Exoplanets & Exomoons

Planetary Complexity Revealed by the Joint Differential Entropy of Eigencolours

By Keith Cowing
Status Report
November 14, 2023
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Planetary Complexity Revealed by the Joint Differential Entropy of Eigencolours
A dual horizontal axis is used to plot both the wavelength average differential entropy (circle ‘◦’ shapes), and the joint differential entropy of the eigencolours (‘x’ shapes), aligning the horizontal axis at the respective values of the original Earth and the least complex synthetic world. The fixed point alignment of the horizontal axes changes the scale of each axis. The vertical axis shows the corresponding wavelength average statistical complexity for both measures. Perforated lines show the distinction between world types. — astro-ph.EP

We propose a measure, the joint differential entropy of eigencolours, for determining the spatial complexity of exoplanets using only spatially unresolved light curve data.

The measure can be used to search for habitable planets, based on the premise of a potential association between life and exoplanet complexity. We present an analysis using disk-integrated light curves from Earth, developed in previous studies, as a proxy for exoplanet data.

We show that this quantity is distinct from previous measures of exoplanet complexity due to its sensitivity to spatial information that is masked by features with large mutual information between wavelengths, such as cloud cover. The measure has a natural upper limit and appears to avoid a strong bias toward specific planetary features.

This makes it a candidate for being used as a generalisable measure of exoplanet habitability, since it is agnostic regarding the form that life could take.

Wavelength average statistical complexity vs. wavelength average differential entropy (top) and complexity vs. joint differential entropy of the eigencolours (bottom). — astro-ph.EP

Gary Segal, David Parkinson, Stuart Bartlett

Comments: 10 pages, 3 figures, 2 tables
Subjects: Earth and Planetary Astrophysics (astro-ph.EP); Instrumentation and Methods for Astrophysics (astro-ph.IM)
Cite as: arXiv:2311.06986 [astro-ph.EP] (or arXiv:2311.06986v1 [astro-ph.EP] for this version)
Submission history
From: David Parkinson
[v1] Sun, 12 Nov 2023 23:40:36 UTC (4,013 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) 🖖🏻