Internal velocity and mass distributions in simulated clusters of galaxies for a variety of cosmogonic models

Abstract

The mass and velocity distributions in the outskirts (0.5-3.0 h^-1^ Mpc) of simulated clusters of galaxies are examined for a suite of cosmogonic models (two {OMEGA}_0_ = 1 and two {OMEGA}_0_ = 0.2 models) utilizing large-scale particle-mesh (PM) simulations (500^3^ cells, 250^3^ particles and box size of 100 h^-1^ Mpc, giving a nominal resolution of 0.2 h^-1^ Mpc with the true resolution ~0.5 h^-1^ Mpc). Through a series of model computations, designed to isolate the different effects, we find that both {OMEGA}_0_ and P_k_ (λ <= 16 h^-1^ Mpc) are important to the mass distributions in clusters of galaxies. There is a correlation between power, P_k_, and density profiles of massive clusters; more power tends to point to the direction of a stronger correlation between α and M(r < 1.5 h^-1^ Mpc) (see eq. [1] for definitions); i.e., massive clusters being relatively extended and small mass clusters being relatively concentrated. A lower {OMEGA}_0_ universe tends to produce relatively concentrated massive clusters and relatively extended small mass clusters compared to their counterparts in a higher {OMEGA}_0_ model with the same power. Models with little (initial) small-scale power, such as the HDM model, produce more extended mass distributions than the isothermal distribution for most of the mass clusters. But the CDM models show mass distributions of most of the clusters more concentrated than the isothermal distribution. X-ray and gravitational lensing observations are beginning providing useful information on the mass distribution in and around clusters; some interesting constraints on {OMEGA}_0_ and/or the (initial) power of the density fluctuations on scales λ <= 16 h^-1^ Mpc (where linear extrapolation is invalid) can be obtained when larger observational data sets, such as the Sloan Digital Sky Survey, become available. With regard to the velocity distribution, we find two interesting points. First, in 0.5 < r < 3.0 h^-1^ Mpc region, all four velocity dispersions (one-dimensional [1D], radial, tangential, line-of-sight) show decreasing distributions as a function of clustercentric distance in the three CDM models; but the HDM model shows just the opposite: weakly increasing velocity dispersions outward. The CDM models can reasonably fit the observed galaxy velocity dispersions in the Coma cluster of galaxies but the HDM model provides a poor fit. Second, we find that for the scales 0.5 < r < 3.0 h^-1^ Mpc, the tangential velocity dispersion is always larger than the radial component by a factor of 1.2-1.6 in the CDM models and 1.3-2.0 in the HDM model. In all models the ratio of radial to tangential velocity dispersions is a decreasing function from 0.5 h^-1^ Mpc to 3.0 h^-1^ Mpc for massive clusters (smaller mass clusters tend to show a minimum for that ratio around 1.5-2.0 h^-1^ Mpc in the CDM models). While the velocity dispersions among the three Cartesian directions are isotropic on average, a large scatter (40%) exists in all models. We also examine the infall issue in detail. Lower {OMEGA}_0_ models are found to have larger turnaround radius for a fixed-mass clump than high {OMEGA}_0_ models; this conclusion is insensitive to P_k_. But we find that the following relation (between the turnaround radius, R_ta_, and the mass within R_ta_, M_ta_), log_10_ R_ta_ = a + b log_10_ M_ta_ (a = -5.2 +/- 0.2, b = 0.40 +/- 0.02 R_ta_ and M_ta_ are in h^-1^ Mpc and h^-1^ M_sun_, respectively) holds for all the models (the uncertainties in a and b indicate the variations among models). In addition, the relation between the overdensity inside the turnaround radius, δ_ta_, and M_ta_ is fitted by log_10_ δ_ta_ = c + d log_10_ M_ta_ (cf. Table 1 for values of c and d). We show that the spherical top-hat collapse model in an Einstein-de Sitter universe, having δ_ta_ = 9π^2^/16 = 5.55, gives a fair fit to results (~4-10) of the nonlinear, nonspherical simulations performed here. Lower {OMEGA}_0_ models have considerably higher δ_ta_~10-30, as expected. Finally, we find that the isothermal approximation (cf. eq. [10]) appears to underestimate the true masses within the Abell radius by 10%- 30% with a scatter of ~50% around the estimated mean (in the three hierarchical models).