Cusped Mass Density Profiles and Magnification Ratios of Double Image
  Gravitational Lenses
  We have been able to connect the statistics of the observed double image
gravitational lenses to the general properties of the internal structure of
dark matter haloes. Our analytical theory for the GNFW lenses with parametrized
cusp slope (alpha) gives us a relation connecting the cusp slope of the lensing
profile to the observed magnification ratio of the produced images and location
of the optical axis. The relation does not depend on cosmology, total lens
mass, concentration or redshifts of the the lens and the lensed object. Simple
geometry of axially symmetric lensing and aforementioned relation enables us to
define a threshold value alpha_CSL for the cusp slope, independent from
location of the optical axis. The threshold cusp slope value alpha=alpha_CSL is
the shallowest slope for the inner part of the GNFW profile that can produce
the observed magnification ratio with any lensing configuration. We use
distribution of these threshold values in a statistical study of the double
image lenses in order to limit the possible cusp slope values, and identify
whether there exists a population of haloes with similar profiles. Our
theoretical fit indicates that within our sample of double image gravitational
lenses, most of the haloes have cusp slope alpha=-1.95 +/- 0.02. We have also
found an indication of a second population of lenses with a cusp slope value
alpha=-1.49 +/- 0.09. We estimate that there is about 99 per cent probability
that the observed feature in the threshold value limit distribution is produced
by the second population of lenses, with their own characteristic density
profile.
