Galaxy mass profiles from strong lensing II: The elliptical power-law model

Conor M. O'Riordan, Stephen J. Warren, Daniel J. Mortlock

Published 2020-04-28Version 1

We present a systematic analysis of the constraints $\sigma_\gamma$ on the mass profile slope $\gamma$ obtainable when fitting a singular power-law ellipsoid model to a typical strong lensing observation of an extended source. These results extend our previous analysis of circular systems, Paper I. We draw our results from 676 mock observations covering a range of image configurations, each created with a fixed signal to noise ratio $S=100$ in the images. We analyse the results using a combination of theory and a simplified modelling technique which identifies the contribution to the constraints of the individual fluxes and positions in each of the two or four images. The main results are: 1. Regardless of the lens ellipticity, the constraints $\sigma_\gamma$ for two image systems are well described by the results of Paper I, transformed to elliptical coordinates; 2. We derive an analytical expression for $\sigma_\gamma$ for systems with the source aligned with the axis of the lens; 3. For both two-image systems and aligned systems the slope uncertainties $\sigma_\gamma$ are limited by the flux uncertainties; 4. The constraints for off-axis four-image systems are a factor of two to eight better, depending on source size, than for two-image systems, and improve with increasing lens ellipticity. We show that the constraints on $\gamma$ in these systems derive from the complementary positional information of the images and the flux measurements do not contribute to $\sigma_\gamma$. The complementarity improves as the offset of the source from the axis increases, such that the best constraints $\sigma_\gamma<0.01$, for $S=100$, occur when the source approaches the caustic.