Realistic uncertainties of red-giant ages and should you trust 𝜈_max?

Asteroseismic modelling is a powerful way to derive stellar properties. However, the derived quantities are limited by built-in assumptions used in stellar models. This work presents a detailed characterisation of stellar model uncertainties in asteroseismic red giants, focusing on the mixing-length parameter (a_mlt), the initial helium fraction (Y_init) etc. First, we estimate error floors due to model uncertainties to be ~0.4% in mass, ~0.2% in radius, and ~17% in age, due to the uncertain state of a_mlt and Y_init. The systematic errors in age exceed typical statistical errors. Second, we demonstrate that the uncertainties from a_mlt can be entirely mitigated by direct radius measurements or partially through 𝜈_max. Utilizing radii from eclipsing binaries, we determined the a_mlt values and calibrated the a_mlt-[M/H] relation. The correlation observed between the two variables is consistent with previous studies using 1D stellar models, but in contrast with 3D simulations. Third, we explore the implications of using asteroseismic modelling to test the 𝜈_max scaling relation. We found that a perceived dependency of 𝜈_max on [M/H] from frequency modelling can be largely removed by incorporating the calibrated a_mlt-[M/H] relation. These findings suggest that 𝜈_max conveys information not fully captured by individual frequencies, and that it should be carefully considered as an important observable for asteroseismic modelling.