The first WIMPy halos

Dark matter direct and indirect detection signals depend crucially on the dark matter distribution. While the formation of large scale structure is independent of the nature of the cold dark matter (CDM), the fate of inhomogeneities on sub-galactic scales, and hence the present day CDM distribution on these scales, depends on the micro-physics of the CDM particles. We study the density contrast of Weakly Interacting Massive Particles (WIMPs) on sub-galactic scales. We calculate the damping of the primordial power spectrum due to collisional damping and free-streaming of WIMPy CDM and show that free-streaming leads to a CDM power spectrum with a sharp cut-off at about $10^{-6} M_\odot$. We also calculate the transfer function for the growth of the inhomogeneities in the linear regime, taking into account the suppression in the growth of the CDM density contrast after matter-radiation equality due to baryons and show that our analytic results are in good agreement with numerical calculations. Combining the transfer function with the damping of the primordial fluctuations we produce a WMAP normalized primordial CDM power spectrum, which can serve as an input for high resolution CDM simulations. We find that the smallest inhomogeneities typically have co-moving radius of about 1 pc and enter the non-linear regime at a redshift of $60 \pm 20$. We study the effect of scale dependence of the primordial power spectrum on these numbers and also use the spherical collapse model to make simple estimates of the properties of the first generation of WIMP halos to form. We find that the very first WIMPy halos may have a significant impact on indirect dark matter searches.