### Asteroseismic inference on the spin-orbit misalignment and stellar parameters of HAT-P-7

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The measurement of obliquities in star-planet systems is of great importance for the understanding of planet system formation and evolution. The bright and well studied HAT-P-7 system is intriguing as several Rossiter-McLaughlin (RM) measurements found a large projected obliquity in this system, but it was so far not possible to determine if the orbit is polar and/or retrograde. The goal of this study is to measure the stellar inclination and hereby the full 3D obliquity of the HAT-P-7 system instead of only the 2D projection as measured by the RM effect. In addition we provide an updated set of stellar parameters for the star. We use the full set of available observations from Kepler spanning Q0-Q17 to produce the power spectrum of HAT-P-7. We extract oscillation mode frequencies via an MCMC peak-bagging routine, and use the results from this to estimate the stellar inclination angle. Combining this with the projected obliquity from RM and the inclination of the orbital plane allows us to determine the stellar obliquity. We use asteroseismology to model the star from the extracted frequencies using two different approaches to the modelling where either the MESA or the GARSTEC stellar evolution codes are adopted. Using our updated asteroseismic modelling we find, i.a., the following stellar parameters for HAT-P-7: M=1.51{+0.04}{-0.05}Msun, $R=2.00{+0.01}{-0.02}Rsun, and age = 2.07{+0.28}{-0.23} Gyr. Our asteroseismic modelling offers a high precision on the stellar parameters, for instance is the uncertainty on age of the order ~11%. For the stellar inclination we estimate i_star<36.5 deg., which translates to an obliquity between 83 and 111 deg. We find that the planet HAT-P-7b is likely retrograde in its orbit, and that the orbit is close to being polar. The new parameters for the star gives an updated planetary density of 0.65+-0.03 g cm^{-3}, which is lower than previous estimates.