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Degeneracy of semi-analytic solution for axially symmetric lens equations |
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| Authors: | P T Mutka P H Mähönen |
| Institution: | University of Oulu, Department of Physical Sciences, Theoretical Physics Division, PO Box 3000, 90014 Oulun Yliopisto, Finland;RWTH Aachen University, Germany |
| Abstract: | We derive a simple semi-analytical approximation for lens equations with an arbitrary radially symmetric mass density ρ( r ), when r /ξ A dark matter (DM) haloes (GNFW model) are parametrized through a shape parameter α, a concentration parameter c In the case of an asymmetric dual image lens system, similar effective degeneracy is produced when the geometry of the lens is relaxed. Because it is impossible to determine the exact location of the source image, a family of solutions is acquired when the mass of the lens object and location of the observed images are fixed. Our results indicate that the amount of degeneration is only weakly affected by the asymmetry in the lensing geometry set-up, e.g. the observational effective degeneracy is very close to the true physical degeneracy of the Einstein ring solutions. Basically with high-enough values for the concentration parameter, the degeneracy spawns the whole range for the shape parameter α=−2.0, −1.0] . |
| Keywords: | gravitational lensing relativity methods: analytical galaxies: haloes dark matter |