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, θ_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 (θ_E,I); 2) a strong lensing analytical method (θ_E,II) combined with a velocity dispersion-concentration relation derived from numerical simulations designed to mimic our group sample; and 3) strong lensing modeling (θ_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 θ_E and R_A, but with large scatter. We estimate θ_E,I = (2.2 ± 0.9) + (0.7 ± 0.2)R_A, θ_E,II = (0.4 ± 1.5) + (1.1 ± 0.4)R_A, and θ_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 θ_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.