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 ⋆ . 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 has 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 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 • 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 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 ⋆ against spectroscopic measurements indicates that the latter suffers from a large uncertainty possibly due to the modeling of macroturbulence, especially for stars with projected rotation speed v sin i ⋆ 5km/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.

Automated approach to measure stellar inclinations: validation through large-scale measurements on the red giant branch

“…6). This is consistent with the conclusion of Kamiaka et al (2018), namely that reliable seismic inclination measurements are possible in the general case for 20 • i 80 • . For i < 27 • , we can only derive an overestimated value of the inclination.…”

“…The other configuration corresponds to stars with a mean HBR P 0 < 8, for which the inclination can in principle be as high as 90 • . However, as stressed by Kamiaka et al (2018), it is in practice impossible to measure i = 90 • , as this would require an infinite HBR corresponding to a strict absence of background noise from granulation. Therefore, we cannot access the inclination regime close to 90 • .…”

“…The majority of transiting exoplanets are detected around F, G, and K solar-type stars on the main sequence, but measuring i is difficult in this evolutionary stage because oscillations have low amplitudes and modes are sometimes blended (see Appourchaux et al 2008). In this context, Kamiaka et al (2018) carried out a systematic verification of the accuracy of the seismic measurement of the stellar inclination angle for main sequence stars using 3000 simulated power spectra and found that reliable seismic inclination measurements are possible for 20…”

“…They also derived inclination measurements for about 100 red giant stars. As Kamiaka et al (2018) did not address red giants and K19 measured inclinations for only a limited number of red giants, it is worthwhile obtaining large-scale measurements of the stellar inclination angle for evolved stars.…”

Linking the rotation of a cluster to the spins of its stars: the kinematics of NGC 6791 and NGC 6819 in 3D

“…This result is based on asteroseismology analysis of Kepler data for stars in NGC 6791 and NGC 6819, two Galactic open clusters with ages of ∼ 8 Gyr and ∼ 2.4 Gyr, respectively. While some caution needs to be taken in interpreting these results, due to potential systematic effects in inferring the stellar inclination angle from Kepler analyses (Kamiaka et al 2018), the results potentially offer an unexpected and intriguing insight into the formation of stellar clusters. There has also been other studies that have found non-isotropic stellar orientations in clusters using photometric rotation periods and spectroscopic rotation velocities (e.g.…”