Determination of the dark matter profile of A2199 from integrated starlight

We have obtained deep, long-slit spectroscopy along the major axis of NGC 6166, the cD galaxy in the cluster A2199, in order to measure the kinematics of intracluster stars at large radii. The velocity dispersion initially decreases from the central value of 300 to 200 km s(-1) within a few kiloparsecs and then steadily rises to 660 km s(-1) at a radius of 60 kpc (H-0 = 75 km s(-1) Mpc(-1), Omega(m) = 0.3, Omega(Lambda) = 0.7), nearly reaching the velocity dispersion of the cluster (sigma(A2199) = 775 +/- 50 km s(-1)). These data suggest that the stars in the halo of the cD galaxy trace the potential of the cluster and that the kinematics of these intracluster stars can be used to constrain the mass pro le of the cluster. In addition, we find evidence for systematic rotation (V/sigma approximate to 0.3) in the intracluster stars beyond 20 kpc. Such rotation is not seen in the kinematics of the cluster members. The surface brightness and velocity dispersion profiles can be fitted using a single-component mass model only by making unphysical assumptions about the level of anisotropy for both the stars in the cD galaxy and the kinematics of the galaxies in the cluster. Two-component mass models for the cD galaxy and its halo are subsequently explored using the kinematics of known cluster members as an additional constraint on the total enclosed mass beyond the extent of the stellar kinematics. Under the assumption of isotropy, the observed major-axis kinematics can be reproduced only if the halo, parameterized by a generalized Navarro-Frenk-White (NFW) profile, has a soft core, i.e., alpha < 1 ( a generalized NFW halo with alpha = 1 is excluded because of low implied stellar mass-to-light ratios). This result is inconsistent with the predictions of current N-body simulations for dark matter halos. To test the consistency of our halo profiles with those derived from strong lensing measurements in intermediate-redshift clusters, we calculate the critical radii for tangential arcs, assuming that our best-fit mass models for A2199 were placed at cosmological redshifts between 0.2 <= z <= 0.5. The calculated critical radii for our best-fit two-component isotropic models range from 5" to 40", depending on the assumed source redshift, consistent with the radii for gravitational arcs observed in intermediate-redshift clusters. We also present the results of Monte Carlo simulations testing the general reliability of velocity dispersion measurements in the regime of low signal-to-noise ratio and large intrinsic Doppler broadening.