Advancing accuracy in age determinations of old-disk stars using an oscillating red giant in an eclipsing binary

The study of resonant oscillation modes in low-mass red giant branch stars enables their ages to be inferred with exceptional ($\sim$10%) precision, unlocking the possibility to reconstruct the temporal evolution of the Milky Way at early cosmic times. Ensuring the accuracy of such a precise age scale is a fundamental yet difficult challenge. Since the age of red giant branch stars primarily hinges on their mass, an independent mass determination for an oscillating red giant star provides the means for such assessment. We analyze the old eclipsing binary KIC10001167, which hosts an oscillating red giant branch star and is a member of the thick disk of the Milky Way. Of the known red giants in eclipsing binaries, this is the only member of the thick disk that has asteroseismic signal of high enough quality to test the seismic mass inference at the 2% level. We measure the binary orbit and obtain fundamental stellar parameters through combined analysis of light curve eclipses and radial velocities, and perform a detailed asteroseismic, photospheric, and Galactic kinematic characterization of the red giant and binary system. We show that the dynamically determined mass $0.9337\pm0.0077 \rm\ M_{\odot}$ (0.8%) of this 10 Gyr-old star agrees within 1.4% with the mass inferred from detailed modelling of individual pulsation mode frequencies (1.6%). This is now the only thick disk stellar system, hosting a red giant, where the mass has been determined both asteroseismically with better than 2% precision, and through a model-independent method at 1% precision, and we hereby affirm the potential of asteroseismology to define an accurate age scale for ancient stars to trace the Milky Way assembly history.