Time-dependent models for dark matter at the galactic center

The prospects for indirect detection of dark matter at the galactic center with $\gamma$-ray experiments like the space telescope GLAST, and air Cherenkov telescopes like HESS, CANGAROO, MAGIC and VERITAS depend sensitively on the mass profile within the inner parsec. We calculate the distribution of dark matter on subparsec scales by integrating the time-dependent Fokker-Planck equation, including the effects of self-annihilations, scattering of dark matter particles by stars, and capture in the supermassive black hole. We consider a variety of initial dark matter distributions, including models with very high densities (“spikes”) near the black hole, and models with “adiabatic compression” of the baryons. The annihilation signal after ${10}^{10}\mathrm{yr}$ is found to be substantially reduced from its initial value, but in dark matter models with an initial spike, order-of-magnitude enhancements can persist compared with the rate in spike-free models.