Strong Lensing Model of SPT-CLJ0356-5337, a Major Merger Candidate at
  Redshift 1.0359
  We present an analysis of the mass distribution inferred from strong lensing
by SPT-CL J0356-5337, a cluster of galaxies at redshift z = 1.0359 revealed in
the follow-up of the SPT-SZ clusters. The cluster has an Einstein radius of
Erad=14 for a source at z = 3 and a mass within 500 kpc of M_500kpc =
4.0+-0.8x10^14Msol. Our spectroscopic identification of three multiply-imaged
systems (z = 2.363, z = 2.364, and z = 3.048), combined with HST F606W-band
imaging allows us to build a strong lensing model for this cluster with an rms
of <0.3'' between the predicted and measured positions of the multiple images.
Our modeling reveals a two-component mass distribution in the cluster. One mass
component is dominated by the brightest cluster galaxy and the other component,
separated by ~170 kpc, contains a group of eight red elliptical galaxies
confined in a ~9'' (~70 kpc) diameter circle. We estimate the mass ratio
between the two components to be between 1:1.25 and 1:1.58. In addition,
spectroscopic data reveal that these two near-equal mass cores have only a
small velocity difference of 300 km/s between the two components. This small
radial velocity difference suggests that most of the relative velocity takes
place in the plane of the sky, and implies that SPT-CL J0356-5337 is a major
merger with a small impact parameter seen face-on. We also assess the relative
contributions of galaxy-scale halos to the overall mass of the core of the
cluster and find that within 800 kpc from the brightest cluster galaxy about
27% of the total mass can be attributed to visible and dark matter associated
with galaxies, whereas only 73% of the total mass in the core comes from
cluster-scale dark matter halos.
