How rare is the Bullet Cluster (in a ΛCDM universe)?
Abstract
The Bullet Cluster (1E 065756) is wellknown as providing visual evidence of dark matter but it is potentially incompatible with the standard ΛCDM cosmology due to the high relative velocity of the two colliding clusters. Previous studies have focussed on the probability of such a high relative velocity amongst selected candidate systems. This notion of `probability' is however difficult to interpret and can lead to paradoxical results. Instead, we consider the expected number of Bulletlike systems on the sky up to a specified redshift, which allows for direct comparison with observations. Using a Hubble volume Nbody simulation with high resolution we investigate how the number of such systems depends on the masses of the halo pairs, their separation, and collisional angle. This enables us to extract an approximate formula for the expected number of halohalo collisions given specific collisional parameters. We use extreme value statistics to analyse the tail of the pairwise velocity distribution and demonstrate that it is fatter than the previously assumed Gaussian form. We estimate that the number of dark matter halo pairs as or more extreme than 1E 065756 in mass, separation and relative velocity is 1.3^{+2.0}_{0.6} up to redshift z=0.3. However requiring the halos to have collided and passed through each other as is observed decreases this number to only 0.1. The discovery of more such systems would thus indeed present a challenge to the standard cosmology.
 Publication:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 April 2015
 DOI:
 10.1088/14757516/2015/04/050
 arXiv:
 arXiv:1412.7719
 Bibcode:
 2015JCAP...04..050K
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 v2, 14 pages, 10 figures. Revised in response to Referee's queries  in particular the expected number of Bulletlike systems drops by an order of magnitude when the halos are required to have collided and passed through each other. Accepted by JCAP