A Universal Power-law Profile of Pseudo-Phase-Space Density-like Quantities in Elliptical Galaxies

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 $\rho_{\rm{DM}}(r)$ and VD anisotropy $\beta(r)$ to investigate radial stellar VD $\sigma_{\rm\star r}(r)$ 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 $\rho(r)/\sigma_{\rm\star r}^3(r)$ with total density $\rho(r)= \rho_{\star}(r)+\rho_{\rm{DM}}(r)$ 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 $\sigma_{\star\rm{r}}(r)$ replaced by the rms velocity of stars $v_{\star\rm{rms}}(r)$ 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 $\rho(r)/\sigma_{\rm\star r}^3(r)$ cannot be fully explained by equilibrium alone, implying that some astrophysical factors conspire and/or it reflects a fundamental principle in collisionless formation processes.