A Redshift Survey of Nearby Galaxy Groups: The Shape of the Mass Density Profile

We constrain the mass profile and orbital structure of nearby groups andclusters of galaxies. Our method yields the joint probability distribution ofthe density slope n, the velocity anisotropy beta, and the turnover radius r0for these systems. The measurement technique does not use results from N-bodysimulations as priors. We incorporate 2419 new redshifts in the fields of 41systems of galaxies with z < 0.04. The new groups have median velocitydispersion sigma=360 km/s. We also use 851 archived redshifts in the fields of8 nearly relaxed clusters with z < 0.1. Within R < 2 r200, the data areconsistent with a single power law matter density distribution with slope n =1.8-2.2 for systems with sigma < 470 km/s, and n = 1.6-2.0 for those with sigma> 470 km/s (95% confidence). We show that a simple, scale-free phase spacedistribution function f(E,L^2) ~ (-E)^(alpha-1/2) L^(-2 \beta) is consistentwith the data as long as the matter density has a cusp. Using this DF, matterdensity profiles with constant density cores (n=0) are ruled out with betterthan 99.7% confidence.Comment: 22 pages; accepted for publication in the Astrophysical Journa