http://arxiv.org/abs/1705.07195
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 determines 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 measurable radii of the arcs. In the same manner, asymmetries in the brightness distributions along an arc determine differences of the deflection angle of the perturber. 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 like the mass of the perturber or its position, models need to be inserted. The same conclusions about the scale of detectable masses (on the order of $10^8 M_\odot$) and model-dependent degeneracies as in other approaches are then found and supported by analysing B1938+666 as an example. Yet, the model-indenpedent equations show that, apart from the radii and brightness distributions of the arcs, independent information on the axisymmetric lens or the perturber has to be employed in order to break a so-far unnoted degeneracy that entangles the axisymmetric lens with the perturber. This degeneracy can be broken by inserting the position of a luminous perturber into the equations, or measuring the velocity dispersion.
J. Wagner
Tue, 23 May 17
25/68
Comments: 8 pages, 3 figures, 1 table, submitted to Astronomy & Astrophysics, comments welcome