The angle \psi 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 \psi 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 2- \sigma 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 \lambda for two of the systems allows us to estimate \psi .
We find that the orbit of the hot-Jupiter HAT-P-7b is likely to be retrograde ( \psi = 116.4 \arcdeg ^ { +30.2 } _ { -14.7 } ) , whereas that of Kepler-25c seems to be well aligned with the stellar spin axis ( \psi = 12.6 \arcdeg ^ { +6.7 } _ { -11.0 } ) .
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 \psi .
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 inclination values .