Evolution of the Dark Matter Distribution at the Galactic Center

Annihilation radiation from neutralino dark matter at the Galactic center(GC) would be greatly enhanced if the dark matter were strongly clusteredaround the supermassive black hole (SBH). The existence of a dark-matter"spike" is made plausible by the observed, steeply-rising stellar density nearthe GC SBH. Here the time-dependent equations describing gravitationalinteraction of the dark matter particles with the stars are solved. Scatteringof dark matter particles by stars would substantially lower the dark matterdensity near the GC SBH over 10^10 yr, due both to kinetic heating, and tocapture of dark matter particles by the SBH. This result suggests thatenhancements in the dark matter density around a SBH would be modest whether ornot the host galaxy had experienced the scouring effects of a binary SBH.Comment: 5 pages, 3 figures. Submitted to Physical Review Letter