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.
