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 and clusters of galaxies. Our method yields the joint probability distribution of the density slope n, the velocity anisotropy beta, and the turnover radius r(0) for these systems. The measurement technique does not use results from N-body simulations as priors. We incorporate 2419 new redshifts (included here) in the fields of 41 systems of galaxies with z < 0.04. The new groups have median velocity dispersion sigma = 360 km s(-1). We also use 979 archived redshifts in the fields of eight nearly relaxed clusters with z < 0.1. Within R less than or similar to 2r(200), the data are consistent with a single power-law matter density distribution with slope n = 1.8 2.2 for systems with sigma < 470 km s(-1) and n = 1.6-2.0 for those with sigma > 470 (95% confidence). We show that a simple, scale-free phase-space distribution function (DF) f (E, L-2) proportional to (-E)(alpha-1/2) L-2beta is consistent with the data as long as the matter density has a cusp. Using this DF, matter density profiles with constant-density cores (n = 0) are ruled out with better than 99.7% confidence.