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

Abstract

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.

arXiv comment17 pages, 10 figures, 3 tables, accepted for publication in MNRAS

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