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 holds significant promise for advancing our understanding of the mechanisms influencing Li depletion. 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 (alpha-MLT) vary dynamically with stellar parameters. 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 and possible oversimplifications in magnetic saturation physics. While the adaptive alpha-MLT converges to the solar-calibrated value ([1.76, 1.78]) at the present age, its variability during earlier phases significantly influences Li depletion. We compare predictions with observational data from 64 open clusters. The results demonstrate that incorporating time-dependent B and alpha-MLT 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 for a more complete model of solar-type stars.

Figures (17)

• Figure 1: The evolution of magnetic field intensity and its upper and lower limits, as a function of time and $\omega_{\mathrm{0}}$ for a 1 $\mathrm{M}_\odot$ model. The model include rotation with $\omega_{\mathrm{0}}$ = 0.1425. The solid lines represent the magnetic field strength, while the dotted lines represent the angular evolution of the star. The dashed vertical line makes reference to the ZAMS.
• Figure 2: The calibrated solar 1$\mathrm{M}_\odot$ model HR diagram. The rotation, overshooting, or magnetic braking effects are deactivated in the model. The luminosity is expressed in terms of $\mathrm{L}_\odot$.
• Figure 3: Ratio of surface [7]Li abundance to [1]H as a function of time is depicted for various 1 $\mathrm{M}_\odot$ models with magnetic field. In the figure (a), the models have initial rotation rates ranging from 0.10 to 0.13. The other colored dots represent surface [7]Li abundances for stars with parameters within the specified selection intervals, corresponding to the evolution curve of the same color. In the figure (b), the magnetic field were not simulated. The rest of lines are models which include initial rotation with $\omega_{\mathrm{0}}$ between 0.0084 and 0.0336, respectively. The purple star is the surface Li abundances for the present-day Sun Asplund2009. The dashed vertical line indicates makes reference to the ZAMS.
• Figure 4: The evolution of mass loss $\Dot{M}$ as a function of time for several 1 $\mathrm{M}_\odot$ models. The models include variable magnetic field intensity and initial rotation with $\omega_{\mathrm{0}}$ between 0.12 and 0.1425. The dashed vertical line makes reference to the ZAMS.
• Figure 5: The evolution of magnetic field intensity and $\omega_{\mathrm{0}} = \Omega / \Omega_{\mathrm{crit}}$ as a function of time for several 1 $\mathrm{M}_\odot$ models. The models include initial rotation with $\omega_{\mathrm{0}}$ between 0.12 and 0.1425. The solid lines represent the magnetic field strength, while the dotted lines represent the angular evolution of the star. The dashed vertical line makes reference to the ZAMS.