Abstract

Aims. Various studies have shown a lensing bias in the mass-concentration relation of cluster-scale structures that is the result of an alignment of the major axis and the line of sight. In this paper, we aim to study this lensing bias through the mass-concentration relation of galaxy groups, thus extending observational constraints to dark matter haloes of mass = 1013 1014 M fi. Methods. Our work is based on the stacked weak-lensing analysis of a sample of 80 strong-lensing galaxy groups. By combining several lenses, we significantly increase the signal-to-noise ratio of the lensing signal, thus providing constraints on the mass profile that cannot be obtained for individual objects. The resulting shear profiles were fitted with various mass models, among them the Navarro-Frank-White (NFW) profile, which provides an estimate of the total mass and of the concentration of the composite galaxy groups. Results. The main results of our analysis are the following: (i) the lensing signal does not allow us to firmly distinguish between a simple singular isothermal sphere mass distribution and the expected NFW mass profile; (ii) we obtain an average concentration c200 = 8 : 6 + 2 : 1 1 : 3 that is much higher than the value expected from numerical simulations for the corresponding average mass M200 = 0 : 73 + 0 : 11 0 : 10 = 1014 M fi; (iii) the combination of our results with those at larger mass scales gives a mass-concentration relation c(M) of more than two decades in mass, whose slope disagrees with predictions from numerical simulations using unbiased populations of dark matter haloes; (iv) our combined c(M) relation matches results from simulations that only used haloes with a large strong-lensing cross-section, that is, elongated with a major axis close to the line of sight; (v) for the simplest case of prolate haloes, we estimate a lower limit on the minor-to-major axis ratio a = c = 0 : 5 for the average SARCS galaxy group with a toy model. Conclusions. Our analysis based on galaxy groups confirmed the results obtained at larger mass scales: strong lenses apparently present concentrations that are too high, which arises because the triaxial haloes are preferentially oriented with the line of sight. Because more massive systems already have large lensing cross-sections, they do not require a strong elongation along the line of sight, contrary to less massive galaxy groups. Therefore it is natural to observe higher lensing (projected) concentrations for such systems, resulting in an overall mass-concentration relation steeper than that of nonlensing haloes.