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

Measuring stellar inclinations is fundamental to understand planetary formation and dynamics as well as 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, making possible accurate measurements of stellar inclinations. This work aims at developing an automated and general approach to measure stellar inclinations, that can be applied to any solar-type pulsator for which oscillation modes are identified, and at validating it using red giant branch stars observed by Kepler. We use the mean height-to-background ratio of dipole mixed modes with different azimuthal orders to measure stellar inclinations. The underlying statistical distribution of inclinations is recovered in an unbiased way using a probability density function for the stellar inclination angle. We derive stellar inclination measurements for 1139 stars on the red giant branch, for which Gehan et al. (2018) have 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. This work highlights the biases that affect inclination measurements and provides the way to infer their underlying statistical distribution. When the star is seen either pole-on or equator-on, measurements are challenging and result in a biased distribution. Correcting biases that appear at the low- and high inclination regimes allows us to recover the underlying inclination distribution.