We analyzed the Einstein radius, $theta_E$, in our sample of SL2S galaxy groups, and compared it with $R_A$ (the distance from the arcs to the center of the lens), using three different approaches: 1.- the velocity dispersion obtained from weak lensi
ng assuming a Singular Isothermal Sphere profile ($theta_{E,I}$), 2.- a strong lensing analytical method ($theta_{E,II}$) combined with a velocity dispersion-concentration relation derived from numerical simulations designed to mimic our group sample, 3.- strong lensing modeling ($theta_{E,III}$) of eleven groups (with four new models presented in this work) using HST and CFHT images. Finally, $R_A$ was analyzed as a function of redshift $z$ to investigate possible correlations with L, N, and the richness-to-luminosity ratio (N/L). We found a correlation between $theta_{E}$ and $R_A$, but with large scatter. We estimate $theta_{E,I}$ = (2.2 $pm$ 0.9) + (0.7 $pm$ 0.2)$R_A$, $theta_{E,II}$ = (0.4 $pm$ 1.5) + (1.1 $pm$ 0.4)$R_A$, and $theta_{E,III}$ = (0.4 $pm$ 1.5) + (0.9 $pm$ 0.3)$R_A$ for each method respectively. We found a weak evidence of anti-correlation between $R_A$ and $z$, with Log$R_A$ = (0.58$pm$0.06) - (0.04$pm$0.1)$z$, suggesting a possible evolution of the Einstein radius with $z$, as reported previously by other authors. Our results also show that $R_A$ is correlated with L and N (more luminous and richer groups have greater $R_A$), and a possible correlation between $R_A$ and the N/L ratio. Our analysis indicates that $R_A$ is correlated with $theta_E$ in our sample, making $R_A$ useful to characterize properties like L and N (and possible N/L) in galaxy groups. Additionally, we present evidence suggesting that the Einstein radius evolves with $z$.
We present VLT spectroscopic observations of 7 discovered galaxy groups between 0.3<z<0.7. The groups were selected from the Strong Lensing Legacy Survey (SL2S), a survey that consists in a systematic search for strong lensing systems in the Canada-F
rance-Hawaii Telescope Legacy Survey (CFHTLS). We give details about the target selection, spectroscopic observations and data reduction for the first release of confirmed SL2S groups. The dynamical analysis of the systems reveals that they are gravitationally bound structures, with at least 4 confirmed members and velocity dispersions between 300 and 800 km/s. Their virial masses are between 10^13 and 10^14 M_sun, and so can be classified as groups or low mass clusters. Most of the systems are isolated groups, except two of them that show evidence of an ongoing merger of two sub-structures. We find a good agreement between the velocity dispersions estimated from the analysis of the kinematics of group galaxies and the weak lensing measurements, and conclude that the dynamics of baryonic matter is a good tracer of the total mass content in galaxy groups.
