We study profiles of mass density , velocity dispersion ( VD ) , and their combination using \sim 2000 nearly spherical and rotation-free SDSS galaxies .
For observational stellar mass density \rho _ { \star } ( r ) we consider a range of dark matter ( DM ) distribution \rho _ { DM } ( r ) and VD anisotropy \beta ( r ) to investigate radial stellar VD \sigma _ { \star 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 \rho ( r ) / \sigma _ { \star r } ^ { 3 } ( r ) with total density \rho ( r ) = \rho _ { \star } ( r ) + \rho _ { DM } ( r ) is nearly universal .
In the optical region the minus of its logarithmic slope has a mean value of \langle \chi \rangle \approx 1.86 – 1.90 with a galaxy-to-galaxy rms scatter of \approx 0.04 – 0.06 , which is a few times smaller than that of \rho ( r ) profiles .
The scatter of \chi 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 ETGs of Coma cluster provided by J. Thomas .
Coma ETGs , with \sigma _ { \starr } ( r ) replaced by the rms velocity of stars v _ { \starrms } ( r ) including net rotation , exhibit a similar universality with a slope of \chi = 1.93 \pm 0.06 .
Remarkably , the inferred values of \chi for ETGs match well the slope \approx 1.9 predicted by N-body simulations of DM halos .
We argue that the inferred universal nature of \rho ( r ) / \sigma _ { \star r } ^ { 3 } ( r ) can not be fully explained by equilibrium alone , implying that some astrophysical factors conspire and/or it reflects a fundamental principle in collisionless formation processes .