THE ABUNDANCE OF BULLET GROUPS IN ACDM

We estimate the expected distribution of displacements between the two dominant dark matter (DM) peaks (DM DM displacements) and between the DM and gaseous baryon peak (DM gas displacements) in DM halos with masses larger than 10(13) h(-1) M-circle dot. As a benchmark, we use the observation of SL2S J08544-0121, which is the lowest mass system (1.0 x 10(14) h(-1) M-circle dot) observed so far, featuring a bi-modal DM distribution with a dislocated gas component. We find that (50 +/- 10)% of the DM halos with circular velocities in the range 300-700 km s(-1) (groups) show DM-DM displacements equal to or larger than 186 +/- 30 h(-1) kpc as observed in SL2S J08544-0121. For DM halos with circular velocities larger than 700 km s(-1) (clusters) this fraction rises to (70 +/- 10)%. Using the same simulation, we estimate the DM gas displacements and find that 0.1%-1.0% of the groups should present separations equal to or larger than 87 +/- 14 h(-1) kpc, corresponding to our observational benchmark; for clusters, this fraction rises to (7 +/- 3)%, consistent with previous studies of DM 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 similar to 6.0 x 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 ACDM by looking for DM gas displacements in low mass clusters and groups.