Mass distribution in the core of MACS J1206: robust modeling from an
  exceptionally large sample of central multiple images
  We present a new strong lensing analysis of the galaxy cluster MACS
J1206.2-0847 (MACS 1206), at z=0.44, using deep spectroscopy from CLASH-VLT and
VLT/MUSE archival data in combination with imaging from the Cluster Lensing and
Supernova survey with Hubble. MUSE observations enable the spectroscopic
identification of 23 new multiply imaged sources, extending the previous
compilations by a factor of approximately five. In total, we use the positional
measurements of 82 spectroscopic multiple images belonging to 27 families at
z=1.0-6.1 to reconstruct the projected total mass distribution of MACS 1206.
Remarkably, 11 multiple images are found within 50 kpc of the brightest cluster
galaxy, making this an unprecedented set of constraints for the innermost
projected mass distribution of a galaxy cluster. We thus find that, although
dynamically relaxed, the smooth matter component (dark matter plus hot gas) of
MACS 1206 shows a significant asymmetry, which closely follows the asymmetric
distribution of the stellar component (galaxy members and intracluster light).
We determine the value of the innermost logarithmic slope of the projected
total mass density profile and find it to be close to the canonical
Navarro-Frenk-White value. We demonstrate that this quantity is very robust
against different parametrizations of the diffuse mass component; however, this
is not the case when only one central image is used in the mass reconstruction.
We also show that the mass density profile from our new strong lensing model is
in very good agreement with dynamical and X-ray measurements at larger radii,
where they overlap.
