Free streaming in mixed dark matter

TL;DR

This paper develops a method to calculate the free-streaming length in mixed dark matter models, accounting for various particle types and decoupling scenarios, with implications for structure formation.

Contribution

It introduces a comprehensive framework to compute free-streaming lengths in mixed dark matter, including fermions, bosons, and WIMPs, considering their decoupling conditions and distribution functions.

Findings

Sterile neutrinos decouple out of equilibrium with free-streaming length around 7 kpc for keV masses.

WIMPs with masses above 100 GeV have negligible free-streaming lengths, behaving as cold dark matter.

Bose-Einstein condensates as dark matter have free-streaming lengths consistent with cold dark matter.

Abstract

Free streaming in a \emph{mixture} of collisionless non-relativistic dark matter (DM) particles is studied by implementing methods from the theory of multicomponent plasmas. The mixture includes Fermionic, condensed and non condensed Bosonic particles decoupling in equilibrium while relativistic, heavy non-relativistic thermal relics (WIMPs), and sterile neutrinos that decouple \emph{out of equilibrium} when they are relativistic. The free-streaming length $\lambda_{fs}$ is obtained from the marginal zero of the gravitational polarization function, which separates short wavelength Landau-damped from long wavelength Jeans-unstable \emph{collective} modes. At redshift $z$ we find $ \frac{1}{\lambda^2_{fs}(z)}= \frac{1}{(1+z)} \big[\frac{0.071}{\textrm{kpc}} \big]^2 \sum_{a}\nu_a g^{2/3}_{d,a}({m_a}/{\mathrm{keV}})^2 I_a $,where $0\leq \nu_a \leq 1$ are the \emph{fractions} of the respective DM components of mass $m_a$ that decouple when the effective number of ultrarelativistic degrees of freedom is $g_{d,a}$, and $I_a$ only depend on the distribution functions at decoupling, given explicitly in all cases. If sterile neutrinos produced either resonantly or non-resonantly that decouple near the QCD scale are the \emph{only} DM component,we find $\lambda_{fs}(0) \simeq 7 \mathrm{kpc} (\mathrm{keV}/m)$ (non-resonant), $\lambda_{fs}(0) \simeq 1.73 \mathrm{kpc} (\mathrm{keV}/m)$ (resonant).If WIMPs with $m_{wimp} \gtrsim 100 \mathrm{GeV}$ decoupling at $T_d \gtrsim 10 \mathrm{MeV}$ are present in the mixture with $\nu_{wimp} \gg 10^{-12}$,$\lambda_{fs}(0) \lesssim 6.5 \times 10^{-3} \mathrm{pc}$ is \emph{dominated} by CDM. If a Bose Einstein condensate is a DM component its free streaming length is consistent with CDM because of the infrared enhancement of the distribution function.