SINGH, VIKASHVIKASHSINGHBONOMO, ALDO STEFANOALDO STEFANOBONOMOSCANDARIATO, GAETANOGAETANOSCANDARIATOCibrario, N.N.CibrarioBarbato, D.D.BarbatoFossati, L.L.FossatiPAGANO, IsabellaIsabellaPAGANOSOZZETTI, AlessandroAlessandroSOZZETTI2022-06-152022-06-1520220004-6361http://hdl.handle.net/20.500.12386/32324We perform a homogeneous search for and analysis of optical occultations and phase variations of the most favorable ultra-short-period (USP) ($P<1$~d) sub-Neptunes ($R_{p}<4 R_{\oplus}$) observed by $\textit{Kepler}$ and K2, with the aim of better understanding their nature. We first selected 16 $\textit{Kepler}$ and K2 USP sub-Neptunes, based on the expected occultation signal. We filtered out stellar variability in the $\textit{Kepler}$ light curves, using a sliding linear fitting and, when required, a more sophisticated approach based on Gaussian Process regression. We simultaneously modeled the primary transit, secondary eclipse, and phase variations in a Bayesian framework, by using information from previous studies and knowledge of the Gaia parallaxes. We confirm the optical secondary eclipses for Kepler-10b ($13\sigma$), Kepler-78b ($9.5\sigma$), and K2-141b ($6.9\sigma$), with marginal evidence for K2-312b ($2.2\sigma$). We report new detections for K2-106b ($3.3\sigma$), K2-131b (3.2$\sigma$), Kepler-407b ($3.0\sigma$), and hints for K2-229b (2.5$\sigma$). For all targets with the exception of K2-229b and K2-312b, we also find phase curve variations with a confidence level higher than $2\sigma$. 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 night-side 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 night side. 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.STAMPAenArticle10.1051/0004-6361/2020390372-s2.0-85124795359https://www.aanda.org/articles/aa/full_html/2022/02/aa39037-20/aa39037-20.htmlhttp://arxiv.org/abs/2111.05716v2FIS/05 - ASTRONOMIA E ASTROFISICAERC sectors::Physical Sciences and Engineering::PE9 Universe sciences: astro-physics/chemistry/biology; solar systems; stellar, galactic and extragalactic astronomy, planetary systems, cosmology, space science, instrumentation