COSMOLOGY
(6c) A Database of COBE-Normalized CDM Simulations
Martel and Matzner (2000)
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 1
and 3 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 Lambda Cold Dark Matter (TLCDM) 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 4-dimensional cosmological
parameter phase space, the parameters being the present density parameter
Omega_0, cosmological constant lambda_0, and Hubble constant H_0,
and the rms density fluctuation sigma_8 at scale 8/h Mpc.
All simulations were performed
using a P3M 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 2-point correlation function, the
velocity moments, and the properties of clusters. Our results are the
following:
- The numerical value sigma_8^num of the
rms density fluctuation differs from the value sigma_8^cont obtained
by integrating the power spectrum at early times and extrapolating linearly
up the 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 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.
- The observed galaxy two-point correlation
function is well reproduced by models with sigma_8 ~ 0.8, nearly
independently of the values of the other parameters, Omega_0,
lambda_0, and H_0. For models with
sigma_8>0.8, the correlation function is too large and its slope is
too steep. For models with
sigma_8<0.8, the correlation function is too small, its slope is
too shallow, and it often has a kink at separations
of order 1-3 Mpc.
- At small separations, r < 1Mpc,
the velocity moments indicate that small
clusters have reached virial equilibrium, while still accreting
matter from the field. The velocity moments depend essentially
upon Omega_0 and sigma_8, and not lambda_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 reconciled the simulations with observations.
- The cluster multiplicity function is decreasing for models with
sigma_8 ~ 0.3. It has a horizontal plateau for models with
sigma_8 in the 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 used 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 clusters are prolate. Rotationally
supported disks do not form in these simulations.