ProbingKepler’s hottest small planets via homogeneous search and analysis of optical secondary eclipses and phase variations

Abstract

Context.High-precision photometry can lead to the detection of secondary eclipses and phase variations of highly irradiated planets.Aims.We performed a homogeneous search and analysis of optical occultations and phase variations of the most favorable ultra-short-period (USP) (P< 1 days) sub-Neptunes (Rp< 4R⊕), observed byKeplerand K2, with the aim to better understand their nature.Methods.We first selected 16Keplerand K2 USP sub-Neptunes based on the expected occultation signal. We filtered out stellar variability in theKeplerlight curves, using a sliding linear fitting and, when required, a more sophisticated approach based on a Gaussian process regression. In the case of the detection of secondary eclipse or phase variation with a confidence level higher than 2σ, we simultaneously modeled the primary transit, secondary eclipse, and phase variations in a Bayesian framework, by using information from previous studies and knowledge of theGaiaparallaxes. We further derived constraints on the geometric albedo as a function of the planet’s brightness temperature.Results.We confirm the optical secondary eclipses for Kepler-10b (13σ), Kepler-78b (9.5σ), and K2-141b (6.9σ), with marginal evidence for K2-312b (2.2σ). We report new detections for K2-106b (3.3σ), K2-131b (3.2σ), Kepler-407b (3.0σ), and hints for K2-229b (2.5σ). For all targets, with the exception of K2-229b and K2-312b, we also find phase curve variations with a confidence level higher than 2σ.Conclusions.Two USP planets, namely Kepler-10b and Kepler-78b, show non-negligible nightside emission. This questions the scenario of magma-ocean worlds with inefficient heat redistribution to the nightside for both planets. Due to the youth of the Kepler-78 system and the small planetary orbital separation, the planet may still retain a collisional secondary atmosphere capable of conducting heat from the day to the nightside. Instead, the presence of an outgassing magma ocean on the dayside and the low high-energy irradiation of the old host star may have enabled Kepler-10b to build up and retain a recently formed collisional secondary atmosphere. The magma-world scenario may instead apply to K2-141b and K2-131b.