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

Context. The measurement of obliquities - the angle between the orbital and stellar rotation -in star-planet systems is of great importance for understanding planet system formation and evolution. The bright and well-studied HAT-P-7 (Kepler-2) system is intriguing because several Rossiter-McLaughlin (RM) measurements found a high projected obliquity in this system, but it was not possible so far to determine whether the orbit is polar and/or retrograde. Aims. 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. Methods. We used the full set of available observations from Kepler spanning Q0-Q17 to produce the power spectrum of HAT-P-7. We extracted oscillation-mode frequencies via an Markov chain Monte Carlo peak-bagging routine and used 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 allowed us to determine the stellar obliquity. Furthermore, we used asteroseismology to model the star from the extracted frequencies using two different approaches to the modelling, for which either the stellar evolution codes MESA or GARSTEC were adopted. Results. Our updated asteroseismic modelling shows, i.a., the following stellar parameters for HAT-P-7: M-* = 1.51(-0.05)(+0.04) M-circle dot, R-* =2.00(-0.02)(+0.01) R-circle dot, and age = 2.07(-0.23)(+0.28) Gyr. The modelling offers a high precision on the stellar parameters, the uncertainty on age, for instance, is of the order similar to 11%. For the stellar inclination we estimate i(*) < 36.5 degrees, which translates into an obliquity of 83 degrees < psi < 111 degrees. The planet HAT-P-7b is likely retrograde in its orbit, and the orbit is close to being polar. The new parameters for the star give an updated planetary density of rho(p) = 0.65 +/- 0.03 g cm(-3), which is lower than previous estimates.