The existence of a bullet cluster ( such as 1E0657-56 ) poses a challenge to the concordance \Lambda cold dark matter model .
Here we investigate the velocity distribution of dark matter halo pairs in large N -body simulations with differing box sizes ( 250 h ^ { -1 } { Mpc } -2 h ^ { -1 } Gpc ) and resolutions .
We examine various basic statistics such as the halo masses , pairwise halo velocities ( v _ { 12 } ) , collisional angles , and pair separation distances .
We then compare our results to the initial conditions required to reproduce the observational properties of 1E0657-56 in non-cosmological hydrodynamical simulations .

We find that the high velocity tail of the v _ { 12 } distribution extends to greater velocities as we increase the simulation box size .
We also find that the number of high- v _ { 12 } pairs increases as we increase the particle count and resolution with a fixed box size , however , this increase is mostly due to lower mass halos which do not match the observed masses of 1E0657-56 .
We find that the redshift evolution effect is not very strong for the v _ { 12 } distribution function between z =0.0 and z \sim 0.5 .

We identify some pairs whose v _ { 12 } resemble the required initial conditions , however , even the best candidates have either wrong halo mass ratios , or too large separations .
Our simulations suggest that it is very difficult to produce such initial conditions at z = 0.0 , 0.296 , & 0.489 in comoving volumes as large as ( 2 h ^ { -1 } Gpc ) ^ { 3 } .
Based on the extrapolation of our cumulative v _ { 12 } function , we find that one needs a simulation with a comoving box size of ( 4.48 h ^ { -1 } Gpc ) ^ { 3 } and 2240 ^ { 3 } DM particles in order to produce at least one pair of halos that resembles the required v _ { 12 } and observed masses of 1E0657-56 .
From our simulated v _ { 12 } probability distribution function , we find that the probability of finding a halo pair with v _ { 12 } \geq 3000 km s ^ { -1 } and masses \geq 10 ^ { 14 } M _ { \odot } to be 2.76 \times 10 ^ { -8 } at z =0.489 .
We conclude that either 1E0657-56 is incompatible with the concordance \Lambda CDM universe , or the initial conditions suggested by the non-cosmological simulations must be revised to give a lower value of v _ { 12 } .