2023MNRAS.518.5552Y

For solar-like oscillators, the asteroseismic relations connect the stellar mean density and surface gravity to observable properties of the oscillations. Since the space missions CoRoT and Kepler, the asteroseismic relations have been massively employed out of their theoretical domain of validity, that is the main-sequence solar-type stars, in particular for red giant stars. However, despite a surprisingly good performance of the asteroseismic relation with red giant stars, they are biased and attempts to parametrize the departure of the relations for evolved stars have been the subject of many recent efforts. In this study, we propose a new parametrization of the asteroseismic relations for red giants of radii up to ${\sim } 50\, \mathrm{R}_\odot$, based on a calibration performed with Gaia parallax data. We find that the asteroseismic scaling relations depend on metallicity and effective temperature. For this solution, we obtain a parallax offset of about -0.026 ± 0.001 mas, and radius ranges from 3.8 to 53.2 R_⊙. Most stars have masses that range from 0.9 to 1.7 M_⊙, with the star count peaking around 1.2 M_⊙. We also use data of the eclipsing binaries with solar-like oscillating components for calibration and discuss the diagnostic potential of the mass-metallicity diagram for our understanding of the evolution of red giants and the chemodynamics of the Galactic disc. Using this diagram, we identify stars that lost and gained mass and estimate the minimum change in mass.