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Appendix A

In Sect. 3.2 we briefly discuss the question of choosing the most likely centre of the halo mass distribution. From the optical luminosity maps, we have shown that several SARCS objects present complex morphology. Assuming that light traces mass on the group and cluster scale (e.g. Bahcall 2000), these substructures in the distribution of galaxies might be associated to massive subhaloes. As the weak-lensing estimator is sensitive to all the mass components where the signal is measured, a fit using a single halo will be affected by all the present substructures. However, the question of the centre remains as a source of uncertainties: substantial miscentering can lead to weak-lensing masses underestimated up to 30% (e.g. George et al. 2012).

Here we explore the effect of changing the position of the centre used to construct the shear profile. We limit the analysis to the SARCS groups with a multi-modal structure in their luminosity maps within a 0.5 Mpc radius from the centre of the strong-lensing system. For group-scale haloes, typical values of the virial radius are ~1 Mpc, so within a 0.5 Mpc radius we expect to instead observe substructures than two distinct haloes. Fitting shear profiles with a single component thus remains valid, so we changed the position of the centre of the shear profile for these groups by simply positioning it either between the two optical over-densities or on the second observed peak, i.e. not associated to the strong-lensing system.

The results we obtained are presented Fig. A.1. For two groups, SA35 and SA83, we managed to obtain better constraints than in the initial configuration. It suggests that the strong-lensing system is not exactly at the mass centre but rather associated to a satellite galaxy. For SA90, we observe a strong change according to the centre’s position, with a σ_SIS much higher when using the strong-lensing system as the centre of the shear profile. For this group, the brightest galaxy is also at the centre of the strong-lensing system, which seems to indicate that the mass associated to the second luminosity peak is negligible compared to the main halo. SA91 presents the opposite behaviour, with a velocity dispersion higher when the centre of the shear profile is moved towards the second luminosity peak. As for SA35 and SA83, we suppose that the strong-lensing system is associated with a satellite galaxy.

In the remaining cases, we only observe slight variations with compatible velocity dispersions within their 1σ error bar, which makes interpretating the results speculative. For groups that have the highest σ_SIS when the centre of the shear profile is taken between the two luminosity over-densities as SA89, one can explain such a variation by the presence of two clumps of galaxies evolving in a single dark matter halo whose mass centre is located in the middle of the galaxy distribution. For instance, SA66 was studied in more detail by Limousin et al. (2010a) with a strong-lensing modelling that requires a substantial external shear, and by Muñoz et al. (2013), with a dynamical analysis that revealed two distinct populations of galaxies. In that case, the results suggest a merging event of two subhaloes. Such a configuration is consistent with the weak-lensing results since moving the centre of the shear profile in both directions from the total mass centre induces a lower SIS velocity dispersion, with a larger decrease when going towards the second luminosity peak (not associated with the strong-lensing system). It is therefore tempting to infer the same for the groups showing the same variation in σ_SIS. One can also think of two distinct dark matter haloes with similar masses that generate their own shear signal, and thus we observe the opposite variation with lower values of σ_SIS when taking the centre of the profiles between the two luminosity over-densities (SA26, SA55). Another possible configuration would be a mass distribution dominated by a halo located on the strong-lensing system, and in that case, the measured velocity dispersion decreases when moving away, such as for SA61.

Even though we observe statistically significant changes for some groups, given the weakness of the signal we measure on single objects, it remains difficult to probe the position of the actual mass centre via weak lensing and draw reliable conclusions from the small observed variations in the shear profile. Our first assumption of positioning the mass centre on the strong-lensing system then remains on average a valid approximation. In specific cases, a deeper analysis combining a strong-lensing modelling (external shear) and dynamical information (two distinct populations of galaxies) might, however, help to increase the precision of the mass determination for such complex configurations.

Fig. A.1 SIS model on the multi-modal SARCS candidates. The centre chosen for the shear profile is located either on the strong-lensing system (black open squares), at the middle of the 2 luminosity over-densities (red open circles) or on the luminosity peak not associated to the strong lensing features (green open triangles). The measured dispersion at the three different positionings can be used as an indicator of the dominance of the strong lens within its group.

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