stellar-mass BHs of mass $\sim10~\mathrm{M}_\odot$, in numbers consistent with the expected rate over $10~\mathrm{Gyr}$. We find that these events do not erase the central overdensity, reducing the density only to approximately $82 \%$ of its initial value at $r \lesssim 10^{-5}~\mathrm{pc}$. Our results indicate that, at least at the Galactic Center, DM overdensities around the central BH are expected to remain largely intact under stellar perturbations and plausible stellar-BH merger histories.