Collisionally regenerated dark matter structures in galactic nuclei

Abstract

We show that the presence of a $\ensuremath{\rho}\ensuremath{\sim}{r}^{\ensuremath{-}3/2}$ dark matter overdensity can be robustly predicted at the center of any galaxy old enough to have grown a power-law density cusp in the stars via the Bahcall-Wolf mechanism. Using both Fokker-Planck and direct $N$-body integrations, we demonstrate collisional generation of these dark matter ``crests'' (collisionally regenerated structures) even in the extreme case that the density of both stars and dark matter were previously lowered by slingshot ejection from a binary supermassive black hole. The time scale for collisional growth of the crest is approximately the two-body relaxation time as defined by the stars, which is $\ensuremath{\lesssim}10\text{ }\text{ }\mathrm{Gyr}$ at the centers of stellar spheroids with luminosities $L\ensuremath{\lesssim}{10}^{9.5}{L}_{\ensuremath{\bigodot}}$, including the bulge of the Milky Way. The presence of crests can robustly be predicted in such galaxies, unlike the steeper enhancements, called ``spikes,'' produced by the adiabatic growth of black holes. We discuss special cases where the prospects for detecting dark matter annihilations from the centers of galaxy halos are significantly affected by the formation of crests.