Systematics in lensing reconstruction: Dark matter rings in the sky?
  Non-parametric lensing methods are a useful way of reconstructing the lensing
mass of a cluster without making assumptions about the way the mass is
distributed in the cluster. These methods are particularly powerful in the case
of galaxy clusters with a large number of constraints. The advantage of not
assuming implicitly that the luminous matter follows the dark matter is
particularly interesting in those cases where the cluster is in a non-relaxed
dynamical state. On the other hand, non-parametric methods have several
limitations that should be taken into account carefully. We explore some of
these limitations and focus on their implications for the possible ring of dark
matter around the galaxy cluster CL0024+17. We project three background
galaxies through a mock cluster of known radial profile density and obtain a
map for the arcs ($\theta$ map). We also calculate the shear field associated
with the mock cluster across the whole field of view (3.3 arcmin). Combining
the positions of the arcs and the two-direction shear, we perform an inversion
of the lens equation using two separate methods, the biconjugate gradient, and
the quadratic programming (QADP) to reconstruct the convergence map of the mock
cluster. We explore the space of the solutions of the convergence map and
compare the radial density profiles to the density profile of the mock cluster.
When the inversion matrix algorithms are forced to find the exact solution, we
encounter systematic effects resembling ring structures, that clearly depart
from the original convergence map. Overfitting lensing data with a
non-parametric method can produce ring-like structures similar to the alleged
one in CL0024.
