Abstract
In galaxy-galaxy strong gravitational lensing, Einstein rings are generated when the lensing galaxy has an axisymmetric lensing potential and the source galaxy is aligned with its symmetry centre along the line of sight. Using a Taylor expansion around the Einstein radius and eliminating the unknown source, I derive a set of analytic equations that determine differences of the deflection angle of the perturber weighted by the convergence of the axisymmetric lens and ratios of the convergences at the positions of the arcs from the measurable thickness of the arcs. In the same manner, asymmetries in the brightness distributions along an arc determine differences in the deflection angle of the perturber if the source has a symmetric brightness profile and is oriented parallel to or orthogonal to the caustic. These equations are the only model-independent information retrievable from observations to leading order in the Taylor expansion. General constraints on the derivatives of the perturbing lens are derived such that the perturbation does not change the number of critical curves. To infer physical properties such as the mass of the perturber or its position, models need to be inserted. The same conclusions about the scale of detectable masses (of the order of 108M⊙) and model-dependent degeneracies as in other approaches are then found and supported by analysing B1938+666 as an example. Yet, the model-independent equations show that there is a fundamental degeneracy between the main lens and the perturber that can only be broken if their relative position is known. This explains the degeneracies between lens models already found in simulations from a more general viewpoint. Hence, apart from the radii and brightness distributions of the arcs, independent information on the axisymmetric lens or the perturber has to be employed to disentangle the axisymmetric lens and the perturber. Depending on the properties of the pertuber, this degeneracy can be broken by characterising the surrounding of the lens or by measuring the time delay between quasar images embedded in the perturbed Einstein ring of the host galaxy.
Highlights
Introduction and motivationIn this third paper in the series by Wagner (2017) and Wagner & Tessore (2018), I investigate which model-independent properties about a gravitational lens or the background source can be determined from two-image configurations caused by lensing mass distributions with perturbed axisymmetry
In this work, I employed the same principle as in Wagner (2017) and Wagner & Tessore (2018) to derive an analytic, modelindependent characterisation of a lens configuration consisting of an axisymmetric main lens and a small perturbation
The resulting equations link observable differences in the arc radii, which almost form an Einstein ring, to differences in the radial component of the deflection angles of the perturber weighted by the convergence of the main lens
Summary
I use a segmentation along the isocontours of the intensity profile of the arcs to define their shape. – the position of its centre of light, – its curvature, called the arc radius, – the two radial segments from the centre of light to each end of an arc. They are called half-lengths, as they are equal for sources with circularly symmetric or elliptical brightness profiles aligned or orthogonal to the caustic when they are mapped by axisymmetric lenses. Depending on the extensions of the two-image configuration on the sky and the resolution of the observation, the shape of the two arcs is measured to varying accuracy and precision. 6. Figure 1a shows the two-image configuration for an axisymmetric lens. It can be observed that the lens centre and the centres of the arcs are aligned, and that the arcs have symmetric half-lengths
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