CLASH-VLT: Constraints on the dark matter equation of state from accurate measurements of galaxy cluster mass profiles

A pressureless scenario for the dark matter (DM) fluid is a widely adopted hypothesis, despite the absence of direct observational evidence. According to general relativity, the total mass-energy content of a system shapes the gravitational potential well, but different test particles perceive this potential in different ways depending on their properties. Cluster galaxy velocities, being ≪c, depend solely on the gravitational potential, whereas photon trajectories reflect the contributions from the gravitational potential plus a relativistic-pressure term that depends on the cluster mass. We exploit this phenomenon to constrain the equation of state (EoS) parameter of the fluid, primarily DM, contained in galaxy clusters. We use complementary information provided by the kinematic and lensing mass profiles of the galaxy cluster MACS 1206.2-0847 at z = 0.44, as obtained in an extensive imaging and spectroscopic campaign within the Cluster Lensing And Supernova survey with Hubble. The unprecedented high quality of our data set and the properties of this cluster are well suited to determine the EoS parameter of the cluster fluid. Since baryons contribute at most 15% to the total mass in clusters and their pressure is negligible, the EoS parameter we derive describes the behavior of the DM fluid. We obtain the most stringent constraint on the DM EoS parameter to date, w = (p_r+2 p_t )/(3 c ²ρ) = 0.00 ± 0.15 (stat) ± 0.08 (syst), averaged over the radial range 0.5 Mpc ≤ r ≤ r₂₀₀, where p_r and p_t are the radial and tangential pressure, and ρ is the density. We plan to further improve our constraint by applying the same procedure to all clusters from the ongoing Cluster Lensing And Supernova Survey with Hubble-Very Large Telescope program.