Strong Lensing In The Inner Halo Of Galaxy Clusters
  We present an axially symmetric formula to calculate the probability of
finding gravitational arcs in galaxy clusters, being induced by their massive
dark matter haloes, as a function of clusters redshifts and virial masses. The
formula includes the ellipticity of the clusters dark matter potential by using
a pseudo-elliptical approximation. The probabilities are calculated and
compared for two dark-matter halo profiles, the Navarro, Frenk and White (NFW)
and the Non-Singular-Isothermal-Sphere (NSIS). We demonstrate the power of our
formulation through a Kolmogorov-Smirnov (KS) test on the strong lensing
statistics of an X-ray bright sample of low redshift Abell clusters. This KS
test allows to establish limits on the values of the concentration parameter
for the NFW profile ($c_\Delta$) and the core radius for the NSIS profile
(\rc), which are related to the lowest cluster redshift ($z_{\rm cut}$) where
strong arcs can be observed. For NFW dark matter profiles, we infer cluster
haloes with concentrations that are consistent to those predicted by
$\Lambda$CDM simulations. As for NSIS dark matter profiles, we find only upper
limits for the clusters core radii and thus do not rule out a purely SIS model.
For alternative mass profiles, our formulation provides constraints through
$z_{\rm cut}$ on the parameters that control the concentration of mass in the
inner region of the clusters haloes. We find that $z_{\rm cut}$ is expected to
lie in the 0.0--0.2 redshift, highlighting the need to include very low-$z$
clusters in samples to study the clusters mass profiles.
