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The inner mass power spectrum of galaxies using strong gravitational lensing: beyond linear approximation
In the last decade the detection of individual massive dark matter sub-halos
has been possible using potential correction formalism in strong gravitational
lens imaging. Here we propose a statistical formalism to relate strong
gravitational lens surface brightness anomalies to the lens potential
fluctuations arising from dark matter distribution in the lens galaxy. We
consider these fluctuations as a Gaussian random field in addition to the
unperturbed smooth lens model. This is very similar to weak lensing formalism
and we show that in this way we can measure the power spectrum of these
perturbations to the potential. We test the method by applying it to simulated
mock lenses of different geometries and by performing an MCMC analysis of the
theoretical power spectra. This method can measure density fluctuations in
early type galaxies on scales of 1-10 kpc at typical rms-levels of a percent,
using a single lens system observed with the Hubble Space Telescope with
typical signal-to-noise ratios obtained in a single orbit
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