A Database of COBE ‐normalized Cold Dark Matter Simulations

Abstract

We have simulated the formation and evolution of large-scale structure in the universe, for 68 different COBE -normalized cosmological models. For each cosmological model, we have performed between one and three simulations, for a total of 160 simulations. This constitutes the largest database of cosmological simulations ever assembled, and the largest cosmological parameter space ever covered by such simulations. We are making this database available to the astronomical community. We provide instructions for accessing the database and for converting the data from computational units to physical units. The database includes tilted cold dark matter (TCDM) models, tilted open cold dark matter (TOCDM) models, and tilted Λ cold dark matter (TΛCDM) 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 parameter phase space, the parameters being the present density parameter Ω 0 , cosmological constant λ 0 , and Hubble constant H 0 , and the rms density fluctuation σ 8 at scale 8 h -1 Mpc. All simulations were performed using a P 3 M 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 reduction and analysis of the final states of the simulations. We computed the rms density fluctuation, the two-point correlation function, the velocity moments, and the properties of clusters. Our results are the following: 1. The numerical value σ ##IMG## [http://ej.iop.org/images/0004-637X/530/2/525/img1.gif] {img1.gif} of the rms density fluctuation differs from the value σ ##IMG## [http://ej.iop.org/images/0004-637X/530/2/525/img2.gif] {img2.gif} obtained by integrating the power spectrum at 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 conditions, and late-time nonlinear evolution. The first of these three effects is negligible. The second and third are comparable, and can both modify the value of σ 8 by up to 10%. Nonlinear effects, however, are important only for models with σ 8 > 0.6, and can result in either an increase or a decrease in σ 8 . 2. The observed galaxy two-point correlation function is well reproduced (assuming an unbiased relation between galaxies and mass) by models with σ 8 ~ 0.8, nearly independently of the values of the other parameters, Ω 0 , λ 0 , and H 0 . For models with σ 8 > 0.8, the correlation function is too large and its slope is too steep. For models with σ 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 small clusters have reached virial equilibrium, while still accreting matter from the field. The velocity moments depend essentially upon Ω 0 and σ 8 , and not λ 0 and H 0 . The pairwise particle velocity dispersions are much larger than the observed pairwise galaxy velocity dispersion, for nearly all models. Velocity bias between galaxies and dark matter is needed to reconcile the simulations with observations. 4. The cluster multiplicity function is decreasing for models with σ 8 ~ 0.3. It has a horizontal plateau for models with σ 8 in the range 0.4-0.9. For models with σ 8 > 0.9, it has a U shape, which is probably a numerical artifact caused by the finite number of particles used in the simulations. For all models, clusters have densities in the range 100-1000 times the mean background density, the spin parameters λ are in the range 0.008-0.2, with the median near 0.05, and about ##IMG## [http://ej.iop.org/images/0004-637X/530/2/525/img3.gif] {img3.gif} of the clusters are prolate. Rotationally supported disks do not form in these simulations.