The rise and fall of a challenger: the Bullet Cluster in $\Lambda$ Cold
  Dark Matter simulations
  The Bullet Cluster has provided some of the best evidence for the $\Lambda$
cold dark matter ($\Lambda\rm{CDM}$) model via direct empirical proof of the
existence of collisionless dark matter, while posing a serious challenge owing
to the unusually high inferred pairwise velocities of its progenitor clusters.
Here we investigate the probability of finding such a high-velocity pair in
large-volume N-body simulations, particularly focusing on differences between
halo finding algorithms. We find that algorithms that do not account for the
kinematics of infalling groups yield vastly different statistics and
probabilities. When employing the ROCKSTAR halo finder that considers particle
velocities, we find numerous Bullet-like pair candidates that closely match not
only the high pairwise velocity, but also the mass, mass ratio, separation
distance, and collision angle of the initial conditions that have been shown to
produce the Bullet Cluster in non-cosmological hydrodynamic simulations. The
probability of finding a high pairwise velocity pair among haloes with $M_{\rm
halo}\geq10^{14} M_{\odot}$ is $4.6\times 10^{-4}$ using ROCKSTAR, while it is
$\approx 34\times$ lower using a friends-of-friends (FOF) based approach as in
previous studies. This is because the typical spatial extent of Bullet
progenitors is such that FOF tends to group them into a single halo despite
clearly distinct kinematics. Further requiring an appropriately high average
mass among the two progenitors, we find the comoving number density of
potential Bullet-like candidates to be on the order of $\approx10^{-10} \,{\rm
Mpc}^{-3}$. Our findings suggest that $\Lambda\rm{CDM}$ straightforwardly
produces massive, high relative velocity halo pairs analogous to Bullet Cluster
progenitors, and hence the Bullet Cluster does not present a challenge to the
$\Lambda\rm{CDM}$ model.
