Multipole models of four-image gravitational lenses with anomalous flux ratios

Abstract

It has been known for over a decade that many four‐image gravitational lenses exhibit anomalous radio flux ratios. These anomalies can be explained by adding a clumpy cold dark matter (CDM) component to the background galactic potential of the lens. As an alternative, Evans & Witt (2003) recently suggested that smooth multipole perturbations provide a reasonable alternative to CDM substructure in some but not all cases. We generalize their method in two ways so as to determine whether multipole models can explain highly anomalous systems. We carry the multipole expansion to higher order, and also include external tidal shear as a free parameter. Fitting for the shear proves crucial to finding a physical (positive‐definite density) model. For B1422+231, working to order kmax= 5 (and including shear) yields a model that is physical but implausible. Going to higher order (kmax≳ 9) reduces global departures from ellipticity, but at the cost of introducing small‐scale wiggles in proximity to the bright images. These localized undulations are more pronounced in B2045+265, where kmax∼ 17 multipoles are required to smooth out large‐scale deviations from elliptical symmetry. Such modes surely cannot be taken at face value; they must indicate that the models are trying to reproduce some other sort of structure. Our formalism naturally finds models that fit the data exactly, but we use B0712+472 to show that measurement uncertainties have little effect on our results. Finally, we consider the system B1933+503, where two sources are lensed by the same foreground galaxy. The additional constraints provided by the images of the second source render the multipole model unphysical. We conclude that external shear must be taken into account to obtain plausible models, and that a purely smooth angular structure for the lens galaxy does not provide a viable alternative to the prevailing CDM clump hypothesis.

COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses

“…The global, large scale shape of the lens found by the semi-linear inversion is well adapted to model the Einstein rings, which are very sensitive to azimuthal asymmetry in the lens, but additional smaller scale structures are needed to slightly modify the positions of the quasar images and make them compatible with the measured astrometry. The disagreement between the astrometry predicted by LENSMODEL and the one predicted by the semi-linear inversion adds support to the presence of multipole-type substructures in the lens (e.g., Congdon & Keeton 2005).…”

Meso‐Structure in Three Strong‐lensing Systems

“…If galaxy-lens potentials are in general significantly different from generalized isothermals, then conclusions derived using this assumption (Congdon & Keeton 2005;Yoo et al 2005Yoo et al , 2006) may need to be revised. A useful test would be to see whether a generalized isothermal plus a perturbation from X can fit the VLBI image structure in J0414+053.…”

On modeling galaxy-scale strong lens systems

“…One approach to free-form models is to fix the radial profile of the lens galaxy but allow an arbitrary angular structure [28,42,43,[76][77][78][79]. If we assume an isothermal profile, we can expand the galaxy potential in a multipole series to order m max ,…”