Constraining the model-based uncertainties of asteroseismic magnetic field measurements in red giants

Magnetic fields inside red giants are measured using shifts to the oscillation frequencies. However, in the asymptotic framework, converting a frequency shift into a radial magnetic field strength requires knowing the global magnetic sensitivity. This parameter (also called the core structure parameter) must be inferred from stellar models, introducing a source of uncertainty. We seek to understand how the global magnetic sensitivity depends on stellar properties such as mass and metallicity, and to quantify the model-based uncertainty on magnetic field measurements. We also explore which stellar properties are key to finding a precise and accurate estimate of the global magnetic sensitivity. Using MESA models, we examine how the global magnetic sensitivity changes with mass, metallicity, and age. We then create a set of synthetic stars and test how well we recover the sensitivity parameter. We consider different grid construction approaches and the choice of which observables are used in the fitting process. We find that the global magnetic sensitivity shows a stronger dependence on mass for higher mass models and a stronger metallicity dependence for lower metallicity models. Our approach recovers the sensitivity parameter well, with an uncertainty of 10% when precise metallicity measurements are used. We apply our method to stars with existing magnetic field measurements. In most cases, the dominant source of uncertainty remains observational, although precise modeling can significantly reduce the magnetic field uncertainty for stars with exceptional data. With careful fitting, models yield accurate values for the global magnetic sensitivity. We recommend that future work obtain the global magnetic sensitivity using both asteroseismic and high-quality spectroscopic data. Under these conditions, we recommend adopting a model-based uncertainty of 10% on the sensitivity parameter.