Dynamical Study of A1689 from Wide-Field VLT/VIMOS Spectroscopy: Mass   Profile, Concentration Parameter, and Velocity Anisotropy
  We examine the dynamics structure of the rich cluster A1689, combining VLT/VIMOS spectroscopy with Subaru/Suprime-Cam imaging. The radial velocity distribution of $\sim 500$ cluster members is bounded by a pair of clearly defined velocity caustics, with a maximum amplitude of $\sim|4000|$ km/s at $\simeq$ 300 h$^{-1}$ kpc, beyond which the amplitude steadily declines, approaching zero velocity at a limiting radius of $\sim$ 2 h$^{-1}$ Mpc. We derive the 3D velocity anisotropy and galaxy number density profiles using a model-independent method to solve the Jeans equation, simultaneously incorporating the observed velocity dispersion profile, the galaxy counts from deep Subaru imaging, and our previously derived cluster mass profile from a joint lensing and X-ray analysis. The velocity anisotropy is found to be predominantly radial at large radius, becoming increasingly tangential towards the center, in accord with expectations. We also analyze the galaxy data independently of our previous analysis using two different methods: The first is based on a solution of the Jeans equation assuming an NFW form for the mass distribution, whereas in the second method the caustic amplitude is used to determine the escape velocity. The cluster virial mass derived by both of these dynamical methods is in good agreement with results from our earlier lensing and X-ray analysis. We also confirm the high NFW concentration parameter, with results from both methods combined to yield $c_{\rm vir}>13$ (1$\sigma$). The inferred virial radius is consistent with the limiting radius where the caustics approach zero velocity and where the counts of cluster members drop off, suggesting that infall onto A1689 is currently not significant. 
Doron Lemze, Tom Broadhurst, Yoel Rephaeli, Rennan Barkana, Keiichi   Umetsu