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 a 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 $\ll$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 the 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 CLASH survey. 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,
$w=(p_r+2\,p_t)/(3\,c^2\rho)=0.00\pm0.15\mathrm{(stat)}\pm0.08\mathrm{(syst)}$,
averaged over the radial range $0.5\,\mathrm{Mpc}\leq$$r$$\leq$$r_{200}$, where
$p_r$ and $p_t$ are the radial and tangential pressure, and $\rho$ is the
density. We plan to further improve our constraint by applying the same
procedure to all clusters from the ongoing CLASH-VLT program.
