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The Rossiter-McLaughlin (RM) effect is a method that allows us to measure the orbital obliquity of planets, which is an important constraint that has been used to understand the formation and migration mechanisms of planets, especially for hot Jupiters. In this paper, we present the RM observation of the Neptune-sized long-period transiting planet HIP41378 d. Those observations were obtained using the HARPS-N/TNG and ESPRESSO/ESO-VLT spectrographs over two transit events in 2019 and 2022. The analysis of the data with both the classical RM and the RM Revolutions methods allows us to confirm that the orbital period of this planet is ~278 days and that the planet is on a prograde orbit with an obliquity of λ = 57.1 −17.9 +26.1 °, a value which is consistent between both methods. HIP41378 d is the longest period planet for which the obliquity has been measured so far. We do not detect transit timing variations with a precision of 30 and 100 minutes for the 2019 and 2022 transits, respectively. This result also illustrates that the RM effect provides a solution to follow up on the transit of small and long-period planets such as those that will be detected by ESA's forthcoming PLATO mission. 

ABSTRACT In this paper, we present high-resolution spectroscopic transit observations from ESPRESSO of the super-Neptune WASP-166 b. In addition to spectroscopic ESPRESSO data, we analyse photometric data from TESS of six WASP-166 b transits along with simultaneous NGTS observations of the ESPRESSO runs. These observations were used to fit for the planetary parameters as well as assessing the level of stellar activity (e.g. spot crossings, flares) present during the ESPRESSO observations. We utilize the reloaded Rossiter McLaughlin (RRM) technique to spatially resolve the stellar surface, characterizing the centre-to-limb convection-induced variations, and to refine the star–planet obliquity. We find WASP-166 b has a projected obliquity of $$\lambda = -15.52^{+2.85}_{-2.76}\, ^{\circ }$$ and vsin (i) = 4.97 ± 0.09 km s−1 which is consistent with the literature. We were able to characterize centre-to-limb convective variations as a result of granulation on the surface of the star on the order of a few km s−1 for the first time. We modelled the centre-to-limb convective variations using a linear, quadratic, and cubic model with the cubic being preferred. In addition, by modelling the differential rotation and centre-to-limb convective variations simultaneously, we were able to retrieve a potential antisolar differential rotational shear (α ∼ −0.5) and stellar inclination (i* either 42.03$$^{+9.13}_{-9.60}\, ^{\circ }$$ or 133.64$$^{+8.42}_{-7.98}\, ^{\circ }$$ if the star is pointing towards or away from us). Finally, we investigate how the shape of the cross-correlation functions change as a function of limb angle and compare our results to magnetohydrodynamic simulations.