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 lensing 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 $z$.
تحميل البحث