| Abstract | Aims. We aim to study the reliability of RA (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 RA as a proxy to characterize some properties of galaxy groups, such as luminosity (L) and richness (N). Methods. We analyzed the Einstein radius, θE, in our sample of Strong Lensing Legacy Survey (SL2S) galaxy groups, and compared it with RA, using three different approaches: 1) the velocity dispersion obtained from weak lensing assuming a singular isothermal sphere profile (θE,I); 2) a strong lensing analytical method (θE,II) combined with a velocity dispersion-concentration relation derived from numerical simulations designed to mimic our group sample; and 3) strong lensing modeling (θE,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, RA 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 θE and RA, but with large scatter. We estimate θE,I = (2.2 ± 0.9) + (0.7 ± 0.2)RA, θE,II = (0.4 ± 1.5) + (1.1 ± 0.4)RA, and θE,III = (0.4 ± 1.5) + (0.9 ± 0.3)RA for each method respectively. We found weak evidence of anti-correlation between RA and z, with Log RA = (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 RA is correlated with L and N (more luminous and richer groups have greater RA), and a possible correlation between RA and the N/L ratio. Conclusions. Our analysis indicates that RA is correlated with θE in our sample, making RA 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. |
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