Imaging point sources with the gravitational lens of an extended Sun

TL;DR

This paper models the solar gravitational lens as an extended, rotating body with zonal harmonics, analyzing its optical properties and imaging capabilities, including caustic formations and image patterns, for potential exoplanet imaging.

Contribution

It provides an analytical framework for modeling the SGL's intensity distribution considering solar quadrupole effects, enabling realistic image simulations for the first time.

Findings

Formation of astroid caustic due to solar quadrupole

Observation of Einstein cross pattern within the caustic

Transition from four to two bright spots outside the caustic

Abstract

We study the optical properties of the solar gravitational lens (SGL) while treating the Sun as an extended, axisymmetric and rotating body. The gravitational field of the Sun is represented using a set of zonal harmonics. We develop an analytical description of the intensity of light that is observed in the image plane in the strong interference region of a realistic SGL. This formalism makes it possible to model not only the point-spread function of point sources, but also actual observables, images that form in the focal plane of an imaging telescope positioned in the image plane. Perturbations of the monopole gravitational field of the Sun are dominated by the solar quadrupole moment, which results in forming an astroid caustic on the image plane. Consequently, an imaging telescope placed inside the astroid caustic observes four bright spots, forming the well-known pattern of an Einstein cross. The relative intensities and positions of these spots change as the telescope is moved in the image plane, with spots merging into bright arcs when the telescope approaches the caustic boundary. Outside the astroid caustic, only two spots remain and the observed pattern eventually becomes indistinguishable from the imaging pattern of a monopole lens at greater distances from the optical axis. We present results from extensive numerical simulations, forming the basis of our ongoing study of prospective exoplanet imaging with the SGL. These results are also applicable to describe a large class of gravitational lensing scenarios involving axisymmetric lenses that can be represented using zonal harmonics.