2014ApJ...788L..15C

We study profiles of mass density, velocity dispersion (VD), and a combination of both using ∼2000 nearly spherical and rotation-free Sloan Digital Sky Survey galaxies. For observational stellar mass density ρ_{sstarf}(r), we consider a range of dark matter (DM) distribution ρ_DM(r) and VD anisotropy β(r) to investigate radial stellar VD σ_{sstarf}r(r) using the spherical Jeans equation. While mass and VD profiles vary appreciably depending on DM distribution and anisotropy, the pseudo-phase-space density-like combination ρ(r)/σ_{sstarf}r³(r) with total density ρ(r) = ρ_{sstarf}(r) + ρ_DM(r) is nearly universal. In the optical region, the negative logarithmic slope has a mean value of < χ > ~ 1.86-1.90 with a galaxy-to-galaxy rms scatter of ~0.04-0.06, which is a few times smaller than that of ρ(r) profiles. The scatter of χ can be increased by invoking wildly varying anisotropies that are, however, less likely because they would produce too large a scatter of line of sight VD profiles. As an independent check of this universality, we analyze stellar orbit-based dynamical models of 15 early-type galaxies (ETGs) of the Coma cluster provided by J. Thomas. Coma ETGs, with σ_{sstarf}r(r) replaced by the rms velocity of stars v_{sstarf}rms(r) including net rotation, exhibit a similar universality with a slope of χ = 1.93±0.06. Remarkably, the inferred values of χ for ETGs match well the slope ~1.9 predicted by N-body simulations of DM halos. We argue that the inferred universal nature of ρ(r)/σ_{sstarf}r³(r) cannot be fully explained by equilibrium alone, implying that some astrophysical factors conspire and/or it reflects a fundamental principle in collisionless formation processes.