We apply two new state-of-the-art methods that model the distribution of observed tracers in projected phase space to lift the mass / velocity anisotropy (VA) degeneracy and deduce constraints on the mass profiles of galaxies, as well as their VA. We
first show how a distribution function based method applied to the satellite kinematics of otherwise isolated SDSS galaxies shows convincing observational evidence of age matching: red galaxies have more concentrated dark matter (DM) halos than blue galaxies of the same stellar or halo mass. Then, applying the MAMPOSSt technique to M87 (traced by its red and blue globular clusters) we find that very cuspy DM is favored, unless we release priors on DM concentration or stellar mass (leading to unconstrained slope). For the Fornax dwarf spheroidal (traced by its metal-rich and metal-poor stars), the inner DM slope is unconstrained, with weak evidence for a core if the stellar mass is fixed. This highlights how priors are crucial for DM modeling. Finally, we find that blue GCs around M87 and metal-rich stars in Fornax have tangential outer VA.
We present the first analysis of extended stellar kinematics of elliptical galaxies where a Yukawa--like correction to the Newtonian gravitational potential derived from f(R)-gravity is considered as an alternative to dark matter. In this framework,
we model long-slit data and planetary nebulae data out to 7 Re of three galaxies with either decreasing or flat dispersion profiles. We use the corrected Newtonian potential in a dispersion-kurtosis Jeans analysis to account for the mass-anisotropy degeneracy. We find that these modified potentials are able to fit nicely all three elliptical galaxies and the anisotropy distribution is consistent with that estimated if a dark halo is considered. The parameter which measures the strength of the Yukawa-like correction is, on average, smaller than the one found previously in spiral galaxies and correlates both with the scale length of the Yukawa-like term and the orbital anisotropy.
