The rotation-magnetism relationship in solar-type stars. Constraining magnetic flux emergence rates

The rotation-activity relationship of G-type stars results from surface magnetic fields emerging from the interior. How the magnetic flux and its emergence rate scale with rotation rate are not well understood, both observationally and theoretically. We aim to constrain the emerging magnetic flux as a function of the rotation rate in solar-type stars by numerical simulations compared to empirical constraints set by direct measurements of stellar magnetic fields. We used our flux emergence and transport (FEAT) model for stars with a range of power-law slopes for the dependence of the emerging flux on rotation. Complementing this with a heuristic account of the main flux components, we modelled the resulting mean unsigned field strength as a function of the rotation rate. We compared the results with the Zeeman-intensification measurements and spectropolarimetric data of solar-type stars. Deviations of the model from observations of G stars correlate strongly with stellar metallicity (r=0.83) and effective temperature (r=-0.76), with a combined coefficient of 0.90, reflecting the dependence of magnetic activity on these two parameters. Correcting for these effects with multilinear regression, we find that magnetic flux emergence rates must scale steeply with rotation (power-law exponent of about 1.9) to reproduce observed field strengths, significantly exceeding the estimates in the literature. We also provide correction factors for metallicity and temperature for measurements of early-G-type stellar magnetic fields. Stellar magnetic flux emergence rates scale steeply with rotation, requiring active-region fields to dominate the total surface flux on rapid rotators, whereas small-scale-dynamo fields dominate for slow rotators such as the Sun. Metallicity significantly influences the rotation-magnetism relationship, necessitating sample-dependent corrections for accurate stellar dynamo modelling.