The first WIMPy halos

Abstract

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 freestreaming of WIMPy CDM and show that free-streaming leads to a CDM power spectrum with a sharp cut-off at about 10 −6 M ⊙ . 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±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.

Thermal decoupling of WIMPs from first principles

“…Subsequently, free streaming of CDM suppresses further the power of structure formation on small scales. In that way, collisional and collisionless damping processes give rise to a fundamental cut-off in the spectrum of linear CDM perturbations [7,8] and thus to a characteristic feature that clearly depends on the CDM microphysics. It was later shown numerically [11] that acoustic oscillations have to be taken into account at kinetic decoupling, however, the order of magnitude of the cut-off scale is correctly given in [7,8].…”

Structure formation with suppressed small-scale perturbations

“…These spectra are compared to the hypothetical case of pure CDM (black line). The suppression of power in WIMP scenarios happens at very high wave-numbers roughly following an exponential cutoff (Green et al 2005). We will show later on that such WIMP models suppress structure formation at a halo mass of about 10 −6 h −1 M .…”

Thermal decoupling and the smallest subhalo mass in dark matter models with Sommerfeld-enhanced annihilation rates

“…This quantity, in turn, can be related to a small-scale cutoff M cut in the power spectrum of matter density fluctuations which corresponds to the mass of the smallest gravitationally bound objects [14].…”

“…At kinetic decoupling, which actually happens on a rather short timescale [9,10], even these scattering processes cease to be effective; in the standard picture, there is then no further interaction between WIMPs and the heat bath. From this point on, density perturbations in the DM component are thus no longer tightly bound to density perturbations in the radiation component and can freely develop, with free-streaming effects setting a lower bound to the size of over-dense regions that will eventually collapse under the influence of gravitation [11][12][13][14]; acoustic oscillations lead to a similar cutoff [15,16].…”