Dynamical Study of A1689 from Wide-field Vlt/vimos Spectroscopy: Mass Profile, Concentration Parameter, and Velocity Anisotropy

We examine the internal dynamics and caustic structure of the rich cluster A1689, combining VLT/VIMOS spectroscopy with Subaru/Suprime-Cam imaging. The radial velocity distribution of ∼ 500 cluster members is bounded by a pair of clearly defined velocity caustics, with a maximum amplitude of ∼ |4000| km/s at ≃ 300 h kpc, beyond which the amplitude steadily declines, meeting at zero velocity at a limiting radius of ≃ 2.1 h Mpc. We derive a 3D velocity anisotropy 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 mass profile from a joint lensing/X-ray analysis. The velocity anisotropy is found to be predominantly radial at large radius and becomes increasing tangential towards the center, in agreement with physical expectations. We also solve the Jeans equation by assuming an NFW form for the mass distribution, finding a high concentration, cvir > 9.75, which is consistent with our joint lensing and X-ray estimate, cvir = 12.2 +0.9 −1 . The caustic amplitude provides an independent mass profile via the escape velocity, after applying a small velocity anisotropy based correction. This mass profile is also in very good agreement with our earlier work and with the Jeans based dynamical analysis. The virial mass derived by both these dynamical methods is also in good agreement with our earlier lensing/Xray analysis, providing an accurate combined constraint, 1.5 < Mvir/(10 15 h M⊙) < 1.65. The inferred virial radius coincides with the limiting radius where the caustics meet at zero velocity and with the radius where the counts of cluster members appears to end, implying that infall onto A1689 is currently not significant. Subject headings: clusters: A1689 – clusters: dynamical analysis – clusters: galaxies, DM