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The dark matter halo surface density, given by the product of the dark mattercore radius ($r_c$) and core density ($\rho_c$) has been shown to be a constantfor a wide range of isolated galaxy systems. Here, we carry out a test of this{\em ansatz} using a sample of 17 relaxed galaxy groups observed using Chandraand XMM-Newton, as an extension of our previous analysis with galaxy clusters.We find that $\rho_c \propto r_c^{-1.35^{+0.16}_{-0.17}}$, with an intrinsicscatter of about 27.3%, which is about 1.5 times larger than that seen forgalaxy clusters. Our results thereby indicate that the surface density isdiscrepant with respect to scale invariance by about 2$\sigma$, and its valueis about four times greater than that for galaxies. Therefore, the elevatedvalues of the halo surface density for groups and clusters indicate that thesurface density cannot be a universal constant for all dark matter dominatedsystems. Furthermore, we also implement a test of the radial accelerationrelation for this group sample. We find that the residual scatter in the radialacceleration relation is about 0.32 dex and a factor of three larger than thatobtained using galaxy clusters. The acceleration scale which we obtain isin-between that seen for galaxies and clusters.

A test of constancy of dark matter halo surface density and radial acceleration relation in relaxed galaxy groups