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 $i_{\star}$. 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 $\lambda$. Although the asteroseismic method has been broadly applied to the Kepler data, its reliability has yet to be assessed intensively. In this work, we evaluate the accuracy of $i_{\star}$ 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 under-estimate (over-estimate) 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 $20^\circ \lesssim i_{\star} \lesssim 80^\circ$ 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 which 33 are planetary hosts. According to our reliability criteria, a third of them (9 with planets, 22 without) have accurate stellar inclination. Comparison of our asteroseismic estimate of $v\sin{i_{\star}}$ against spectroscopic measurements indicates that the latter suffers from a large uncertainty possibly due to the modeling of macro-turbulence, especially for stars with projected rotation speed $v\sin{i_{\star}} \lesssim 5$ km/s. 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.