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

Abstract

Context. Measuring stellar inclinations is fundamental to understanding planetary formation and dynamics as well as the physical conditions during star formation. Oscillation spectra of red giant stars exhibit mixed modes that have both a gravity component from the radiative interior and a pressure component from the convective envelope. Gravity-dominated (g-m) mixed modes split by rotation are well separated inside frequency spectra, allowing accurate measurement of stellar inclinations. Aims. We aim to develop an automated and general approach to measuring stellar inclinations that can be applied to any solar-type pulsator for which oscillation modes are identified. We also aim to validate this approach using red giant branch stars observed by Kepler. Methods. Stellar inclination impacts the visibility of oscillation modes with azimuthal orders m = { - 1, 0, +1}. We used the mean height-to-Background: ratio of dipole mixed modes with different azimuthal orders to measure stellar inclinations. We recovered the underlying statistical distribution of inclinations in an unbiased way using a probability density function for the stellar inclination angle. Results. We derive stellar inclination measurements for 1139 stars on the red giant branch for which Gehan et al. (2018, A&A, 616, A24) identified the azimuthal order of dipole g-m mixed modes. Raw measured inclinations exhibit strong deviation with respect to isotropy which is expected for random inclinations over the sky. When taking uncertainties into account, the reconstructed distribution of inclinations actually follows the expected isotropic distribution of the rotational axis. Conclusions. This work highlights the biases that affect inclination measurements and provides a way to infer their underlying statistical distribution. When a star is seen either pole on or equator on, measurements are challenging and result in a biased distribution. Correcting biases that appear in low- and high-inclination regimes allows us to recover the underlying inclination distribution.