Dark matter scaling relations in intermediate z haloes

Abstract

We investigate scaling relations between the dark matter (DM) halo model parameters for a sample of intermediate redshift early - type galaxies (ETGs) resorting to a combined analysis of Einstein radii and aperture velocity dispersions. Modeling the dark halo with a Navarro - Frenk - White profile and assuming a Salpeter initial mass function (IMF) to estimate stellar masses, we find that the column density ${\cal{S}}$ and the Newtonian acceleration within the halo characteristic radius $r_s$ and effective radius $R_{eff}$ are not universal quantities, but correlate with the luminosity $L_V$, the stellar mass $M_{\star}$ and the halo mass $M_{200}$, contrary to recent claims in the literature. We finally discuss a tight correlation among the DM mass $M_{DM}(R_{eff})$ within the effective radius $R_{eff}$, the stellar mass $M_{\star}(R_{eff})$ and $R_{eff}$ itself. The slopes of the scaling relations discussed here strongly depend, however, on the DM halo model and the IMF adopted so that these ingredients have to be better constrained in order to draw definitive conclusions on the DM scaling relations for ETGs.