Small-scale clumps in the galactic halo and dark matter annihilation

Abstract

Production of small-scale dark matter (DM) clumps is studied in the standard cosmological scenario with an inflation-produced primeval fluctuation spectrum. Special attention is given to the three following problems. (i) The mass spectrum of small-scale clumps with $M\ensuremath{\lesssim}{10}^{3}{M}_{\ensuremath{\bigodot}}$ is calculated with the tidal destruction of the clumps taken into account within a hierarchical model of clump structure. Only 0.1--0.5 % of small clumps survive the stage of tidal destruction in each logarithmic mass interval $\ensuremath{\Delta}\mathrm{ln}M\ensuremath{\sim}1.$ (ii) The mass distribution of clumps has a cutoff at ${M}_{\mathrm{min}}$ due to the diffusion of DM particles out of fluctuation and free streaming at later stages. ${M}_{\mathrm{min}}$ is a model-dependent quantity. In the case that the neutralino, considered as a pure B-ino, is a DM particle, ${M}_{\mathrm{min}}\ensuremath{\sim}{10}^{\ensuremath{-}8}{M}_{\ensuremath{\bigodot}}.$ (iii) The evolution of the density profile in a DM clump does not result in a singularity because of the formation of the core under the influence of tidal interaction. The radius of the core is ${R}_{c}\ensuremath{\sim}0.1R,$ where R is the radius of the clump. The applications for annihilation of DM particles in the Galactic halo are studied. The number density of clumps as a function of their mass, radius, and distance to the Galactic center is presented. The enhancement of the annihilation signal due to clumpiness, valid for arbitrary DM particles, is calculated. In spite of a small survival probability, the global annihilation signal in most cases is dominated by clumps. For the observationally preferable value of the index of the primeval fluctuation spectrum ${n}_{p}\ensuremath{\approx}1,$ the enhancement of the annihilation signal is described by a factor of 2 to 5 for different density profiles in a clump.