The Bullet Cluster ( 1E 0657-56 ) is well-known as providing visual evidence of dark matter but it is potentially incompatible with the standard \Lambda CDM 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 Bullet-like systems on the sky up to a specified redshift , which allows for direct comparison with observations .
Using a Hubble volume N-body 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 halo-halo 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 0657-56 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 .