Structural and dynamical modeling of WINGS clusters

III. The pseudo phase-space density profile

¹ INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
e-mail: andrea.biviano@inaf.it
² IFPU-Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
³ Institut d’Astrophysique de Paris, UMR 7095: CNRS & Sorbonne Université, 98 bis Bd Arago, 75014 Paris, France

Received: 29 July 2022
Accepted: 28 November 2022

Abstract

Numerical simulations indicate that cosmological halos display power-law radial profiles of pseudo phase-space density (PPSD), Q ≡ ρ/σ³, where ρ is the mass density and σ is the velocity dispersion. We tested these predictions for Q(r) using the parameters derived from the Markov chain Monte Carlo (MCMC) analysis performed with the MAMPOSSt mass-orbit modeling code on the observed kinematics of a velocity dispersion based stack (σ_v) of 54 nearby regular clusters of galaxies from the WINGS data set. In the definition of PPSD, the density is either in total mass ρ (Q_ρ) or in galaxy number density ν (Q_ν) of three morphological classes of galaxies (ellipticals, lenticulars, and spirals), while the velocity dispersion (obtained by inversion of the Jeans equation using the MCMC parameters) is either the total (Q_ρ and Q_ν) or its radial component (Q_r, ρ and Q_r, ν). We find that the PPSD profiles are indeed power-law relations for nearly all MCMC parameters. The logarithmic slopes of our observed Q_ρ(r) and Q_r, ρ(r) for ellipticals and spirals are in excellent agreement with the predictions for particles in simulations, but slightly shallower for S0s. For Q_ν(r) and Q_r, ν(r), only the ellipticals have a PPSD slope matching that of particles in simulations, while the slope for spirals is much shallower, similar to that of subhalos. However, for cluster stacks based on the richness or gas temperature, the fraction of power-law PPSDs is lower (esp. Q_ν) and the Q_ρ slopes are shallower, except for S0s. The observed PPSD profiles, defined using ρ rather than ν, appear to be a fundamental property of galaxy clusters. They would be imprinted during an early phase of violent relaxation for dark matter and ellipticals, and later for spirals as they move toward dynamical equilibrium in the cluster gravitational potential, while S0s are either intermediate (richness and temperature-based stacks) or a mixed class (σ_v stack).