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 β, and the turnover radius r0 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 470 (95% confidence). We show that a simple, scale-free phase-space distribution function (DF) f(E,L2) ∝ (-E)α-1/2L-2β 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.