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 Title: Galaxy mass profiles from strong lensing III: The two-dimensional broken power-law model Authors: O'Riordan, CMWarren, SJMortlock, DJ Item Type: Journal Article Abstract: When modelling strong gravitational lenses, i.e., where there are multiple images of the same source, the most widely used parameterisation for the mass profile in the lens galaxy is the singular power-law model $\rho(r)\propto r^{-\gamma}$. This model may be insufficiently flexible for very accurate work, for example measuring the Hubble constant based on time delays between multiple images. Here we derive the lensing properties - deflection angle, shear, and magnification - of a more adaptable model where the projected mass surface density is parameterised as a continuous two-dimensional broken power-law (2DBPL). This elliptical 2DBPL model is characterised by power-law slopes $t_1$, $t_2$ either side of the break radius $\theta_\mathrm{B}$. The key to the 2DBPL model is the derivation of the lensing properties of the truncated power law (TPL) model, where the surface density is a power law out to the truncation radius $\theta_\mathrm{T}$ and zero beyond. This TPL model is also useful by itself. We create mock observations of lensing by a TPL profile where the images form outside the truncation radius, so there is no mass in the annulus covered by the images. We then show that the slope of the profile interior to the images may be accurately recovered for lenses of moderate ellipticity. This demonstrates that the widely-held notion that lensing measures the slope of the mass profile in the annulus of the images, and is insensitive to the mass distribution at radii interior to the images, is incorrect. Date of Acceptance: 27-Nov-2020 URI: http://hdl.handle.net/10044/1/85973 DOI: 10.1093/mnras/staa3747 ISSN: 0035-8711 Publisher: Oxford University Press (OUP) Start Page: 3687 End Page: 3694 Journal / Book Title: Monthly Notices of the Royal Astronomical Society Volume: 501 Issue: 3 Copyright Statement: ©2020 Oxford University Press. This is a pre-copy-editing, author-produced version of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. The definitive publisher-authenticated version C M O’Riordan, S J Warren, D J Mortlock, Galaxy mass profiles from strong lensing – III. The two-dimensional broken power-law model, Monthly Notices of the Royal Astronomical Society, Volume 501, Issue 3, March 2021, Pages 3687–3694, is available online at: https://doi.org/10.1093/mnras/staa3747 Sponsor/Funder: Science and Technology Facilities Council (STFC) Funder's Grant Number: ST/S000372/1 Keywords: astro-ph.GAastro-ph.GAastro-ph.GAastro-ph.GAAstronomy & Astrophysics0201 Astronomical and Space Sciences Notes: 8 pages, 3 figures, for submission to MNRAS Publication Status: Published Online Publication Date: 2021-12-08 Appears in Collections: PhysicsAstrophysicsFaculty of Natural Sciences