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) 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.

Magnetic signatures on mixed-mode frequencies

“…Stello et al 2016a), intermediate-mass stars seems more likely to host strong magnetic fields than low-mass stars during the RGB. There are a few stars in the study of Gehan et al (2020) that are observed with low-inclination angles, with a mass above 1.3 solar masses, and that present a rather low value of ∆Π 1 from the study of Vrard et al (2016). The detection of magnetic fields inside these stars is out of the scope of this paper and its focus on methodology, but we are able to identify these stars as the best sample for the search of buried magnetic fields.…”

“…In addition, amplitudes in the PSD are modulated by the inclination angle of the star compared to the line of sight i, following (e.g., Gehan et al 2020):…”

A census of OBe stars in nearby metal-poor dwarf galaxies reveals a high fraction of extreme rotators

“…We note that Dufton et al (2013) assume random spin axis orientation. Alignment of spin axes (as found by Corsaro et al 2017, in old open clusters) could affect the distribution of Dufton et al (2013), although other work does support random spin axis orientation (Hummel et al 1999;Jackson & Jeffries 2010;Mosser et al 2018;Gehan et al 2021).…”

KIC 7955301: A hierarchical triple system with eclipse timing variations and an oscillating red giant

“…It also performs a likelihood ratio test to validate the measured ν max and check whether oscillations are present. The FRA pipeline was used in Huber et al (2022) and is explained in detail in Gehan et al (2022). The large spacing ∆ν was measured by using the EACF.…”

“…The FRA pipeline was used in Huber et al (2022) and is explained in detail in Gehan et al (2022). The large spacing ∆ν was measured by using the EACF.…”