[Paper Review] Stellar evolution with rotation and magnetic fields:III: The interplay of circulation and dynamo

A. Maeder, G. Meynet|ArXiv.org|Jun 15, 2005

Stellar, planetary, and galactic studies16 references92 citations

TL;DR

This paper investigates the interplay between meridional circulation and the Tayler–Spruit dynamo in differentially rotating stars, showing that magnetic fields enforce nearly solid-body rotation, which dramatically enhances chemical transport via circulation. The key result is that magnetic fields amplify surface nitrogen and helium enrichments—up to 11× for N/C—beyond what rotation alone produces, offering a mechanism consistent with observed OB star abundances.

ABSTRACT

We examine the effects of the magnetic field created by the Tayler--Spruit dynamo in differentially rotating stars. Magnetic fields of the order of a few $10^4$ G are present through most of the stellar envelope, with the exception of the outer layers. The diffusion coefficient for the transport of angular momentum is very large and it imposes nearly solid body rotation during the MS phase. In turn, solid body rotation drives meridional circulation currents which are much faster than usual and leads to much larger diffusion coefficients than the magnetic diffusivity for the chemical species. The consequence is that the interplay of the thermal and magnetic instabilities favours the chemical transport of elements, while there would be no transport in models with magnetic field only. We also discuss the effects on the stellar interior, lifetimes and HR diagram.

Motivation & Objective

• To understand the feedback between magnetic fields generated by the Tayler–Spruit dynamo and meridional circulation in rotating stars.
• To resolve inconsistencies in prior models by developing a unified framework for magnetic and thermal instabilities across all adiabatic and non-adiabatic conditions.
• To assess how the interplay between magnetic field, rotation, and circulation affects chemical element transport and stellar evolution in massive stars.
• To compare model predictions with observational data on surface abundances in OB stars, particularly nitrogen and helium enrichments.
• To evaluate the potential of asteroseismology as a test for internal rotation profiles and magnetic field effects.

Proposed method

• Develops a consistent system of equations for the Tayler–Spruit dynamo that applies to both adiabatic and non-adiabatic stellar interiors.
• Incorporates the Alfvén frequency and magnetic energy density to model the magnetic field's influence on angular momentum transport.
• Solves the coupled system of equations for magnetic field generation, differential rotation, and meridional circulation using numerical stellar evolution models.
• Introduces a feedback loop: magnetic fields suppress differential rotation, which enhances meridional circulation, which in turn restores differential rotation.
• Uses transport coefficients derived from magnetic diffusivity and circulation-driven mixing to quantify chemical element transport.
• Compares models with rotation only, magnetic fields only, and both rotation and magnetic fields to isolate the effects of the interplay.

Experimental results

Research questions

• RQ1 How does the Tayler–Spruit dynamo influence angular momentum transport and rotation profiles in massive stars?
• RQ2 What is the role of meridional circulation in enhancing chemical element transport when magnetic fields enforce solid-body rotation?
• RQ3 To what extent do magnetic fields amplify surface nitrogen and helium enrichments compared to rotation alone?
• RQ4 Can the predicted surface abundance enhancements be reconciled with observational data from OB stars?
• RQ5 What observational diagnostics, such as g-mode oscillations, could test the predicted internal rotation and magnetic field structure?

Key findings

• Magnetic fields generated by the Tayler–Spruit dynamo enforce nearly solid-body rotation throughout the stellar envelope during the main sequence, suppressing differential rotation.
• The suppression of differential rotation strongly enhances meridional circulation, increasing chemical transport coefficients beyond those from magnetic diffusion alone.
• Surface helium mass fraction increases to Y_s = 0.31 at the end of the main sequence in models with both rotation and magnetic fields, exceeding the solar value.
• Nitrogen-to-carbon and nitrogen-to-oxygen ratios increase by factors of 11 and 6, respectively, due to enhanced mixing, significantly exceeding predictions from rotation-only models.
• The model with rotation and magnetic fields reaches higher luminosity and bluer colors at the end of the main sequence due to larger cores and reduced opacity from surface helium enrichment.
• The predicted surface abundance enhancements are broadly consistent with observations of fast-rotating OB stars, though observational constraints remain limited by data scarcity.