Cold plus hot and cold dark matter cosmologies: Analysis of numerical simulations

We present a series of four simulations of cold dark matter (CDM) and cold + hot dark matter (CHDM) cosmologies, which we analyze together in this and subsequent papers. These dissipationless simulations were done using the particle mesh method with a 512(3) mesh, corresponding to a resolution of approximately 200 kpc for an assumed Hubble parameter of H-0 = 50 km s(-1) Mpc-l, and with approximately 17 x 10(6) cold and (for CHDM) an additional 34 x 10(6) hot particles. In this paper we discuss the power spectrum and correlation functions in real and redshift space, with comparisons to the CfA2 and IRAS redshift data, the pairwise velocity of galaxies in-real-space, and the distribution of hot and cold particles in CHDM simulations. We confirm that CHDM with cold/hot/baryon density ratios Omega(c)/Omega(v)/Omega(b) = 0.6/0.3/0.1 is a good fit to a wide variety of present-epoch data, much better than CDM. In particular, with reasonable assumptions about identification of galaxies and biasing, we find that the power spectrum from our CHDM simulations agrees rather well with both the CfA2 and IRAS power spectra in both the nonlinear and linear regimes. New variants of the CHDM scenario (e.g., with 20% of the mass in hot particles or with two massive neutrinos) predict a significantly larger rate of formation of galaxies at high redshift, which may be needed to explain some observational data. At the same time, the difference between the variants is rather small at z = 0. The results presented in this paper are interesting for two purposes: (i) For a rough comparison with other classes of models (like CDM or models with cosmological constant ACDM) at z = 0-indeed, we have used the simulations described here as a test bed for developing a number of new statistics for quantifying large-scale structure and comparing it to observations; (ii) As a reference point for comparison between different variants of the CHDM model. In addition, we explain here how we modify the usual Zeldovich approximation used to set up the initial conditions for both cold and hot particles in our simulations, taking into account that the growth rates of both kinds of fluctuations are different from the usual CDM case. We have also added an Appendix on issues of resolution in particle mesh simulations.