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Moderately misaligned orbit of the warm sub-Saturn HD 332231 b

Measurements of exoplanetary orbital obliquity angles for different classes of planets are an essential tool in testing various planet formation theories. Measurements for those transiting planets on relatively large orbital periods ($P$\,$>$\,10\,d) present a rather difficult observational challenge. Here we present the obliquity measurement for the warm sub-Saturn planet HD\,332231\,b, which was discovered through Transiting Exoplanet Survey Satellite (TESS) photometry of sectors 14 and 15, on a relatively large orbital period (18.7\,d). Through a joint analysis of previously obtained spectroscopic data and our newly obtained CARMENES transit observations, we estimated the spin-orbit misalignment angle, \textlambda, to be $-42.0^{+11.3}_{-10.6}$\,$°$, which challenges Laplacian ideals of planet formation. Through the addition of these new radial velocity (RV) data points obtained with CARMENES, we also derived marginal improvements on other orbital and bulk parameters for the planet, as compared to previously published values. We showed the robustness of the obliquity measurement through model comparison with an aligned orbit. Finally, we demonstrated the inability of the obtained data to probe any possible extended atmosphere of the planet, due to a lack of precision, and place the atmosphere in the context of a parameter detection space.