| 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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