The first WIMPy halos

TL;DR

The authors show that WIMP microphysics imposes a sharp small-scale cut-off in the dark matter power spectrum, driven by collisional damping and free streaming, yielding a characteristic first-halo mass around M_cut ~ 1e-6 M_sun. They develop analytic transfer functions, normalize to WMAP, and map the impact of a scale-dependent primordial spectrum on the formation time and properties of the first WIMP halos, predicting non-linear collapse at z ~ 60 ± 20 for typical fluctuations and identifying rare, highly dense halos as potential bright sources for indirect detection. The results imply that most nascent halos may not survive hierarchical assembly, but the rare surviving halos could dominate indirect detection signals, with significant implications for interpreting experimental searches and motivating high-resolution simulations of early structure formation. Overall, the work provides a physically grounded small-scale regulator for CDM structure and quantifies the expected initial halo population for WIMPs, linking particle physics to observable dark matter phenomenology.

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 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.

Figures (9)

• Figure 1: The dependence of the WIMP chemical and kinetic decoupling temperatures, $T_{\rm cd}$ and $T_{kd}$, on the WIMP mass (indicated by the grey scale) for WIMPs with $\omega_{\rm wimp} = 0.076 - 0.156$. The upper and lower bands are for l=1 (Majorana) and 0 (Dirac) respectively.
• Figure 2: The variation of the characteristic damping and free streaming comoving wavenumbers, $k_{\rm d}$ and $k_{fs}$, with WIMP mass (indicated by grey scale). The lower and upper bands are for l=1 (Majorana) and 0 (Dirac) respectively.
• Figure 3: The CDM density contrast $\Delta$ at $z=300$ (lower lines) and $z=100$ (upper lines) for $\omega_{\rm cdm}=0.116$, $\omega_{\rm b}=0.024$ and $\omega_{\rm cdm}=0.14$, $\omega_{\rm b}=0.00$ (bottom and top line of each pair respectively), using our analytic expression (\ref{['sol2']}) (solid line) and also the COSMICS package (dotted line). The analytic superhorizon normalisation (\ref{['neutrinonormalisation']}) is shown as a dashed line for $k< 10^{-2} k_{\rm eq}$. The vertical dashed line denotes $k_b$. Our approximation applies best at $k>k_{\rm b}$ but, as the comparison shows, it is also pretty good for smaller wavenumbers.
• Figure 4: The dimensionless power spectrum of the WIMP density contrast at $z = 300$ for our four benchmark WIMP models assuming a scale-invariant primordial power spectrum (full lines, from left to right models A, B, C and D). Without the effects of collisional damping and free streaming, the power spectra would be given by the dotted line. The vertical dashed line denotes $k_b$, the wavenumber below which baryons follow CDM. Our approximations are optimised for $k > k_{\rm b}$.
• Figure 5: The primordial power spectra of the three benchmark inflation models discussed in the text (from top to bottom: hybrid, power law and $m^2 \phi^2$ chaotic inflation) for the standard power law parameterisation of the power spectrum (equation (\ref{['prim1']}), solid line) and for the expansion in $\ln{(k/k_{0})}$ (equation (\ref{['prim2']}), dotted line).