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 } h ^ { -1 } { { M _ { \odot } } } .
We use as a benchmark the observation of SL2S J08544-0121 , which is the lowest mass system ( 1.0 \times 10 ^ { 14 } h ^ { -1 } { { M _ { \odot } } } ) 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 { { { \mathrm { km s } ^ { -1 } } } } to 700 { { { \mathrm { km s } ^ { -1 } } } } ( groups ) show DM-DM displacements equal or larger than 186 \pm 30 h ^ { -1 } kpc as observed in SL2S J08544-0121 .
For dark matter halos with circular velocities larger than 700 { { { \mathrm { km s } ^ { -1 } } } } ( 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 87 \pm 14 h ^ { -1 } kpc 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 6.0 \times 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 \Lambda CDM by looking for DM-gas displacements in low mass clusters and groups .