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Keywords:

  • gravitational lensing: strong;
  • methods: analytical;
  • galaxies: haloes;
  • dark matter

ABSTRACT

We have been able to connect statistics of the observed double-image gravitational lenses to general properties of the internal structure of lens haloes. Our analytical theory for the generalization of the Navarro, Frenk & White (NFW) profile (GNFW) lenses with a parametrized cusp slope (α) gives a relation connecting the cusp slope of a lens mass profile to the observed magnification ratio of the produced images and location of the optical axis. The relation does not depend on the cosmology, total lens mass, concentration or redshifts of the the lens and the lensed object. Simple geometry of axially-symmetric lensing and the aforementioned relation enables us to define the cusp slope limit value, αCSL, for the cusp slope, independent of the location of the optical axis. The threshold cusp slope value α=αCSL 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 a distribution of these threshold values that depend only on the observed flux ratio of the lensed images, 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 the cusp slope α=−1.95 ± 0.02. We have also found an indication of a second population of lenses with a cusp slope value α=−1.51 ± 0.02. We estimate that there is about 97 per cent probability that the observed feature in the threshold value limit distribution is produced by a second population of lenses, with their own characteristic density profile. The data indicating the exact characteristics of the subpopulation are noisy. Roughly one out of eight haloes within the sample belongs to this shallower cusp slope group. We investigate the accuracy of our analysis by constructing mock catalogues with Monte Carlo method.