Abstract

Aims. We aim to study the reliability of R-A (the distance from the arcs to the center of the lens) as a measure of the Einstein radius in galaxy groups. In addition, we want to analyze the possibility of using R-A as a proxy to characterize some properties of galaxy groups, such as luminosity (L) and richness (N). Methods. We analyzed the Einstein radius, theta(E), in our sample of Strong Lensing Legacy Survey (SL2S) galaxy groups, and compared it with R-A, 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; and 3) strong lensing modeling (theta(E,III)) of eleven groups (with four new models presented in this work) using Hubble Space Telescope (HST) and Canada-France-Hawaii Telescope (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). Results. We found a correlation between theta(E) and R-A, but with large scatter. We estimate theta(E),(I) = (2.2 +/- 0.9) + (0.7 +/- 0.2) R-A, theta(E,II) = (0.4 +/- 1.5) + (1.1 +/- 0.4)R-A, and theta(E,III) = (0.4 +/- 1.5) + (0.9 +/- 0.3)R-A for each method respectively. We found weak evidence of anti-correlation between R-A and z, with Log R-A = (0.58 +/- 0.06) - (0.04 +/- 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. Conclusions. Our analysis indicates that R-A is correlated with theta(E) in our sample, making R-A useful for characterizing properties like L and N (and possibly N/L) in galaxy groups. Additionally, we present evidence suggesting that the Einstein radius evolves with z.