Astronomy & Telescopes

Identifying and Fitting Eclipse Maps of Exoplanets with Cross-Validation

By Keith Cowing
Status Report
June 6, 2024
Filed under , , , , , , , ,
Identifying and Fitting Eclipse Maps of Exoplanets with Cross-Validation
TOP: An eclipse map fitted to the data in Figure 9, using a model M (ℓmax = 2). Table 2 and Figure 12 show how this model is strongly preferred over the Fourier series model (the null hypothesis) by the cross-validation metric. Hammond et al. (2024) discussed how the structure of this ℓmax = 2 map is limited by its limited spatial freedom. BOTTOM: An eclipse map fitted to the data in Figure 9 using a model M (𝛼 = 4641.6, ℓmax = 4). This value of 𝛼 gives the optimal cross-validation score in Figure 12. We suggest that this value imposes an information content which reflects a combination of the spatial scale of the true map and the level of mapping precision achievable given the precision of the data itself. — astro-ph.EP

Eclipse mapping uses the shape of the eclipse of an exoplanet to measure its two-dimensional structure. Light curves are mostly composed of longitudinal information, with the latitudinal information only contained in the brief ingress and egress of the eclipse.

This imbalance can lead to a spuriously confident map, where the longitudinal structure is constrained by out-of-eclipse data and the latitudinal structure is wrongly determined by the priors on the map. We present a new method to address this issue. The method tests for the presence of an eclipse mapping signal by using k-fold cross-validation to compare the performance of a simple mapping model to the null hypothesis of a uniform disk.

If a signal is found, the method fits a map with more degrees of freedom, optimising its information content. The information content is varied by penalising the model likelihood by a factor proportional to the spatial entropy of the map, optimised by cross-validation.

We demonstrate this method for simulated datasets then apply it to three observational datasets. The method identifies an eclipse mapping signal for JWST MIRI/LRS observations of WASP-43b but does not identify a signal for JWST NIRISS/SOSS observations of WASP-18b or Spitzer Space Telescope observations of HD 189733b.

It is possible to fit eclipse maps to these datasets, but we suggest that these maps are overfitting the eclipse shape. We fit a new map with more spatial freedom to the WASP-43b dataset and show a flatter east-west structure than previously derived.

Mark Hammond, Neil T. Lewis, Sasha Boone, Xueqing Chen, João M. Mendonça, Vivien Parmentier, Jake Taylor, Taylor Bell, Leonardo dos Santos, Nicolas Crouzet, Laura Kreidberg, Michael Radica, Michael Zhang

Comments: Submitted to MNRAS
Subjects: Earth and Planetary Astrophysics (astro-ph.EP); Instrumentation and Methods for Astrophysics (astro-ph.IM)
Cite as: arXiv:2405.20689 [astro-ph.EP] (or arXiv:2405.20689v1 [astro-ph.EP] for this version)
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Submission history
From: Mark Hammond
[v1] Fri, 31 May 2024 08:34:48 UTC (6,421 KB)

Explorers Club Fellow, ex-NASA Space Station Payload manager/space biologist, Away Teams, Journalist, Lapsed climber, Synaesthete, Na’Vi-Jedi-Freman-Buddhist-mix, ASL, Devon Island and Everest Base Camp veteran, (he/him) 🖖🏻