Characterisation of starspot structure and differential rotation of Kepler-411

TL;DR

Kepler-411’s surface magnetic activity is dissected with two complementary photometric mappings: transit-based spot occultation mapping using Kepler-411 c’s transits and rotational modulation mapping from long-baseline Kepler light curves. A Bayesian adaptive-sampling framework yields three robust spot occultations and a population of evolving surface spots, while finding no evidence for differential rotation, consistent with rigid-body rotation at $P_{rot}=10.52\pm0.34$ days. The analysis provides quantitative spot properties (sizes, contrasts, temperatures) and demonstrates cross-method consistency, highlighting the complex, time-varying nature of spots on a young exoplanet host. The work showcases how transit photometry and rotational modulation can jointly constrain stellar activity, informing dynamo theory and exoplanet-star interaction studies.

Abstract

Starspots and their movements on stellar surfaces enable investigating the mechanisms of stellar magnetic activity. Information on the spot distribution and differential rotation provide important constraints for the behaviour of stellar magnetic dynamos. We analyse the Kepler photometry of Kepler-411, a known exoplanet host, to determine the distribution and properties of star spots on the stellar surface with two independent and complementary methods: modelling the photometric effect of rotation of spots on the stellar surface and mapping of spots by transiting planets. By constructing a spot model accounting for geometry, differential rotation and spot evolution, we model the spots of the stellar surface giving rise to the observed brightness variations. We also search for evidence for occultations of starspots in high-cadence photometry. Our spot models reproduce the observed photometric variations well and we are able to obtain information on the distribution and movement of spots on the stellar surface. We do not obtain evidence for differential rotation -- the rotational profile is consistent with rigid-body rotation with a period of 10.52$\pm$0.34 days. We detect three occultations of spots by planet c. The positions of these spots coincide well with the positions of larger spot structures identified by our modelling of the rotational modulation of the light curve.

Figures (14)

• Figure 1: Identified occultations of spots by Kepler-411 c during transit events 116, 117, and 121 and a flare-event occurring during the transit 164. The yellow, red and orange curves denote the reference model, a model with a spot occultation, and a model with a flare-event, respectively.
• Figure 2: The flare-event occurring outside transit events modelled for reference with both spot occultation model and a simple exponential flare morphology model. The latter model was favoured by our significance tests.
• Figure 3: Each row of panels contains Kepler-411 data (red dots) and maximum a posteriori (MAP) solutions (black curves), model residuals, and estimated spot maps for epochs 1044.016 and 1051.851 corresponding to the mean times of transits 116 and 117. The rows from top to bottom are for models with $k = 1, ..., 5$. The blue vertical dashed lines denote the surface visible at those epochs. The greyscale denotes a range of spot sizes and contrasts as estimated based on the effect of the corresponding spot on the flux. The red circles and the corresponding uncertainty intervals denote MAP spot positions and standard errors. The reference time is $t_0 = 1034.0$ days. Only absolute values of latitude are known and all spots are placed on the same hemisphere.
• Figure 4: Markov chains of the phase parameters of the signals identifying the solutions for models with $k=3, 4, 5$ (left to right) for the data subset S1034. The different colours denote independent samplings.
• Figure 5: Estimated latitudes (black circles) of the five spots identified in the data subset S1034. The red dots show where high posterior probabilities (above 1% of the global maximum) were first identified by five samplings for which spots were randomly truncated to positions near the equator or the pole.