Dark matter annihilation near a black hole: plateau vs. weak cusp

Abstract

Dark matter annihilation in so-called ``spikes'' near black holes is believed to be an important method of indirect dark matter detection. In the case of circular particle orbits, the density profile of dark matter has a plateau at small radii, the maximal density being limited by the annihilation cross-section. However, in the general case of arbitrary velocity anisotropy the situation is different. Particulary, for isotropic velocity distribution the density profile cannot be shallower than r^{-1/2} in the very centre. Indeed, a detailed study reveals that in many cases the term ``annihilation plateau'' is misleading, as the density actually continues to rise towards small radii and forms a weak cusp, rho ~ r^{-(beta+1/2)}, where beta is the anisotropy coefficient. The annihilation flux, however, does not change much in the latter case, if averaged over an area larger than the annihilation radius.