2016ApJ...819...85C

The angle ψ between a planet's orbital axis and the spin axis of its parent star is an important diagnostic of planet formation, migration, and tidal evolution. We seek empirical constraints on ψ by measuring the stellar inclination i_s via asteroseismology for an ensemble of 25 solar-type hosts observed with NASA's Kepler satellite. Our results for i_s are consistent with alignment at the 2σ level for all stars in the sample, meaning that the system surrounding the red-giant star Kepler-56 remains as the only unambiguous misaligned multiple-planet system detected to date. The availability of a measurement of the projected spin-orbit angle λ for two of the systems allows us to estimate ψ. We find that the orbit of the hot Jupiter HAT-P-7b is likely to be retrograde (ψ=116○ / . 4_–14.7^+30.2), whereas that of Kepler-25c seems to be well aligned with the stellar spin axis (ψ=12○ / . 6_–11.0^+6.7). While the latter result is in apparent contradiction with a statement made previously in the literature that the multi-transiting system Kepler-25 is misaligned, we show that the results are consistent, given the large associated uncertainties. Finally, we perform a hierarchical Bayesian analysis based on the asteroseismic sample in order to recover the underlying distribution of ψ. The ensemble analysis suggests that the directions of the stellar spin and planetary orbital axes are correlated, as conveyed by a tendency of the host stars to display large values of inclination.