Measuring the velocity dispersion function of red cluster galaxies with deep MUSE observations

Galaxy clusters are privileged tracers of the formation of massive structures by hierarchical mergers and of the evolution of galaxies in dense environments. The stellar velocity dispersion of red galaxies in clusters is an effective and unbiased probe of the mass distribution of the sub-haloes that host them. Crucially, it is not impacted by the complex physics guiding the evolution of the stellar population of the members, and it can be enhanced by combination with other mass probes, such as strong gravitational lensing (SL). In my talk, I will present the first determination, based on MUSE data, of the velocity dispersion function for the red members in the cores of four Hubble Frontier Fields SL clusters (z=0.3-0.55). With our deep (up to 17 hours) MUSE observations, I measured the velocity dispersion for a few hundred members between the four clusters, and used the Fundamental Plane relation to extend the catalogue to more than a thousand red galaxies. Thanks to the integral-field nature of MUSE, the sample is unprecedented in terms of size and completeness for galaxy clusters at this redshift. I will present the velocity dispersion function for the four clusters, compare the results with lower-z clusters and field galaxies, and discuss the implications for galaxy formation and evolution in cluster environments. Finally, I will address the implications of my results on the recently reported discrepancy between the compactness of observed and simulated cluster galaxies.