Reliability of stellar inclination estimated from asteroseismology: analytical criteria, mock simulations, and Kepler data analysis

Advances in asteroseismology of solar-like stars now provide a unique method to estimate the stellar inclination i_⋆. This enables to evaluate the spin-orbit angle of transiting planetary systems in a complementary fashion to the Rossiter-McLaughlin effect, a well-established method to estimate the projected spin-orbit angle λ. Although the asteroseismic method has been broadly applied to the Kepler data, its reliability is yet to be assessed intensively. In this work, we evaluate the accuracy of i_⋆ from asteroseismology of solar-like stars using 3000 simulated power spectra. We find that the low-signal-to-noise ratio of the power spectra induces a systematic underestimate (overestimate) bias for stars with high (low) inclinations. We derive analytical criteria for the reliable asteroseismic estimate, which indicates that reliable measurements are possible in the range of 20° ≲ i_⋆ ≲ 80° only for stars with high-signal-to-noise ratio. We also analyse and measure the stellar inclination of 94 Kepler main-sequence solar-like stars, among that 33 are planetary hosts. According to our reliability criteria, a third of them (nine with planets, 22 without) have accurate stellar inclination. Comparison of our asteroseismic estimate of vsin i_⋆ against spectroscopic measurements indicates that the latter suffers from a large uncertainty possibly due to the modelling of macroturbulence, especially for stars with projected rotation speed vsin i_⋆ ≲ 5 km s^-1. This reinforces earlier claims, and the stellar inclination estimated from the combination of measurements from spectroscopy and photometric variation for slowly rotating stars needs to be interpreted with caution.