The inner mass power spectrum of galaxies using strong gravitational lensing: beyond linear approximation

TL;DR

This paper introduces a statistical method to measure the power spectrum of dark matter potential fluctuations in galaxies using strong gravitational lensing, extending beyond linear approximations and applicable to real observational data.

Contribution

It develops a Gaussian random field formalism for lens potential fluctuations and demonstrates its effectiveness with simulated lenses and MCMC analysis.

Findings

Can measure density fluctuations on 1-10 kpc scales

Achieves percent-level accuracy with single HST observations

Validates method with simulated lens data

Abstract

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.