A CALCULATION OF THE FULL NEUTRINO PHASE-SPACE IN COLD PLUS HOT DARK-MATTER MODELS

This paper presents a general-relativistic N-body technique for evolvi ng the phase space distribution of massive neutrinos in linear perturb ation theory. The method provides a more accurate sampling of the neut rino phase space for the HDM initial conditions of N-body simulations in a cold + hot dark matter (CDM + HDM) universe than previous work. I nstead of directly sampling the phase space at the end of the linear e ra, we first compute the evolution of the metric perturbations by nume rically integrating the coupled, linearized Einstein, Boltzmann, and f luid equations for all particle species (CDM, baryons, photons, massle ss neutrinos, and massive neutrinos). (Details of this calculation are discussed in a separate paper.) We then sample the phase space shortl y after neutrino decoupling at redshift z = 10(9) when the distributio n is Fermi-Dirac. To follow the trajectory of each neutrino, we subseq uently integrate the geodesic equations for each neutrino in the pertu rbed background spacetime from z = 10(9) to z = 13.55, using the linea rized metric found in the previous calculation to eliminate discretene ss noise. The positions and momenta resulting from this integration re present a fair sample of the full neutrino phase space and can be used as HDM initial conditions for N-body simulations of nonlinear structu re evolution in CDM + HDM models. A total of approximately 21 million neutrino particles are used in a 100 Mpc comoving box, with OMEGA(cdm) = 0.65, OMEGA(hdm) = 0.30, OMEGA(baryon) = 0.05, and Hubble constant H0 = 50 km s-1 MpC-1. The power spectrum is normalized to the rms quad rupole moment of Q(rms-PS) = 14 muK. We find that correlations develop in the neutrino densities and momenta which are absent when only the zeroth-order Fermi-Dirac distribution is considered.