Free streaming in mixed 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 $\frac{1}{{\lambda }_{fs}^2(z)}=\frac{1}{(1+z)}[\frac{0.071}{\text{kpc}}{]}^2{\sum }_a{\nu }_a{g}_{d,a}^{2/3}(m_a/\mathrm{keV}{)}^2{I}_a$,where $0\le {\nu }_a\le 1$ 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.

19 pages, 2 figures. More discussions same conclusions and results. Version to appear in Phys. Rev. D

References in corpus (5)

• Lighting the Universe with filaments
• Sterile neutrinos as subdominant warm dark matter
• Precision Cosmology: Successes and Challenges
• Production of a sterile species via active-sterile mixing: an exactly solvable model
• Non equilibrium dynamics of mixing, oscillations and equilibration: a model study

Cited by in corpus (5)

• Constraints on dark matter particles from theory, galaxy observations and N-body simulations
• Clustering properties of a sterile neutrino dark matter candidate
• Small-scale structure formation properties of chilled sterile neutrinos as dark matter
• Lepton Number-Driven Sterile Neutrino Production in the Early Universe
• The dark matter transfer function: free streaming, particle statistics and memory of gravitational clustering