World map small

A lensed radio jet at milli-arcsecond resolution I: Bayesian comparison of parametric lens models

by Devon M. Powell (MPA, Germany), Simona Vegetti (MPA, Germany), J. P. McKean (Kapeteyn and ASTRON, the Netherlands), Cristiana Spingola (INAF, Italy), Hannah R. Stacey (MPA, Germany), Christopher D. Fassnacht (UC Davis, USA)

Powell 1
Figure 1: Best-fit source (left) and lens-plane (centre) surface brightness reconstructions, as well as the surface mass density (right) for the smooth lens model of MG J0751+2716 from Powell et al. (2022). Caustics and critical curves are plotted as dashed white lines. The colour maps, which are normalised to the peak surface brightness, show the continuum radio emission, while the overlaid white contours show the source and sky emission reconstructed from a 2.12 μm Keck AO observation. The convergence map is in units of critical density Σc. The middle panel illustrates the long, thin gravitational arcs resolved with VLBI which are highly sensitive to detailed features in the gravitational potential.


Strong gravitational lensing by galaxies is a powerful astronomical tool, as the lensing effect is sensitive to the total surface mass density in the lens galaxy.  This provides an observational window, independent from and complementary to light-based modelling, into the complex physical processes that shape the distribution of mass in galaxies.  For instance, gravitational lensing observables are sensitive to different baryonic processes, such as adiabatic contraction or AGN feedback, that can cause galaxies to become more or less concentrated (e.g. Duffy et al. 2010, Peirani et al. 2017, Mukherjee at all. 2021). Gravitational lensing can also reveal the presence of low-mass dark matter haloes in several lens systems, which are detectable only through their gravitational effect (Vegetti et al. 2010, 2012, Hezaveh et al. 2016).  Measurements of the Hubble constant are possible using time-delays between multiple images of a lensed quasar (e.g. Birrer et al. 2019, Rusu et al. 2020, Birrer & Treu 2021).

The success of such studies depends on the level of detail that can be detected in the mass distribution of a gravitational lens galaxy, which in turn is strongly dependent on the angular resolution of the observation. So far, most existing gravitational lens systems have been observed with Hubble Space Telescope (~120 mas resolution), with some followed up using the W.M. Keck adaptive optics system (~70 mas), and still fewer with ALMA (~25 mas).  These observations are sufficient to constrain the slope of an elliptical power-law mass model, or to detect dark subhaloes as small as 108 solar masses.  Pushing the field of gravitational lens modelling into the milli-arcsecond (mas) regime drastically increases the amount of astrophysical information we can extract from gravitational lens observations; at present, global very long baseline interferometry (VLBI) is the only observational tool which can provide such high angular resolution.

In this work, we present the first analysis of a gravitational lens system observed at < 5 mas resolution using global VLBI, in which both a detailed model for the mass of the lens galaxy and a pixelated source surface brightness map are jointly inferred.  The analysis was done using the Bayesian visibility-space lens modelling technique developed by Powell et al. (2021).  This observation of the lensed radio jet MG J0751+2716 exhibits extremely long, thin lensed arcs covering a wide range of angular and radial positions around the lens galaxy, which are perfect for revealing the underlying gravitational landscape.  In Figure 1, one can clearly see the jet morphology of the reconstructed source, with bright knots of radio continuum emission stretching several hundred parsecs (in projection) from the host galaxy (shown in white contours modelled from Keck AO data).  

We found during the modelling process that significant lens model complexity is needed to recover such a clearly reconstructed source.  In addition to a basic elliptical power-law mass distribution, we added extra angular structure in the form of multipole perturbations, as well as higher-order terms in the potential corresponding to gradients in the external convergence and shear.  It is important to include sufficient complexity in smooth gravitational lens models: Searches for dark substructures and line-of-sight haloes around the main lens can be biased by inaccurate knowledge of the large-scale mass distribution; this is also a concern for flux-ratio analyses and time-delay cosmography.  VLBI observations can therefore play a key role in informing several types of gravitational lens analyses, by revealing structure in the gravitational potential that is otherwise inaccessible with current optical telescopes. 

Published in Powell et al 2022 MNRAS, 516, 2, 1808–1828