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 at constraining 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 use our Flux Emergence And Transport (FEAT) model for stars with a range of power-law slopes for the dependence of emerging flux on rotation. Complementing this with a heuristic account of the main flux components, we model the resulting mean unsigned field strength as a function of the rotation rate. We compare 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 like the Sun. Metallicity significantly influences the rotation-magnetism relationship, necessitating sample-dependent corrections for accurate stellar dynamo modelling.

💡 Research Summary

The paper tackles a long‑standing problem in stellar astrophysics: how the surface magnetic flux and its emergence rate depend on stellar rotation in solar‑type (G‑type) stars. While the empirical rotation‑activity relationship is well established through various proxies (chromospheric emission, X‑ray luminosity, photometric variability), the underlying quantity that drives these proxies—the unsigned magnetic flux—has been measured for only a handful of stars, and the scaling of its emergence rate with rotation remains poorly constrained.

To address this, the authors employ the Flux Emergence And Transport (FEAT) model, which couples a thin‑flux‑tube rise calculation with a surface flux‑transport (SFT) module. For a set of rotation rates ω = Ω★/Ω⊙ = {1, 2, 4, 8}, they pre‑compute emergence latitudes and tilt angles of magnetic loops, then generate synthetic bipolar magnetic region (BMR) sequences based on solar sunspot‑group statistics. The total unsigned flux injected by emerging BMRs is parameterised as s = s⊙ ω^p, where p is an unknown power‑law index to be constrained by observations. The same exponent scales the initial polar dipole field to keep the SFT model internally consistent.

The SFT module integrates the radial induction equation on a spherical grid (ℓ ≤ 64), advecting the BMR flux by differential rotation, meridional flow, and turbulent diffusion. The model outputs the surface‑averaged unsigned field ⟨|B_SFT|⟩, measured over a 100‑day window centred on the synthetic cycle maximum. Because the FEAT model resolves only the large‑scale flux associated with spot‑bearing BMRs, the authors supplement it with two heuristic components: (1) a constant small‑scale dynamo (SSD) contribution, anchored to the Sun‑as‑a‑star Zeeman‑intensification measurement of ≈180 G (Kochukhov et al. 2020), and (2) an empirical “small‑scale emergence” (SSE) term representing flux from ephemerals and other sub‑spot bipoles.

Observational constraints come from Zeeman‑intensification measurements of 14 early‑G stars (Kochukhov et al. 2020) and a Sun‑as‑a‑star reference. The authors first compare raw model outputs to the observed mean unsigned fields ⟨B⟩_obs. They find systematic residuals that correlate strongly with stellar metallicity (