Recovering the mass distribution of an extended gravitational lens

TL;DR

This paper explores how wave-optical lensing observations can be used to recover detailed mass distribution characteristics of extended gravitational lenses, including shape, orientation, and symmetry properties, by analyzing the PSF and its caustics.

Contribution

It introduces a method to determine the mass distribution of gravitational lenses through wave-optical analysis of the PSF, considering multipole moments beyond the quadrupole.

Findings

Higher-order multipole moments reveal symmetry properties of the lens.

Octupole moments break north-south symmetry.

Hexadecapole moments indicate axial symmetry breaking.

Abstract

We investigate the possibility of determining the mass distribution of a gravitational lens via lensing observations. We consider an extended, compact gravitational lens, representing its static external gravitational potential via an infinite set of symmetric trace free (STF) multipole moments. Within the wave-optical treatment, we evaluate the caustics formed in the lens's point spread function (PSF). We study the only quantity that is available in astronomical lensing observations: the image of that PSF formed by an imaging telescope. This observable may be used to recover some physical characteristics of the lens, including its shape, orientation and composition. Illustrating this, we study exotic gravitational lenses formed by several well-known solids with uniform density. We show that when moments beyond the quadrupole are observed, some of the symmetry properties of the lens can be recovered. The presence of an octupole moment implies breaking the "north-south" symmetry of the mass distribution in the lens. The presence of a rotated hexadecapole moment implies breaking axial symmetry. As such, if observations of lensed images allow the reconstruction of these moments, important information about the mass distribution and dynamics of the lens can be obtained. This may help with choosing the most appropriate mass profile that is used to characterize the mass distribution of astrophysical lenses, such as the dark matter halos that are presumed to contain most of the mass of galaxies and clusters of galaxies. Our results are novel and offer new insight into gravitational lensing by realistic astrophysical systems.