Fundamental properties of stars from Kepler and Gaia data: parallax offset and revised scaling relations.

Data from the space missions Gaia, Kepler, CoRoT and TESS , make it possible to compare parallax and asteroseismic distances. From the ratio of two densities ρsca/ρπ, we obtain an empirical relation f Δν between the asteroseismic large frequency separation and mean density, which is important for more accurate stellar mass and radius. This expression for main-sequence (MS) and subgiant stars with K -band magnitude is very close to the one obtained from interior MS models by Yıldız, Çelik & Kayhan. We also discuss the effects of effective temperature and parallax offset as the source of the difference between asteroseismic and non-asteroseismic stellar parameters. We have obtained our best results for about 3500 red giants (RGs) by using 2MASS data and model values for f Δν from Sharma et al. Another unknown scaling parameter |$f_{\nu _{\rm max}}$| comes from the relationship between the frequency of maximum amplitude and gravity. Using different combinations of |$f_{\nu _{\rm max}}$| and the parallax offset, we find that the parallax offset is generally a function of distance. The situation where this slope disappears is accepted as the most reasonable solution. By a very careful comparison of asteroseismic and non-asteroseismic parameters, we obtain very precise values for the parallax offset and |$f_{\nu _{\rm max}}$| for RGs of –0.0463 ± 0.0007 mas and 1.003 ± 0.001, respectively. Our results for mass and radius are in perfect agreement with those of APOKASC-2: the mass and radius of ∼3500 RGs are in the range of about 0.8–1.8 M⊙ (96 per cent) and 3.8–38 R⊙, respectively. [ABSTRACT FROM AUTHOR]