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

Current data suggest that the central mass densities $\rho_0$ and phase-spacedensities $Q\equiv\rho_0/\sigma_V^3$ of cosmological halos in the presentuniverse are correlated with their velocity dispersions $\sigma_V$ over a verywide range of $\sigma_V$ from less than 10 to more than 1000 $\rm km s^{-1}$.Such correlations are an expected consequence of the statistical correlation ofthe 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 haloslater. We have derived the $Q-\sigma_V$ and $\rho_0-\sigma_V$ correlations fordifferent CDM cosmologies and compared the predicted correlations with theobserved properties of a sample of low-redshift halos ranging in size fromdwarf spheroidal galaxies to galaxy clusters. Our predictions are generallyconsistent with the data, with preference for the currently-favored, flat$\Lambda$CDM model. Such a comparison serves to test the basic CDM paradigmwhile constraining the background cosmology and the power-spectrum ofprimordial density fluctuations, including larger wavenumbers than havepreviously been constrained.Comment: 12 pages, 3 figures, ApJ Letters, in press (2002); Changed to match the accepted version. Results and figures unchanged; text revisions onl