What Mass Are the Smallest Protohalos?

We calculate the kinetic-decoupling temperature for weakly interacting massive particles (WIMPs) in supersymmetric (SUSY) and extra dimensional models that can account for the cold-dark-matter abundance determined from cosmic microwave background measurements. Depending on the parameters of the particle-physics model, a wide variety of decoupling temperatures is possible, ranging from several MeV to a few GeV. These decoupling temperatures imply a range of masses for the smallest protohalos much larger than previously thought—ranging from ${10}^{-6}{M}_{\oplus }$ to ${10}^2{M}_{\oplus }$. We expect the range of protohalos masses derived here to be characteristic of most particle-physics models that can thermally accommodate the required relic abundance of WIMP dark matter, even beyond SUSY and extra dimensions.

Figure 1

Neutralino-electron scattering cross section as a function of the electron energy $E_l$ for the four benchmark models $\mathbf{A}–\mathbf{D}$ discussed in the text.

Figure 2

Feynman diagrams contributing to the scattering of a $B^{(1)}$ LKP (a.1 and a.2) and a $\nu$-like $X$ particle (b) off fermions.

Figure 3

The kinetic-decoupling temperature $T_{\mathrm{kd}}$ as a function of the WIMP mass for supersymmetric models (red empty dots are for the general MSSM while light-blue filled dots are for mSUGRA) giving a neutralino thermal relic abundance consistent with cosmology, for UED models featuring a $B^{(1)}$ LKP, and for a model featuring a $\nu$-like $X$ particle. The four benchmark models $\mathbf{A}–\mathbf{D}$ discussed in the text are also shown.

Figure 4

The WIMP protohalo characteristic comoving wave number $k_c$ (left axis) and mass $M_c$ (right axis) as a function of the WIMP mass, for the same models as in Fig. 3.