An analytic model for non-spherical lenses in covariant MOdified Newtonian Dynamics

TL;DR

This paper introduces a class of analytic non-spherical models for gravitational lensing in MOND, enabling better fits to complex lensing systems than previous spherical models, though some systems remain challenging.

Contribution

It presents a new analytic approach for modeling non-spherical gravitational lenses in MOND, improving the ability to fit double and quadruple-imaged systems.

Findings

Successfully fit 10 double-imaged systems with MOND

Successfully fit the quadruple-imaged system Q2237+030

Could not fit some systems, indicating limitations of the models

Abstract

Strong gravitational lensing by galaxies in MOdified Newtonian Dynamics (MOND) has until now been restricted to spherically symmetric models. These models were able to account for the size of the Einstein ring of observed lenses, but were unable to account for double-imaged systems with collinear images, as well as four-image lenses. Non-spherical models are generally cumbersome to compute numerically in MOND, but we present here a class of analytic non-spherical models that can be applied to fit double-imaged and quadruple-imaged systems. We use them to obtain a reasonable MOND fit to ten double-imaged systems, as well as to the quadruple-imaged system Q2237+030 which is an isolated bulge-disc lens producing an Einstein cross. However, we also find five double-imaged systems and three quadruple-imaged systems for which no reasonable MOND fit can be obtained with our models. We argue that this is mostly due to the intrinsic limitation of the analytic models, even though the presence of small amounts of additional dark mass on galaxy scales in MOND is also plausible.