[Paper Review] Rotational mixing in low-mass stars II. Self-consistent models of Pop II RGB stars

A. Palacios, C. Charbonnel+2 more|ArXiv.org|Feb 17, 2006

Stellar, planetary, and galactic studies73 references120 citations

TL;DR

This study presents the first self-consistent evolutionary models of low-metallicity Pop II red giant branch (RGB) stars including rotational mixing via meridional circulation and shear turbulence. Despite assuming differential rotation in the convective envelope—which enhances mixing—the models still fail to reproduce the observed abundance anomalies (e.g., low 12C/13C, enhanced N, depleted Li) at the RGB bump, indicating that shear-induced turbulence alone is insufficient to explain the extra mixing.

ABSTRACT

In this paper we study the effects of rotation in low-mass, low-metallicity RGB stars. We present the first evolutionary models taking into account self-consistently the latest prescriptions for the transport of angular momentum by meridional circulation and shear turbulence in stellar interiors as well as the associated mixing processes for chemicals computed from the ZAMS to the upper RGB. We discuss in details the uncertainties associated with the physical description of the rotational mixing and study carefully their effects on the rotation profile, diffusion coefficients, structural evolution, lifetimes and chemical signatures at the stellar surface. We focus in particular on the various assumptions concerning the rotation law in the convective envelope, the initial rotation velocity distribution, the presence of mean molecular weight gradients and the treatment of the horizontal and vertical turbulence. This exploration leads to two main conclusions : (1) After the completion of the first dredge-up, the degree of differential rotation (and hence mixing) is maximised in the case of a differentially rotating convective envelope (i.e., j_CE(r) = cst), as anticipated in previous studies. (2) Even with this assumption, and contrary to some previous claims, the present treatment for the evolution of the rotation profile and associated meridional circulation and shear turbulence does not lead to enough mixing of chemicals to explain the abundance anomalies in low-metallicity field and globular cluster RGB stars observed around the bump luminosity. This study raises questions that need to be addressed in a near future. These include for example the interaction between rotation and convection and the trigger of additional hydrodynamical instabilities.

Motivation & Objective

• To investigate the impact of rotational mixing on low-mass, low-metallicity RGB stars using self-consistent evolutionary models.
• To assess how uncertainties in rotational transport mechanisms affect surface abundances, structural evolution, and lifetimes.
• To determine whether current prescriptions for meridional circulation and shear turbulence can reproduce observed abundance anomalies in field and globular cluster giants.
• To evaluate the role of differential rotation in the convective envelope on mixing efficiency.
• To identify gaps in current models, particularly regarding the coupling between rotation and convection and the role of additional hydrodynamical instabilities.

Proposed method

• Evolved stellar models from the zero-age main sequence (ZAMS) to the upper RGB using updated transport prescriptions for angular momentum and chemical mixing.
• Incorporated self-consistent treatments of meridional circulation and shear turbulence based on Zahn's formalism, with variable diffusion coefficients dependent on rotation profile.
• Varied key assumptions: rotation law in the convective envelope (uniform vs. differential), initial rotation velocity distribution, presence of μ-gradients, and treatment of horizontal and vertical turbulence.
• Tracked evolution of rotation profiles, diffusion coefficients, structural parameters, and surface abundances (e.g., 12C/13C, Li, N) across the RGB.
• Compared model predictions with observational data from open clusters, field stars, and globular clusters (e.g., M67, NGC 6528, M4) at the RGB bump luminosity.
• Evaluated the role of the 'Li flash' and structural response to rotation-induced mixing as potential amplifiers of extra-mixing.

Experimental results

Research questions

• RQ1 Does differential rotation in the convective envelope enhance rotational mixing in low-metallicity RGB stars compared to uniform rotation?
• RQ2 Can current prescriptions for shear-induced turbulence and meridural circulation reproduce the observed low 12C/13C and enhanced nitrogen in RGB stars at the bump luminosity?
• RQ3 How do uncertainties in initial rotation velocity distribution and μ-gradient treatment affect the predicted surface abundances?
• RQ4 What is the role of additional hydrodynamical instabilities (e.g., baroclinic, GSF, Solberg-Høiland) in enhancing mixing beyond secular shear instability?
• RQ5 Is the structural and nuclear response to rotation-induced mixing, such as the 'Li flash', sufficient to explain the observed abundance anomalies?

Key findings

• Differential rotation in the convective envelope (j_CE(r) = constant) maximizes the degree of differential rotation and associated mixing, confirming prior theoretical expectations.
• Even with differential rotation, the shear-induced turbulence model fails to produce sufficient chemical mixing to explain the observed low 12C/13C ratios and nitrogen enhancements at the RGB bump.
• The model's predicted diffusion coefficients remain too low to match observations, indicating that shear turbulence alone is insufficient to account for the extra-mixing process.
• The study identifies a critical need to include additional transport mechanisms, such as internal gravity waves or other hydrodynamical instabilities, in future models.
• The 'Li flash' scenario—where energy release from 7Li burning enhances mixing—remains a viable but untested mechanism that could amplify mixing, though not yet incorporated into the current framework.
• The results suggest that the current coupling between rotation and convection is inadequate, and future models must account for more complex interactions, including potential transitions in rotation regime during evolution.