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 sub-parsec 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 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.
PACS numbers:FERMILAB-PUB-05-013-AThere is compelling evidence that the matter density of the Universe is dominated by some sort of non-baryonic, "dark", matter, the best candidates being weakly interacting massive particles [1,2]. Numerical N -body simulations suggest dark matter (DM) density profiles following broken power laws, ρ ∝ r −γ , with γ ≈ 3 in the outer parts of halos and 1 < ∼ γ < ∼ 1.5 ("cusps") inside the Solar circle. Although these profiles reproduce with sufficently good accuracy the observed properties of galactic halos on large scales, as inferred by rotation curves, little is known about the DM distribution on smaller scales, where the gravitational potential is dominated by baryons. The situation at the Galactic center (GC) is further complicated by the presence of a supermassive black hole (SBH), with mass ∼ 10 6.5 M ⊙ [3], whose sphere of gravitational influence extends out to ∼ 1 pc.The prospects for indirect detection depend crucially on the distribution of DM within this small region. The flux of gamma-rays from the GC, from the annihilation of DM particles of mass m and annihilation cross section in the non-relativistic limit σv, can be written:where Φ 0 = 5.6 × 10 −12 cm −2 s −1 and and σv th = 3 × 10 −26 cm 3 s −1 is the value of the thermally averaged cross section at decoupling that reproduces the observed cosmological abundance of Dark Matter (although in presence of resonance effects like co-annihilations, the correct relic abundance can be achieved with smaller cross sections). For more details and a review on DM candidates and detection see e.g. Refs. [1,2]. J ∆Ω is a factor containing all the information on the DM profile [4]:where dl is the distance element along the line of sight at angle ψ with respect to the GC, ∆Ω is the solid angle of the detector, and K is a normalizing factor, K −1 = (8.5kpc)(0.3GeV/cm 3 ) 2 . We denote by J 5 and J 3 the values of J when ∆Ω = 10 −5 sr and 10 −3 sr respectively; the former is the approximate field of view of the detectors in GLAST [5] and in atmospheric Cerenkov telescopes like VERITAS [6] and HES...