[Paper Review] Rotational mixing in low-mass stars : I Effect of the mu-gradients in main sequence and subgiant Pop I stars

A. Palacios, S. Talon+2 more|ArXiv.org|Oct 23, 2002

Stellar, planetary, and galactic studies44 references102 citations

TL;DR

This study presents a comprehensive model of rotating low-mass Pop I stars, incorporating meridional circulation, shear turbulence, and gravitational settling with full treatment of mean molecular weight (μ) gradients. It demonstrates that μ-currents—driven by horizontal μ variations—significantly shape the internal rotation profile and dominate chemical transport, preventing the 'creeping paralysis' of circulation seen in homogeneous models, thus resolving key aspects of the lithium dip in subgiants.

ABSTRACT

We present a first set of results concerning stellar evolution of rotating low-mass stars. Our models include fully consistent transport of angular momentum and chemicals due to the combined action of rotation induced mixing (according to Maeder & Zahn 1998) and element segregation. The analysis of the effects of local variations of molecular weight due to the meridional circulation on the transport of angular momentum and chemicals are under the scope of this study. We apply this mechanism to low mass main sequence and subgiant stars of population I. We show that the so-called $μ$-currents are of major importance in setting the shape of the rotation profile, specially near the core. Furthermore, as shown by Talon & Charbonnel (1998) and Charbonnel & Talon (1999) using models without $μ$-currents, we confirm that rotation-induced mixing in stars braked via magnetic torquing can explain the blue side of the Li dip, as well as the low Li abundances observed in subgiants even when $μ$-currents are taken into account. We emphasize that $μ$ variations are not to be neglected when treating rotation-induced mixing, and that they could be of great importance for latter evolutionary stages.

Motivation & Objective

• To investigate the impact of mean molecular weight (μ) gradients on rotational mixing in low-mass main sequence and subgiant stars.
• To assess how μ-currents—resulting from meridional circulation in chemically inhomogeneous regions—affect angular momentum and chemical transport.
• To determine whether rotation-induced mixing with μ-gradients can explain the lithium dip and low surface lithium abundances in subgiants.
• To test the validity of previous models that neglect μ-gradient feedback on circulation, particularly in the context of magnetic braking and differential rotation.
• To clarify whether the 'creeping paralysis' of meridional circulation, predicted in homogeneous models, occurs when μ-variations are included.

Proposed method

• The study employs stellar evolution models that fully couple angular momentum and chemical transport via meridional circulation, shear turbulence, and gravitational settling using the Maeder & Zahn (1998) formalism.
• Horizontal variations in mean molecular weight (μ) are explicitly computed and their feedback on circulation is modeled through the μ-currents, which modify the effective diffusion and rotation profiles.
• The models include magnetic braking to simulate angular momentum loss, allowing for differential rotation and avoiding the solid-body rotation assumption of earlier works.
• Chemical transport is calculated using effective diffusion coefficients, with turbulent diffusion dominating in inhomogeneous stars due to μ-gradient effects.
• The models are applied to low-mass (M ≲ 2.2 M⊙) Pop I stars on the hot side of the lithium dip, consistent with observations in open clusters like the Hyades.
• The results are compared with observational lithium abundances in field and cluster subgiants to test model predictions.

Experimental results

Research questions

• RQ1 How do μ-gradients generated by meridional circulation affect the internal rotation profile in low-mass rotating stars?
• RQ2 To what extent do μ-currents alter the efficiency of rotational mixing in radiative zones compared to homogeneous models?
• RQ3 Can models including μ-gradient feedback reproduce the observed lithium depletion in subgiants on the hot side of the lithium dip?
• RQ4 Does the inclusion of μ-variations prevent the 'creeping paralysis' of meridional circulation predicted in earlier homogeneous models?
• RQ5 How does the dominant transport mechanism for chemicals shift when μ-gradients are included—specifically, does turbulent diffusion surpass effective diffusion?

Key findings

• μ-currents, driven by horizontal molecular weight gradients, are critical in shaping the internal rotation profile, especially near the core, and lead to stronger differential rotation.
• The presence of μ-gradients prevents the 'creeping paralysis' of meridional circulation, which was predicted in homogeneous models, because mirrored terms (Λ and Θ) do not cancel out under differential rotation.
• In inhomogeneous stars, the turbulent diffusion coefficient dominates chemical transport, whereas in homogeneous stars, the effective diffusion coefficient is the primary contributor.
• Rotating models with μ-gradient feedback reproduce the observed lithium depletion in evolved stars more accurately than classical models, with surface lithium depletion occurring at higher effective temperatures (Teff > 5850 K).
• The models successfully explain the low lithium abundances in subgiants and the dispersion in lithium evolution among stars with masses >1.4 M⊙, even when magnetic braking is included.
• The study confirms that μ-variations must not be neglected in rotating stellar models, as they significantly alter mixing efficiency and are likely crucial for post-main sequence evolution.