A Hydrodynamic Approach to Cosmology: The Mixed Dark Matter Cosmological Scenario

Abstract

We compute the evolution of spatially flat, mixed cold and hot dark matter (``MDM") models containing both baryonic matter and two kinds of dark matter. The mean final Zeldovich-Sunyaev $y$ parameter is estimated to be $\bar y=(5.4\pm 2.7)\times 10^{-7}$, with a rms fluctuation of approximately $\bar{δy}=(6.0\pm 3.0)\times 10^{-7}$ on arc minute scales. The rate of galaxy formation peaks at an even later epoch ($z\sim 0.3$) than in the standard ($Ω=1$, $σ_8=0.67$) CDM model ($z\sim 0.5$) and, at a redshift of z=4 is nearly a factor of a hundred lower than for the CDM model with the same value of $σ_8$. The model yields a cluster mass function which is about a factor of 4 higher than observed but a cluster-cluster correlation length lower by a factor of 2 than what is observed but both are closer to observations than in the COBE normalized CDM model. The one dimensional pairwise velocity dispersion is $605\pm 8$km/s at $1h^{-1}$ separation, lower than that of the CDM model normalized to COBE, but still significantly higher than observations (Davis \& Peebles 1983). A plausible velocity bias $b_v=0.8\pm 0.1$ on this scale will reduce but not remove the discrepancy. Overall, the model is similar both on large and intermediate scales to the standard CDM model normalized to the same value of $σ_8$, but the problem with regard to late formation of galaxies is more severe in this model than in that CDM model. Adding hot dark matter significantly improves the ability of COBE normalized CDM scenario to fit existing observations, but the model is in fact not as good as the CDM model with the same $σ_8$ and is still probably unsatisfactory with regard to several critical tests.