Variable magnetic field and adaptive mixing-length: reproducing Li abundances and constraining rotational evolution of solar-type stars in clusters

Abstract Investigating the apparent anomalies in lithium (Li) surface abundance observed in the Sun and young stellar globular clusters within contemporary astrophysical contexts holds significant promise for advancing our understanding of the mechanisms influencing Li depletion throughout stellar evolution. This study delves into the intricate interplay between rotational mixing and rotational hydrostatic effects in pre-main-sequence (PMS) and main-sequence (MS) solar-type stars by employing grids of rotating models. We implement a novel approach in which both the magnetic field strength (B) and the mixing-length parameter (αMLT) vary dynamically with stellar parameters, following prescriptions based on dynamo theory and 3D atmosphere calibrations. This avoids fixed values and aims to reduce free parameters while capturing key physical variability. Our models reproduce the observed Li abundance of Sun-like stars (A(Li) ≈ 1.12 dex) consistent with the present-day solar value (1.1 ± 0.1 dex) and yield qualitatively consistent rotational spin-down trends across PMS and MS phases. However, at the solar age (4.57 Gyr), the same models over-predict the equatorial rotation rate (v ≈ 4.72 kms−1 vs. 2.0 kms−1) and the mean surface magnetic field (B ≈ 36.9 G vs. 1 G). These discrepancies reflect the omission of additional angular momentum loss mechanisms—such as disk locking and internal magnetic coupling—and possible oversimplifications in magnetic saturation physics. While the adaptive αMLT converges to the solar-calibrated value ([1.76, 1.78]) at the present age, its variability during earlier phases significantly influences Li depletion. To validate our models, we compare predictions with observational data from 64 open clusters obtained through the Gaia-ESO Survey (GES), sampling a wide range of ages. The results demonstrate that incorporating time-dependent B and αMLT improves Li predictions and captures rotational evolution trends, but cannot yet reproduce the present-day solar rotation and magnetic flux without additional physics. We discuss these limitations and outline future work to integrate disk locking and internal angular momentum transport for a more complete model of solar-type stars.