The Central Mass and Phase-Space Densities of Dark Matter Halos: Cosmological Implications

Abstract

Current data suggest that the central mass densities $ρ_0$ and phase-space densities $Q\equivρ_0/σ_V^3$ of cosmological halos in the present universe are correlated with their velocity dispersions $σ_V$ over a very wide range of $σ_V$ from less than 10 to more than 1000 $\rm km s^{-1}$. Such correlations are an expected consequence of the statistical correlation of the formation epochs of virialized objects in the CDM model with their masses; the smaller-mass halos typically form first and merge to form larger-mass halos later. We have derived the $Q-σ_V$ and $ρ_0-σ_V$ correlations for different CDM cosmologies and compared the predicted correlations with the observed properties of a sample of low-redshift halos ranging in size from dwarf spheroidal galaxies to galaxy clusters. Our predictions are generally consistent with the data, with preference for the currently-favored, flat $Λ$CDM model. Such a comparison serves to test the basic CDM paradigm while constraining the background cosmology and the power-spectrum of primordial density fluctuations, including larger wavenumbers than have previously been constrained.