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Systematic variations of central mass density slopes in early-type galaxies

We study the total density distribution in the central regions (~ 1 effective radius, $R_e$) of early-type galaxies (ETGs), using data from SPIDER and $\rm ATLAS^{3D}$. Our analysis extends the range of galaxy stellar mass ($M_{\star}$) probed by gravitational lensing, down to ~ $10^{10}\, \rm M_{\odot}$. We model each galaxy with two components (dark matter halo + stars), exploring different assumptions for the dark matter (DM) halo profile (i.e. NFW, NFW-contracted, and Burkert profiles), and leaving stellar mass-to-light ($M_{\star}/L$) ratios as free fitting parameters to the data. For all plausible halo models, the best-fitting $M_{\star}/L$, normalized to that for a Chabrier IMF, increases systematically with galaxy size and mass. For an NFW profile, the slope of the total mass profile is non-universal, independently of several ingredients in the modeling (e.g., halo contraction, anisotropy, and rotation velocity in ETGs). For the most massive ($M_{\star}$ ~ $10^{11.5} \, M_{\odot}$) or largest ($R_{\rm e}$ ~ $15 \, \rm kpc$) ETGs, the profile is isothermal in the central regions (~$R_{\rm e}/2$), while for the low-mass ($M_{\star}$ ~ $10^{10.2} \, M_\odot$) or smallest ($R_{\rm e}$ ~ $0.5 \, \rm kpc$) systems, the profile is steeper than isothermal, with slopes similar to those for a constant-$M/L$ profile. For a steeper concentration-mass relation than that expected from simulations, the correlation of density slope with galaxy mass tends to flatten, while correlations with $R_{\rm e}$ and velocity dispersions are more robust. Our results clearly point to a "non-homology" in the total mass distribution of ETGs, which simulations of galaxy formation suggest may be related to a varying role of dissipation with galaxy mass.