[Paper Review] Stellar Evolution with Rotation and Magnetic Fields IV: The Solar Rotation Profile

P. Eggenberger, A. Maeder+1 more|ArXiv.org|Aug 22, 2005

Stellar, planetary, and galactic studiesPhysics and Astronomy17 references115 citations

TL;DR

This paper proposes that the Tayler–Spruit dynamo, driven by magnetic fields in the solar radiative interior, explains the Sun's nearly solid-body rotation profile. By balancing meridional circulation (which enhances differential rotation) with magnetic coupling (which enforces uniform rotation), the model achieves near-constant angular velocity between 0.2 and 0.7 R⊙, in excellent agreement with helioseismic observations.

ABSTRACT

We examine the generation of a magnetic field in a solar-like star and its effects on the internal distribution of the angular velocity. We suggest that the evolution of a rotating star with magnetic fields leads to an equilibrium value of the differential rotation. This equilibrium is determined by the magnetic coupling, which favours a constant rotation profile, and meridional circulation which tends to build differential rotation. The global equilibrium stage is close to solid body rotation between about 0.7 and 0.2 R_sun, in good agreement with helioseismic measurements.

Motivation & Objective

• Explain the observed near-constant angular velocity in the solar radiative interior, which contradicts predictions from standard rotational models.
• Investigate whether magnetic fields generated by the Tayler–Spruit dynamo can provide sufficient internal coupling to enforce solid-body rotation.
• Assess the role of magnetic fields in angular momentum transport compared to rotational and turbulent diffusion mechanisms.
• Determine if the magnetic dynamo mechanism operates efficiently in slowly rotating stars like the Sun.
• Compare model predictions with helioseismic measurements of the solar rotation profile.

Proposed method

• Formulate a consistent set of dynamo equations based on the Tayler–Spruit instability, incorporating Alfvén frequency and Brunt–Väisälä frequency.
• Implement a stellar evolution code that includes both rotational effects and magnetic field generation via the Spruit dynamo mechanism.
• Use the magnetic field's diffusion coefficient ν to model vertical transport of angular momentum, which suppresses differential rotation.
• Apply constraints from marginal stability: l < r·ω_A/N and l² > ηΩ/ω_A² to determine the growth rate and spatial scale of magnetic instabilities.
• Solve the equilibrium condition ω_A/Ω = q·Ω/N, where q = -∂lnΩ/∂lnr, to derive the balance between magnetic coupling and meridional circulation.
• Compare model outputs with helioseismic data from GOLF+MDI and LOWL instruments, using initial surface velocities of 20 and 50 km s⁻¹.

Experimental results

Research questions

• RQ1 Can the Tayler–Spruit dynamo explain the flat rotation profile observed in the solar radiative interior via helioseismology?
• RQ2 How does the inclusion of magnetic fields alter the internal angular velocity distribution compared to models with only rotation and turbulent diffusion?
• RQ3 What is the relative importance of magnetic diffusion (ν) versus shear turbulent mixing (D_shear) in angular momentum transport in solar-like stars?
• RQ4 Does the magnetic dynamo mechanism remain effective in slowly rotating stars such as the Sun, where differential rotation is weak?
• RQ5 To what extent do magnetic models reproduce the observed angular velocity profile within the 0.2–0.7 R⊙ range?

Key findings

• The model with both rotation and magnetic fields produces a nearly constant angular velocity in the radiative interior between 0.2 and 0.7 R⊙, matching helioseismic measurements.
• The magnetic diffusion coefficient ν dominates angular momentum transport, reaching large values that enforce near-solid-body rotation.
• The azimuthal magnetic field component B_φ reaches a few ×10² G, sufficient to generate strong magnetic coupling.
• Shear turbulent mixing coefficient D_shear is reduced by about four orders of magnitude compared to non-magnetic models, indicating weaker rotational mixing.
• The ratio η/K is very small, validating the simplifications used in deriving the dynamo equations.
• Models with initial surface velocities of 20 and 50 km s⁻¹ produce very similar internal rotation profiles, with only slightly faster cores in the 50 km s⁻¹ case.