Integral field spectroscopy with the solar gravitational lens

TL;DR

This paper explores the use of integral field spectroscopy combined with the solar gravitational lens to resolve and analyze the surfaces and atmospheres of extrasolar planets, addressing optical, navigational, and noise challenges.

Contribution

It provides an analytical and numerical framework for orbit design, optical properties, and image reconstruction techniques for SGL-based exoplanet observation missions.

Findings

Analytical models of hyperbolic orbits and gravity assists for SGL missions.

Demonstration of image reconstruction of Earth-like planets from single Einstein ring measurements.

Identification of noise sources and a spectral-spatial separation strategy for improved SNR.

Abstract

The prospect of combining integral field spectroscopy with the solar gravitational lens (SGL) to spectrally and spatially resolve the surfaces and atmospheres of extrasolar planets is investigated. The properties of hyperbolic orbits visiting the focal region of the SGL are calculated analytically, demonstrating trade offs between departure velocity and time of arrival, as well as gravity assist maneuvers and heliocentric angular velocity. Numerical integration of the solar barycentric motion demonstrates that navigational acceleration of $\textrm{d}v \lesssim 80 \frac{\textrm{m}}{\textrm{s}} + 6.7 \frac{\textrm{m}}{\textrm{s}} \frac{t}{\textrm{year}}$ is needed to obtain and maintain alignment. Obtaining target ephemerides of sufficient precision is an open problem. The optical properties of an oblate gravitational lens are reviewed, including calculations of the magnification and the point-spread function that forms inside a telescope. Image formation for extended, incoherent sources is discussed when the projected image is smaller than, approximately equal to, and larger than the critical caustic. Sources of contamination which limit observational SNR are considered in detail, including the sun, the solar corona, the host star, and potential background objects. A noise mitigation strategy of spectrally and spatially separating the light using integral field spectroscopy is emphasized. A pseudoinverse-based image reconstruction scheme demonstrates that direct reconstruction of an Earth-like source from \textit{single} measurements of the Einstein ring is possible when the critical caustic and observed SNR are sufficiently large. In this arrangement, a mission would not require multiple telescopes or navigational symmetry breaking, enabling continuous monitoring of the atmospheric composition and dynamics on other planets.