Analytic Interferometry of Rotating Stellar Surfaces

Abstract: The surfaces of rotating stars serve as a window into their interiors, magnetic dynamos, and are important in other areas including exoplanet discovery and atmospheric characterization. While indirect techniques such as photometry and Doppler imaging have been studied for their ability to map stellar surfaces, the gold standard remains optical long-baseline interferometry. In this paper, we develop new closed-form solutions for the interferometric visibility of a rotating star with an arbitrary inhomogeneous surface. We introduce the concept of 'stellar rotation synthesis' in interferometry--an analog of Earth rotation synthesis--where stellar rotation adds information to the spherical harmonic modes representing the star's surface intensity. We implement these solutions in the open-source package harmonix, written in JAX with automatic differentiation, providing a rich ecosystem for fitting and inference. Inspired by similar studies for photometry and Doppler imaging, we use simulations of a fiducial star as observed by the CHARA Array and intensity interferometers to perform a comprehensive theoretical study of the information theory of the starspot mapping problem in interferometry. We show that adding simultaneous photometry from a space-based instrument such as TESS adds complementary spatial information to interferometry and can improve the precision on the map coefficients by over an order of magnitude, enabling the detailed mapping of nearby main-sequence stars with current facilities. Finally, we evaluate the performance of existing and proposed intensity interferometers for stellar surface mapping.