The velocity dispersion function of red galaxies in four Hubble Frontier Fields galaxy clusters

We present a detailed study of the stellar kinematic properties of red member galaxies in the cores of four strong lensing galaxy clusters at intermediate redshifts included in the Hubble Frontier Fields programme: Abell 2744 ( z = 0.307), Abell S1063 ( z = 0.346), MACS J0416.1−2403 ( z = 0.397), and MACS J1149.6+2223 ( z = 0.542). We focussed on a large sample of 723 red cluster members in the four clusters, selected spectroscopically and photometrically, and we measured their structural parameters using MORPHOFIT for all Hubble Frontier Fields bands. Taking advantage of deep (3.1 h to 17 h of exposure time) integral-field spectroscopic data from the Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope, available for the cores of all four clusters, we tested a pipeline based on the public spectral fitting code pPXF to reliably and systematically measure the line-of-sight stellar velocity dispersion σ of cluster members with a spectral S / N ≥ 10, with a statistical uncertainty consistently below 5%. The resulting catalogue contains 213 measured σ values across the four clusters. Combining stellar kinematics and multi-band galaxy morphology, we calibrated the Fundamental Plane relation in the rest-frame r band for the early-type cluster members, selected from their colour and morphology; we found compatible parameters both across the clusters and in comparison with large samples of early-type field galaxies, and noted hints of zero-point evolution with redshift. Finally, we used the calibrated Fundamental Plane relations to assign a velocity dispersion value to all 723 red cluster members and studied the velocity dispersion function for each cluster, down to log σ [km s −1 ] = 1.5. In spite of the intrinsic variability between the four clusters resulting from their assembly history, a Schechter function fit of the velocity functions suggests compatible parameters: a positive α slope with values in the range 0.55 − 1.60 and log σ * [km s −1 ] between 2.18 and 2.47. Unlike previous works, we extended the systematic study of the central velocity dispersion of cluster galaxies to lower- σ regimes. We suggest that deeper insights on the evolution of member galaxies may be obtained with a larger cluster sample spanning a wider redshift range.