Exoplanets & Exomoons

Gaussian Processes and Nested Sampling Applied to Kepler’s Small Long-period Exoplanet Candidates

By Keith Cowing
Status Report
astro-ph.EP
January 26, 2024
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Gaussian Processes and Nested Sampling Applied to Kepler’s Small Long-period Exoplanet Candidates
Our sample population of KOIs (big colored circles with black outlines) and the remaining KOI background population (small black dots), distributed according to planetary radius, Rp, orbital period, P (left), and insolation flux, S0 (right). Note that our sample uses the newly fitted/derived results of this work whereas background KOIs draw from the preceding MCMC solutions of Lissauer et al. (2023). Our KOIs are colored by their logged Bayes’s factor, B—as recovered by the modelling of each individual KOI under PC (transit plus Gaussian process, TGP) and FA (Gaussian process only, GP) hypotheses—such that greater positive values indicate strong planet-candidacy and vice-versa for FAs, while those near-zero can be interpreted as possessing inconclusive/weak significance either way (see § 2.1). The B values corresponding to our solutions are also used to outline associated Lissauer et al. (2023) results (small black dots with colored outlines) in order to facilitate a visual comparison of the physical parameters recovered for each KOI analyzed by both studies. Green lines outline the range within which a KOI may be deemed sufficiently “Earth–Sun-like”; these are defined according to nominal Earth values for Rp, and either P or S0 as x ∈ 1 ± √ 2 − 1  x⊕. Note that all KOIs were also uniformly filtered by R⋆ with respect to solar values according to these same bounds. We are complete in both boxes drawn by these lines. For ease of reference, Earth (⊕) and Venus (♀) are also plotted. — astro-ph.EP

There are more than 5000 confirmed and validated planets beyond the solar system to date, more than half of which were discovered by NASA’s Kepler mission.

The catalog of Kepler’s exoplanet candidates has only been extensively analyzed under the assumption of white noise (i.i.d. Gaussian), which breaks down on timescales longer than a day due to correlated noise (point-to-point correlation) from stellar variability and instrumental effects.

Statistical validation of candidate transit events becomes increasingly difficult when they are contaminated by this form of correlated noise, especially in the low-signal-to-noise (S/N) regimes occupied by Earth–Sun and Venus–Sun analogs. To diagnose small long-period, low-S/N putative transit signatures with few (roughly 3–9) observed transit-like events (e.g., Earth–Sun analogs), we model Kepler’s photometric data as noise, treated as a Gaussian process, with and without the inclusion of a transit model.

Nested sampling algorithms from the Python UltraNest package recover model evidences and maximum a posteriori parameter sets, allowing us to disposition transit signatures as either planet candidates or false alarms within a Bayesian framework.

Michael R. B. Matesic (1 and 2), Jason F. Rowe (2), John H. Livingston (3 and 4 and 5), Shishir Dholakia (6), Daniel Jontof-Hutter (7), Jack J. Lissauer (8)

Comments: 15 pages, 9 figures, 2 tables, uses AASTeX631
Subjects: Earth and Planetary Astrophysics (astro-ph.EP); Instrumentation and Methods for Astrophysics (astro-ph.IM)
Cite as: arXiv:2401.13041 [astro-ph.EP] (or arXiv:2401.13041v1 [astro-ph.EP] for this version)
Journal reference: The Astronomical Journal 167.2.68 (2024)
Related DOI:
https://doi.org/10.3847/1538-3881/ad0fe9
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Submission history
From: Michael Matesic
[v1] Tue, 23 Jan 2024 19:00:29 UTC (2,866 KB)
https://arxiv.org/abs/2401.13041
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