The GOGREEN survey: Internal dynamics of clusters of galaxies at redshift 0.9 − 1.4

Context. The study of galaxy cluster mass profiles ( M ( r )) provides constraints on the nature of dark matter and on physical processes a ff ecting the mass distribution. The study of galaxy cluster velocity anisotropy profiles ( β ( r )) informs the orbits of galaxies in clusters, which are related to their evolution. The combination of mass profiles and velocity anisotropy profiles allows us to determine the pseudo phase-space density profiles ( Q ( r )); numerical simulations predict that these profiles follow a simple power law in cluster-centric distance. Aims. We determine the mass, velocity anisotropy, and pseudo phase-space density profiles of clusters of galaxies at the highest redshifts investi- gated in detail to date. Methods. We exploited the combination of the GOGREEN and GCLASS spectroscopic data-sets for 14 clusters with mass M 200 ≥ 10 14 M (cid:12) at redshifts 0 . 9 ≤ z ≤ 1 . 4. We constructed an ensemble cluster by stacking 581 spectroscopically identified cluster members with stellar mass M (cid:63) ≥ 10 9 . 5 M (cid:12) . We used the MAMPOSSt method to constrain several M ( r ) and β ( r ) models, and we then inverted the Jeans equation to determine the ensemble cluster β ( r ) in a non-parametric way. Finally, we combined the results of the M ( r ) and β ( r ) analysis to determine Q ( r ) for the ensemble cluster. Results. The concentration c 200 of the ensemble cluster mass profile is in excellent agreement with predictions from Λ cold dark matter ( Λ CDM) cosmological numerical simulations, and with previous determinations for clusters of similar mass and at similar redshifts, obtained from gravita- tional lensing and X-ray data. We see no significant di ff erence between the total mass density and either the galaxy number density distributions or the stellar mass distribution. Star-forming galaxies are spatially significantly less concentrated than quiescent galaxies. The orbits of cluster galaxies are isotropic near the center and more radial outside. Star-forming galaxies and galaxies of low stellar mass tend to move on more radially elongated orbits than quiescent galaxies and galaxies of high stellar mass. The profile Q ( r ), determined using either the total mass or the number density profile, is very close to the power-law behavior predicted by numerical simulations. Conclusions. The internal dynamics of clusters at the highest redshift probed in detail to date are very similar to those of lower-redshift clusters, and in excellent agreement with predictions of numerical simulations. The clusters in our sample have already reached a high degree of dynamical relaxation.