Establishing the accuracy of asteroseismic mass and radius estimates of giant stars – I. Three eclipsing systems at [Fe/H] ∼ −0.3 and the need for a large high-precision sample

Abstract

We aim to establish and improve the accuracy level of asteroseismic estimates of mass, radius, and age of giant stars. This can be achieved by measuring independent, accurate, and precise masses, radii, effective temperatures and metallicities of long period eclipsing binary stars with a red giant component that displays solarlike oscillations. We measured precise properties of the three eclipsing binary systems KIC 7037405, KIC 9540226, and KIC 9970396 and estimated their ages be 5.3 ± 0.5, 3.1±0.6, and 4.8±0.5 Gyr. The measurements of the giant stars were compared to corresponding measurements of mass, radius, and age using asteroseismic scaling relations and grid modeling. We found that asteroseismic scaling relations without corrections to ∆ν systematically overestimate the masses of the three red giants by 11.7%, 13.7%, and 18.9%, respectively. However, by applying theoretical correction factors f ∆ν according to Rodrigues et al. (2017), we reached general agreement between dynamical and asteroseismic mass estimates, and no indications of systematic differences at the precision level of the asteroseismic measurements. The larger sample investigated by Gaulme et al. (2016) showed a much more complicated situation, where some stars show agreement between the dynamical and corrected asteroseismic measures while others suggest significant overestimates of the asteroseismic measures. We found no simple explanation for this, but indications of several potential problems, some theoretical, others observational. Therefore, an extension of the present precision study to a larger sample of eclipsing systems is crucial for establishing and improving the accuracy of asteroseismology of giant stars.

Asteroseismology of the Hyades red giant and planet host ϵ Tauri

“…6 (bottom panel) in Brogaard et al (2018) reveals that the same value for f ∆ν is not found if one uses T eff as reference to determine f ∆ν instead of ν max , as in Rodrigues et al (2017), even if everything else is unchanged. This may be caused by a too low temperature scale for the models used by Rodrigues et al (2017), as also discussed by Brogaard et al (2018). Retaining the view from Brogaard et al (2018) that it is better to use ν max than T eff to estimate f ∆ν , we find evidence based on our empirical correction factor pointing to the RGB as the present evolutionary phase of ǫ Tau.…”

Testing asteroseismology with Gaia DR2: hierarchical models of the Red Clump

“…We only extracted the correction values f ∆ν from the models, and used the seismic parameters and temperature values from our original set, and not the results for these values returned from the grids, in the rest of this work. We did not include corrections for the ν max scaling relation, because these are more difficult to obtain theoretically (Belkacem et al 2011), and are probably negligible (Brogaard et al 2018). Note that Brogaard et al (2018) found that using corrections by Rodrigues et al (2017) delivers on average slightly smaller stellar properties than using due to differences in how these methods treat the solar surface effect.…”

“…We did not include corrections for the ν max scaling relation, because these are more difficult to obtain theoretically (Belkacem et al 2011), and are probably negligible (Brogaard et al 2018). Note that Brogaard et al (2018) found that using corrections by Rodrigues et al (2017) delivers on average slightly smaller stellar properties than using due to differences in how these methods treat the solar surface effect. Since we used a wide range of bolometric corrections for various temperature perturbations, the method by Rodrigues et al (2017) would be too computationally expensive, and we thus elected to use , which may lead to differences of the order of ∼ 2% in radius than if we had used Rodrigues et al (2017) (White et al 2011).…”

Scaling Relations for Solar-Like Oscillations: A Review

“…In a similar approach as Gaulme et al (2016), Brogaard et al (2018) and Themeßl et al (2018) tested the asteroseismic masses and radii against masses and radii obtained from binary orbits for three eclipsing binary systems each (one system in overlap). Both studies found that asteroseismic scaling relations without corrections to the ∆ν scaling relations would overestimate the masses and radii.…”