The Mass Distribution of the Unusual Merging Cluster Abell 2146 from
  Strong Lensing
  Abell 2146 consists of two galaxy clusters that have recently collided close
to the plane of the sky, and it is unique in showing two large shocks on
$\textit{Chandra X-ray Observatory}$ images. With an early stage merger,
shortly after first core passage, one would expect the cluster galaxies and the
dark matter to be leading the X-ray emitting plasma. In this regard, the
cluster Abell 2146-A is very unusual in that the X-ray cool core appears to
lead, rather than lag, the Brightest Cluster Galaxy (BCG) in their
trajectories. Here we present a strong lensing analysis of multiple image
systems identified on $\textit{Hubble Space Telescope}$ images. In particular,
we focus on the distribution of mass in Abell 2146-A in order to determine the
centroid of the dark matter halo. We use object colours and morphologies to
identify multiple image systems; very conservatively, four of these systems are
used as constraints on a lens mass model. We find that the centroid of the dark
matter halo, constrained using the strongly lensed features, is coincident with
the BCG, with an offset of $\approx$ 2 kpc between the centres of the dark
matter halo and the BCG. Thus from the strong lensing model, the X-ray cool
core also leads the centroid of the dark matter in Abell 2146-A, with an offset
of $\approx$ 30 kpc.
