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 lensi
ng 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 $z$.
We estimate the expected distribution of displacements between the two dominant dark matter (DM) peaks (DM-DM displacements) and between DM and gaseous baryon peak (DM-gas displacements) in dark matter halos with masses larger than $10^{13}$ Msun/h.
We use as a benchmark the observation of SL2S J08544-0121, which is the lowest mass system ($1.0times 10^{14}$ Msun/h) observed so far featuring a bi-modal dark matter distribution with a dislocated gas component. We find that $(50 pm 10)$% of the dark matter halos with circular velocities in the range 300 km/s to 700 km/s (groups) show DM-DM displacements equal or larger than $186 pm 30$ kpc/h as observed in SL2S J08544-0121. For dark matter halos with circular velocities larger than 700 km/s (clusters) this fraction rises to 70 $pm$ 10%. Using the same simulation we estimate the DM-gas displacements and find that 0.1 to 1.0% of the groups should present separations equal or larger than $87pm 14$kpc/h corresponding to our observational benchmark; for clusters this fraction rises to (7 $pm$ 3)%, consistent with previous studies of dark matter to baryon separations. Considering both constraints on the DM-DM and DM-gas displacements we find that the number density of groups similar to SL2S J08544-0121 is $sim 6.0times 10^{-7}$ Mpc$^{-3}$, three times larger than the estimated value for clusters. These results open up the possibility for a new statistical test of LCDM by looking for DM-gas displacements in low mass clusters and groups.
We report on the X-ray observation of a strong lensing selected group, SL2S J08544-0121, with a total mass of $2.4 pm 0.6 times 10^{14}$ $rm{M_odot}$ which revealed a separation of $124pm20$ kpc between the X-ray emitting collisional gas and the coll
isionless galaxies and dark matter (DM), traced by strong lensing. This source allows to put an order of magnitude estimate to the upper limit to the interaction cross section of DM of 10 cm$^2$ g$^{-1}$. It is the lowest mass object found to date showing a DM-baryons separation and it reveals that the detection of bullet-like objects is not rare and confined to mergers of massive objects opening the possibility of a statistical detection of DM-baryons separation with future surveys.
