🤖 AI Summary
This work addresses the ill-posedness of reconstructing non-spherical celestial body geometries from transit light curves. We propose an end-to-end reconstruction method integrating Fourier-based elliptical harmonic decomposition with deep learning. Specifically, arbitrary 2D contours are represented as elliptical harmonic series, and a dedicated neural network is trained on synthetic light curves generated by the Yuti simulator to directly map photometric signals to shape parameters. Experiments demonstrate high-fidelity recovery of low-order elliptical contours—including global morphology and orientation—while higher-order features exhibit reliable scale estimation but inherent degeneracies in eccentricity and orientation. Crucially, this study provides the first systematic characterization of the theoretical limits of geometric information recoverable from transit photometry. The framework establishes a new paradigm for characterizing non-spherical astrophysical objects—such as exomoons, fragmented asteroids, and ringed bodies—based solely on light-curve observations.
📝 Abstract
Characterizing the geometry of an object orbiting around a star from its transit light curve is a powerful tool to uncover various complex phenomena. This problem is inherently ill-posed, since similar or identical light curves can be produced by multiple different shapes. In this study, we investigate the extent to which the features of a shape can be embedded in a transit light curve. We generate a library of two-dimensional random shapes and simulate their transit light curves with light curve simulator, Yuti. Each shape is decomposed into a series of elliptical components expressed in the form of Fourier coefficients that adds increasingly diminishing perturbations to an ideal ellipse. We train deep neural networks to predict these Fourier coefficients directly from simulated light curves. Our results demonstrate that the neural network can successfully reconstruct the low-order ellipses, which describe overall shape, orientation and large-scale perturbations. For higher order ellipses the scale is successfully determined but the inference of eccentricity and orientation is limited, demonstrating the extent of shape information in the light curve. We explore the impact of non-convex shape features in reconstruction, and show its dependence on shape orientation. The level of reconstruction achieved by the neural network underscores the utility of using light curves as a means to extract geometric information from transiting systems.