The power spectrum of SUSY-CDM on sub-galactic scales

TL;DR

The paper investigates how micro-physics of SUSY-CDM, specifically bino-like WIMPs, shapes the small-scale matter power spectrum. It combines collisional damping, kinetic free streaming, and gravitational growth to produce a WMAP-normalized spectrum with a sharp cut-off at around $M \sim 10^{-6} M_\odot$ and a nearby maximum, along with analytic transfer functions for subhorizon growth. The damping scales $k_d$ and $k_{fs}$ and the damping factor $D(k)$ are computed and used to construct the dimensionless power spectra ${\cal P}_\Delta$, ${\cal P}_v$, and ${\cal P}_\phi$, suitable as input for high-resolution simulations. The study estimates that typical fluctuations on the smallest scales become non-linear at $z_{nl}^{max} \sim 60$, predicting Mars-mass microhalos with radii of order tens of milli-parsecs, which has implications for dark matter detection signals and astronomical discrimination among CDM candidates.

Abstract

The formation of large scale structure is independent of the nature of the cold dark matter (CDM), however the fate of very small scale inhomogeneities depends on the micro-physics of the CDM particles. We investigate the matter power spectrum for scales that enter the Hubble radius well before matter-radiation equality, and follow its evolution until the time when the first inhomogeneities become non-linear. Our focus lies on weakly interacting massive particles (WIMPs), and as a concrete example we analyze the case when the lightest supersymmetric particle is a bino. We show that collisional damping and free-streaming of WIMPs lead to a matter power spectrum with a sharp cut-off at about 10^(-6) M_odot and a maximum close to that cut-off. We also calculate the transfer function for the growth of the inhomogeneities in the linear regime. These three effects (collisional damping, free-streaming and gravitational growth) are combined to provide a WMAP normalized primordial CDM power spectrum, which could serve as an input for high resolution CDM simulations. The smallest inhomogeneities typically enter the non-linear regime at a redshift of about 60.

Figures (2)

• Figure 1: The dimensionless power spectrum of the CDM density contrast at $z = 500$ for models A and B from the text (full lines). Without the effects of collisional damping and free streaming, the power spectra would be given by the dotted lines.
• Figure 2: The redshift at which typical fluctuations of comoving scale $R$ become non-linear, for the two models discussed in the text. The full lines take into account the effects of collisional damping and free streaming, whereas the dashed lines show the behaviour without a cut-off in the power spectrum.