Neutrino Clustering in Cold Dark Matter Halos : Implications for Ultra High Energy Cosmic Rays

Abstract

We develop a method based on the collisionless Boltzmann equation to calculate the gravitational clustering of relic neutrinos in realistic cosmological models dominated by cold dark matter (CDM) and the cosmological constant. This method can be used to estimate the phase-space distribution of any light particles in CDM halos. We find that neutrinos with masses > 0.3 eV cluster appreciably in dark matter halos above the galactic size. The resulting neutrino overdensity above the cosmic mean neutrino density increases with both the neutrino mass and the halo mass, ranging from about 10 for 0.3 eV neutrinos in 10^13 M_sun halos, to about 1500 for 1.8 eV neutrinos in 10^15 M_sun halos. We examine the implications of neutrino clustering for the Z-burst model of ultra high energy cosmic rays (UHECR), which interprets the observed events at E > 4 x 10^19 eV as decay products of Z-bosons from the resonant scattering between relic and high energy neutrinos and anti-neutrinos. We estimate the UHECR energy spectrum for various neutrino masses towards five of the most massive clusters in the local universe (within 100 Mpc): Virgo, Perseus-Pisces, Hydra, Centaurus, and Coma. The UHECR flux in the Z-burst model is expected to be significantly higher towards these clusters if m_nu > 0.3 eV and nearly isotropic otherwise.