A database of COBE-normalized cold dark matter simulations

We have simulated the formation and evolution of large-scale structure in t he universe, for 68 different COBE-normalized cosmological models. For each cosmological model, we have performed between one and three simulations, f or a total, of 160 simulations. This constitutes the largest database of co smological simulations ever assembled, and the largest cosmological paramet er space ever covered by such simulations. We are making this database avai lable to the astronomical community. We provide instructions for accessing the database and for converting the data from computational units to physic al units. The database includes tilted cold dark matter (TCDM) models, tilt ed open cold dark matter (TOCDM) models, and tilted Lambda cold dark matter (TACDM) models. (For several simulations, the primordial exponent n of the power spectrum is near unity, hence these simulations can be considered as "untilted.") The simulations cover a four-dimensional cosmological paramet er phase space, the parameters being the present density parameter Omega(0) , cosmological constant lambda(0), and Hubble constant H-0, and the rms den sity fluctuation sigma(8) at scale 8 h(-1) Mpc. All simulations were perfor med using a (PM)-M-3 algorithm with 64(3) particles on a 128(3) mesh, in a cubic volume of comoving size 128 Mpc. Each simulation starts at a redshift of 24 and is carried up to the present. More simulations will be added to the database in the future, We have performed a limited amount of data redu ction and analysis of the final states of the simulations. We computed the rms density fluctuation, the two-point correlation function, the velocity m oments, and the properties of clusters. Our results are the following: 1. The numerical value sigma(8)(num) of the rms density fluctuation differs from the value sigma(8)(cont) obtained by integrating the power spectrum a t early times and extrapolating linearly up the present. This results from the combined effects of discreteness in the numerical representation of the power spectrum, the presence of a Gaussian factor in the initial condition s, and late-time nonlinear evolution. The first of these three effects is n egligible. The second and third are comparable, and can both modify the val ue of sigma(8) by up to 10%. Nonlinear effects, however, are important only for models with sigma(8) > 0.6, and can result in either an increase or a decrease in sigma(8). 2. The observed galaxy two-point correlation function is well reproduced (a ssuming an unbiased relation between galaxies and mass) by models with sigm a(8) similar to 0.8, nearly independently of the values of the other parame ters, Omega(0), lambda(0), and H-0. For models with sigma(8) > 0.8, the cor relation function is too large and its slope is too steep. For models with sigma(8) > 0.8, the correlation function is too small and its slope is too shallow. 3. At small separations, r < 1 Mpc, the velocity moments indicate that smal l clusters have reached virial. equilibrium, while still accreting matter f rom the field. The velocity moments depend essentially upon Omega(0) and si gma(8), and not lambda(0) and H-0. The pairwise particle velocity dispersio ns are much larger than the observed pairwise galaxy velocity dispersion, f or nearly all models. Velocity bias between galaxies and dark matter is nee ded to reconcile the simulations with observations. 4. The cluster multiplicity function is decreasing for models with sigma(8) similar to 0.3. It has a horizontal plateau for models with sigma(8) in th e range 0.4-0.9. For models with sigma(8) > 0.9, it has a U shape, which is probably a numerical artifact caused by the finite number of particles use d in the simulations. For all models, clusters have densities in the range 100-1000 times the mean background density, the spin parameters lambda are in the range 0.008-0.2, with the median near 0.05, and about 2/3 of the clu sters are prolate. Rotationally supported disks do not form in these simula tions.