Cusped Density Profiles of Gravitational Lens Objects

Mathematics – Probability

Scientific paper

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Cosmology, Redshift, Dark Matter, Cosmic Background Radiation, Origin And Formation Of The Universe, Distances, Redshifts, Radial Velocities, Spatial Distribution Of Galaxies, Dark Matter, Background Radiations

Scientific paper

We have developed an analytic formulation for axially symmetric GNFW lens model with parametrized cusp slope (α). The lensing theory has several implications, for example strong lensing is very difficult without cusped mass profile. Required cusp strength for strong lensing depends on the lens object mass and concentration. Exceedingly high concentrations are required for profiles, that have α>-1 in order to produce multiple lensed images.
We study mass profiles of lens objects with double image lenses, since they are resilient against deviations from axial symmetry, perturbations from microlensing, and halo substructure. The statistics of the observed image flux ratios is connected to the general properties of the of the lens mass density profiles. Our analysis is based on a limiting value for the shallowest cusp slope αCSL able to produce the observed flux ratio with any lens geometry and lens-source alignment. The cusp slope limit (CSL) does not depend on cosmology, total lens mass, concentration or redshifts of the the lens and the lensed object. In case of axial symmetry the limiting value is depending only on the magnification ratio (observed flux ratio of the images). This removes uncertainties in the lens and source distributions from the statistical analysis.
Distribution of these threshold values reveals existence of halo population(s) with similar profiles in the sample; most of the halos have cusp slope α = -1.95+/-0.02. We have also found an imprint of a second population with a cusp slope value α = -1.49+/-0.09. There is about 99 per cent estimated probability, that the observed feature in the distribution is produced by the second population of lenses, with their own characteristic density profile. We analyze error sources in our analysis with mock catalogues, and discuss about alternative explanations for the second population signature.

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