Establishing the accuracy of asteroseismic mass and radius estimates of giant stars III. KIC4054905, an eclipsing binary with two 10 Gyr thick disk RGB stars

Eclipsing binary stars with an oscillating giant component allow accurate stellar parameters to be derived and asteroseismic methods to be tested and calibrated. To this aim, suitable systems need to be firstly identified and secondly measured precisely and accurately. KIC 4054905 is one such system, which has been identified, but with measurements of a relatively low precision and with some confusion regarding its parameters and evolutionary state. Our aim is to provide a detailed and precise characterisation of the system and to test asteroseismic scaling relations. Dynamical and asteroseismic parameters of KIC4054905 were determined from Kepler photometry and multi-epoch high-resolution spectra from FIES at the Nordic Optical Telescope. KIC 4054905 was found to belong to the thick disk and consist of two lower red giant branch (RGB) components with nearly identical masses of 0.95$M_{\odot}$ and an age of $9.9\pm0.6$ Gyr. The most evolved star displays solar-like oscillations, which suggest that the star belongs to the RGB, supported also by the radius, which is significantly smaller than the red clump phase for this mass and metallicity. Masses and radii from corrected asteroseismic scaling relations can be brought into full agreement with the dynamical values if the RGB phase is assumed, but a best scaling method could not be identified. We measured dynamical masses and radii with a precision better than 1.0%. We firmly establish the evolutionary nature of the system to be that of two early RGB stars with an age close to 10 Gyr, unlike previous findings. The metallicity and Galactic velocity suggest that the system belongs to the thick disk of the Milky Way. We investigate the agreement between dynamical and asteroseismic parameters for KIC 4054905. Consistent solutions exist, but the need to analyse more systems continues in order to establish the accuracy of asteroseismic methods.