SARCS strong-lensing galaxy groups: II - mass-concentration relation and strong-lensing bias

Our work is based on the stacked weak-lensing analysis of a sample of 80 strong-lensing galaxy groups. Our main results are the following: (i) the lensing signal does not allow us to firmly reject a simple singular isothermal sphere mass distribution compared to the expected NFW mass profile; (ii) we obtain an average concentration $c_{200}=8.6_{-1.3}^{+2.1}$ that is much higher than the expected value from numerical simulations for the corresponding average mass $M_{200}=0.73_{-0.10}^{+0.11}\times10^{14}\mathrm{M_{\odot}}$; (iii) the combination of our results with those at larger mass scales gives a mass-concentration relation $c(M)$ over nearly two decades in mass, with a slope in disagreement with predictions from numerical simulations using unbiased populations of dark matter haloes; (iv) our combined $c(M)$ relation matches results from simulations using only haloes with a large strong-lensing cross section, i.e. elongated with a major axis close to the line of sight; (v) for the simplest case of prolate haloes, we estimate with a toy model a lower limit on the minor:major axis ratio $a/c=0.5$ for the average SARCS galaxy group. Our analysis based on galaxy groups confirmed the results obtained at larger mass scales: strong lenses present apparently too large concentrations, which can be explained by triaxial haloes preferentially oriented with the line of sight. Because more massive systems already have large lensing cross sections, they do not require a large elongation along the line of sight, contrary to less massive galaxy groups. Therefore, it is natural to observe larger lensing (projected) concentrations for such systems, resulting in an overall mass-concentration relation steeper than that of non-lensing haloes.