Polka-dotted Stars II: Starspots and obliquities of Kepler-17 and Kepler-63

TL;DR

This paper demonstrates the use of the StarryStarryProcess Bayesian surface-mapping framework to jointly infer planetary and stellar surface properties from long-baseline Kepler photometry for Kepler-63 and Kepler-17. By segmenting the light curves into rotation-epoch chunks and modeling both rotational modulation and transit spot-crossings, the method constrains stellar obliquities, inclinations, and the latitudinal distributions of starspots, reporting $\psi_\star = 163.9^{+3.8}_{-4.2}$ degrees for Kepler-63 and $\psi_\star = 0.23^{+0.35}_{-0.43}$ degrees for Kepler-17. The results reveal two active-latitude belts and a characteristic spot radius around $10^\circ$ for both stars, illustrating diversity in magnetic topologies across similar spectral types. The work validates joint transit-rotation surface mapping, aligns with prior studies, and points to population-level studies with future surveys (e.g., TESS, PLATO) to test dynamo theory and obliquity’s role in planet formation.

Abstract

Starspots trace stellar magnetic activity and influence both stellar evolution and exoplanet characterization. While occultation-based spot analyses have been applied to individual systems, comparative studies remain limited. We apply the StarryStarryProcess Bayesian surface-mapping framework to archival Kepler light curves of two planet hosts, Kepler-63 and Kepler-17, extending the validation established on TOI-3884 (Paper I). Across both systems, we infer characteristic spot radii smaller than 10 degrees. The latitudinal spot distributions of these G dwarfs show active latitudes: Kepler-63 near 30 degrees and Kepler-17 near 15 degrees. Our analysis yields stellar obliquity measurements in excellent agreement with previous studies, validating our methodology and demonstrating that transit-based surface mapping can simultaneously recover planetary parameters, stellar orientations, and magnetic morphologies. Together, these results reveal a range of stellar geometries from nearly aligned (Kepler-17) to highly misaligned (Kepler-63).

Figures (11)

• Figure 1: Light curve of Kepler-63 showing relative flux measurements over time for quarters 3, 4, 5, and 6 of the Kepler mission. The red points show the transits. The data spans approximately 350 days (from BJD 2457250 to 2457600) and shows periodic transit events appearing as characteristic dips in the stellar brightness against the background of rotational modulation from starspots.
• Figure 2: Transit photometry and model fits for Kepler-63. Top: Complete light curve showing eight detected transits over 80 days of observations. Black points show binned detrended photometry; orange lines represent model averages of 200 samples. The numbers above the boxes indicate the transit number to match the bottom panel. Bottom panels: Individual transit events with observed photometry (grey points with error bars) and the average model across 200 samples (orange lines) with $1\sigma$ uncertainty. Model parameters were determined through simultaneous fitting of all transits and the rotational modulation.
• Figure 3: Corner plot showing posterior distributions and parameter correlations from our analysis of stellar spot properties for Kepler-63. Diagonal panels display marginal posterior distributions for the flux decrement due to spots ($\mathbb{d}$), $\rm{RMS}_{\rm{spot}}$, and mean and standard deviation of spot latitudes ($\mu_\phi$ and $\sigma_\phi$). Diagonal panels show marginalized posterior distributions; dashed vertical lines mark the 16th and 84th percentiles ($1\sigma$ credible intervals). Off-diagonal panels show two-dimensional kernel density estimates with three iso-density contours illustrating correlations between parameters. The tight correlations between parameters demonstrate well-constrained solutions from the photometric modeling.
• Figure 4: Latitudinal distribution of stellar activity for Kepler-63 derived from spot modeling. The plot shows Posterior distributions of the absolute active latitude, shown from $0^\circ$ to $90^\circ$. Thin colored curves indicate individual posterior samples, while the thick black curve shows the mean distribution.
• Figure 5: Corner plot showing posterior distributions and parameter correlations from our comprehensive analysis of Kepler-63. Diagonal panels display marginal posterior distributions for orbital inclination ($i_p$), stellar inclination ($i_\star$), stellar obliquity ($\psi_\star$), rotation period ($P_\star$), planet-to-star radius ratio ($R_p/R_\star$), projected stellar rotation velocity ($v \sin{i}$), and stellar density ($\rho_\star$). Off-diagonal panels show 2D posterior distributions with contour levels indicating parameter covariances. Red shaded regions and dashed lines indicate literature values from Sanchis2013 for comparison. The excellent agreement demonstrates the reliability of our joint modeling approach while providing enhanced precision for several key parameters.