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

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.