A JWST Transit of a Jupiter Analog I: Constraints on the Oblateness of Kepler-167e

TL;DR

This study tackles the challenge of constraining the oblateness of a Jupiter-analog exoplanet, Kepler-167 e, from a long JWST transit by exploring a comprehensive grid of data reductions, limb-darkening treatments, and trend models. Using gradient-based MLE and Bayesian nested sampling across 60–72 viable combinations, the authors find that spherical and oblate planet models fit the data comparably well, with the 95% upper bound on the projected oblateness $f$ reaching $<0.097$ (and as tight as $<0.065$ in some pipelines). Translating $f$ into a rotation period via the Darwin–Radau relation yields $P\gtrsim7.11$–$7.18$ hours for aligned spin axes, though orientation uncertainties can relax this bound to a few hours. The work highlights the critical role of correlated noise and pipeline choice in oblateness measurements with JWST and argues for end-to-end, multi-pipeline analyses and single-exposure designs to achieve tighter constraints in future studies.

Abstract

In October 2024 JWST observed a transit of Kepler-167e, a Jupiter-analog planet on a 1000+ day orbit. These observations, recorded over a long baseline of nearly 60 hours, were designed to search for signatures of planetary oblateness and/or exomoons comparable to Ganymede. In this first in a series of studies analyzing these data we report on constraints on Kepler-167e's oblateness. We explored a large grid of data reduction pipelines and modeling choices, including a new entirely independent reduction pipeline ("katahdin") and two new treatments for limb darkening. We find that under a Bayesian model comparison framework the data are fit equally well by both spherical and oblate planet models, and that our ability to constrain the oblateness is negatively impacted by the influence of exposure-long trends. Using the most conservative of our posteriors, we place a 95% upper bound on the projected oblateness of $f<0.097$, which corresponds to a rotation period of $P\geq7.11$ hours if the planet's spin axis is aligned with the sky plane. We note, however, that the final bound depends on the choice of reduction pipeline and systematics model, and that our suite of end-to-end analyses produced bounds as low as $f<0.065$ at 95%. We conclude that leveraging JWST to make tighter constraints on planetary oblateness will require further investigation into mitigating exposure-long trends and correlated noise.

Figures (15)

• Figure 1: All 18 white light curves, each normalized by the median of flux in exposure 1. The discontinuities occur at exposure boundaries; the large dip in the middle corresponds to the transit of Kepler-167 e, while the smaller dip in exposure 6 corresponds to a transit of Kepler-167 c. Note that moving forwards this study only considers the first 5 exposures.
• Figure 2: A zoom-in on exposure 1 of all 18 5-minute light curves after dividing out the best-fit quadratic trend from each. Note that all reductions tend to agree on the overall structure of the time series, and that reductions derived from the same pipeline tend to agree with each other.
• Figure 3: Correlations between the different light curves plotted in Fig. \ref{['fig:exp_1_zoom']}. Each point represents a comparison between two different reductions at a single data point; the panels in the top row are limited to comparisons between reductions that used different settings of the same underlying pipeline, while the panels in the bottom row show comparisons between reductions created with different pipelines. As noted, the three pipelines tend to agree, and light curves derived from the same pipeline using different settings are even more strongly correlated.
• Figure 4: Draws from the priors of the five different limb darkening models. Note that all three of the physical models land essentially on top of one another, but there is still a finite width to their distribution.
• Figure 5: The impact of limb darkening polynomial order on transit light curves. We first simulated a transit of a Kepler-167 e-sized planet across a Kepler-167-like star, using a 10th order polynomial approximation to the stellar intensity profile generated using the Kurucz stellar grid. We then simulated 4 other transits using successively lower polynomial orders for the stellar intensity approximation, and differenced the resulting transits with the fiducial one. The differenced curves, shown above for 2nd-10th order, 4th-10th order, etc, reveal that low-order approximations impart residuals of 10s of ppm over the course of the transit.