A Radon Transform Perspective on Exoplanet Transits
Abstract
Transit light curves are usually analyzed under the assumption that the transiting planet has a circular sky-projected silhouette. However, planetary rotation, tides, rings, or atmospheric inhomogeneities can produce non-circular silhouettes. This raises the question of what information transit light curves can provide about the underlying two-dimensional attenuation map. In this paper, we show that, in a simple and transparent limit, the time derivative of the transit light curve during ingress or egress can be interpreted as a Radon-transform measurement of the planetary attenuation map, with the projection direction set by the local normal to the stellar limb. This viewpoint makes the information content of a single transit clear. Ingress and egress provide at most two projection angles, so the data constrain the Fourier transform of the attenuation map only along at most two radial slices, leaving a large null space. Physical constraints on the attenuation values and shape priors can reduce the range of viable solutions, but non-uniqueness generally remains. We further examine how realistic effects modify this picture. In particular, small stellar-limb curvature introduces weak sensitivity to transverse Fourier-space structure around the ideal slices, a sensitivity that is absent in the strict Radon-transform limit. These results provide a framework for understanding what transit light curves can and cannot reveal about non-circular planetary silhouettes.
Versions
Related
- Quasiperiodic Eruptions from Recurrent Satellite Black Hole Transits through Magnetized Galactic Nucleus Accretion Disks
- Quasi-periodic Eruptions from Recurrent Satellite Black Hole Transits through Magnetized Galactic Nucleus Accretion Disks
- Signature of exocomet transits observed with Ariel
- A TESS Disappearing Act: The Vanishing Transits of TOI-2535 b
- Strict Limits on Helium Absorption from LHS 1140 b from Four JWST NIRISS Transits
BibTeX
@misc{tada2026radon,
title = {{A Radon Transform Perspective on Exoplanet Transits}},
author = {Shotaro Tada},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.13163},
eprint = {2608.13163},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.13163},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Radon Transform Perspective on Exoplanet Transits
AU - Shotaro Tada
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2608.13163
UR - https://arxiv.org/abs/2608.13163
AB - Transit light curves are usually analyzed under the assumption that the transiting planet has a circular sky-projected silhouette. However, planetary rotation, tides, rings, or atmospheric inhomogeneities can produce non-circular silhouettes. This raises the question of what information transit light curves can provide about the underlying two-dimensional attenuation map. In this paper, we show that, in a simple and transparent limit, the time derivative of the transit light curve during ingress or egress can be interpreted as a Radon-transform measurement of the planetary attenuation map, with the projection direction set by the local normal to the stellar limb. This viewpoint makes the information content of a single transit clear. Ingress and egress provide at most two projection angles, so the data constrain the Fourier transform of the attenuation map only along at most two radial slices, leaving a large null space. Physical constraints on the attenuation values and shape priors can reduce the range of viable solutions, but non-uniqueness generally remains. We further examine how realistic effects modify this picture. In particular, small stellar-limb curvature introduces weak sensitivity to transverse Fourier-space structure around the ideal slices, a sensitivity that is absent in the strict Radon-transform limit. These results provide a framework for understanding what transit light curves can and cannot reveal about non-circular planetary silhouettes.
ER -