We investigate the non-linear evolution of the relic cosmic neutrino background by running large box-size , high resolution N-body simulations which incorporate cold dark matter ( CDM ) and neutrinos as independent particle species .
Our set of simulations explore the properties of neutrinos in a reference \Lambda CDM model with total neutrino masses between 0.05-0.60 eV in cold dark matter haloes of mass 10 ^ { 11 } -10 ^ { 15 } h ^ { -1 } M _ { \odot } , over a redshift range z = 0 - 2 .
We compute the halo mass function and show that it is reasonably well fitted by the Sheth-Tormen formula , once the neutrino contribution to the total matter is removed .
More importantly , we focus on the CDM and neutrino properties of the density and peculiar velocity fields in the cosmological volume , inside and in the outskirts of virialized haloes .
The dynamical state of the neutrino particles depends strongly on their momentum : whereas neutrinos in the low velocity tail behave similarly to CDM particles , neutrinos in the high velocity tail are not affected by the clustering of the underlying CDM component .
We find that the neutrino ( linear ) unperturbed momentum distribution is modified and mass and redshift dependent deviations from the expected Fermi-Dirac distribution are in place both in the cosmological volume and inside haloes .
The neutrino density profiles around virialized haloes have been carefully investigated and a simple fitting formula is provided .
The neutrino profile , unlike the cold dark matter one , is found to be cored with core size and central density that depend on the neutrino mass , redshift and mass of the halo , for halos of masses larger than \sim 10 ^ { 13.5 } h ^ { -1 } M _ { \odot } .
For lower masses the neutrino profile is best fitted by a simple power-law relation in the range probed by the simulations .
The results we obtain are numerically converged in terms of neutrino profiles at the 10 % level for scales above \sim 200 h ^ { -1 } kpc at z = 0 , and are stable with respect to box-size and starting redshift of the simulation .
Our findings are particularly important in view of upcoming large-scale structure surveys , like Euclid , that are expected to probe the non-linear regime at the percent level with lensing and clustering observations .