Free streaming in mixed dark matter

Free streaming in a mixture of collisionless nonrelativistic dark matter (DM) particles is studied by solving the linearized Vlasov equation implementing methods from the theory of multicomponent plasmas. The mixture includes fermionic, condensed and noncondensed bosonic particles decoupling in equilibrium while relativistic, heavy thermal relics that decoupled when nonrelativistic [weakly interacting massive particles (WIMPs)], and sterile neutrinos that decouple out of equilibrium when they are relativistic. The different components interact via the self-consistent gravitational potential that they source. 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 collective modes. At redshift z I find 1/lambda(2)(fs)(z)=1/(1+z)[0.071/kpc](2) Sigma(a)nu(a)g(d,a)(2/3)(m(a)/keV)I-2(a), where 0 <=nu(a)<= 1 are the 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 are dimensionless ratios of integrals of the distribution functions which only depend on the microphysics at decoupling and are obtained explicitly in all the cases considered. If sterile neutrinos produced either resonantly or nonresonantly that decouple near the QCD scale are the only DM component, I find lambda(fs)(0)similar or equal to 7 kpc (keV/m) (nonresonant), lambda(fs)(0)similar or equal to 1.73 kpc (keV/m) (resonant). If WIMPs with m(wimp)greater than or similar to 100 GeV decoupling at T-d greater than or similar to 10 MeV are present in the mixture with nu(wimp)>> 10(-12), lambda(fs)(0)less than or similar to 6.5x10(-3) pc is dominated by cold dark matter (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.