Realistic Uncertainties for Fundamental Properties of Asteroseismic Red Giants and the Interplay Between Mixing Length, Metallicity and $ν_{ max}$

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 αMLT, the initial helium fraction Yᵢₙᵢₜ, the solar abundance scale, and the overshoot parameters. First, we estimate error floors due to model uncertainties to be ≈0.4% in mass, ≈0.2% in radius, and ≈17% in age, primarily due to the uncertain state of αMLT and Yᵢₙᵢₜ. The systematic uncertainties in age exceed typical statistical uncertainties, suggesting the importance of their evaluation in asteroseismic applications. Second, we demonstrate that the uncertainties from αMLT can be entirely mitigated by direct radius measurements or partially through νₘₐₓ. Utilizing radii from Kepler eclipsing binaries, we determined the αMLT values and calibrated the αMLT--[M/H] relation. The correlation observed between the two variables is positive, consistent with previous studies using 1-D stellar models, but in contrast with outcomes from 3-D simulations. Third, we explore the implications of using asteroseismic modelling to test the νₘₐₓ scaling relation. We found that a perceived dependency of νₘₐₓ on [M/H] from individual frequency modelling can be largely removed by incorporating the calibrated αMLT--[M/H] relation. Variations in Yᵢₙᵢₜ can also affect νₘₐₓ predictions. These findings suggest that νₘₐₓ conveys information not fully captured by individual frequencies, and that it should be carefully considered as an important observable for asteroseismic modelling.