[Paper Review] Rotation of the solar interior

J. Christensen‐Dalsgaard, M. J. Thompson|arXiv (Cornell University)|Oct 29, 2001

Solar and Space Plasma Dynamics1 references3 citations

TL;DR

This paper reviews helioseismic observations revealing the Sun's internal rotation, showing that the convection zone exhibits strong differential rotation while the radiative interior rotates nearly uniformly, with a sharp transition at the tachocline. Advanced numerical simulations suggest that turbulent convection and magnetic coupling can reproduce observed rotation profiles, challenging earlier theoretical models predicting a rapidly spinning core.

ABSTRACT

Helioseismology has allowed us to infer the rotation in the greater part of the solar interior with high precision and resolution. The results show interesting conflicts with earlier theoretical expectations, indicating that the the Sun is host to complex dynamical phenomena, so far hardly understood. This has important consequences for our ideas about the evolution of stellar rotation, as well as for models for the generation of the solar magnetic field. Here we provide an overview of our current knowledge about solar rotation, much of it obtained from observations from the SOHO spacecraft, and discuss the broader implications.

Motivation & Objective

• To summarize current knowledge of solar internal rotation derived from helioseismology.
• To identify discrepancies between observed rotation and theoretical models, particularly regarding the core's rotation rate.
• To evaluate the role of convection and magnetic fields in shaping the Sun's rotation profile.
• To assess the progress and limitations of numerical simulations in reproducing helioseismic observations.
• To highlight open questions regarding high-latitude flows and temporal variations near the tachocline.

Proposed method

• Helioseismology is used to infer internal rotation by analyzing the frequencies and spherical harmonic modes of solar oscillations.
• Global helioseismic techniques measure radial and latitudinal variations in wave frequencies to reconstruct rotation profiles.
• Local helioseismology probes near-surface flows, including meridional circulation and banded differential rotation.
• Numerical simulations of convection zones model angular momentum transport under varying boundary conditions and resolution.
• Simulations compare rotation profiles against helioseismic data, testing the effects of turbulence, penetration, and magnetic fields.
• Boundary conditions and parameter values in simulations are varied to assess their impact on reproducing observed differential rotation.

Experimental results

Research questions

• RQ1 How does the Sun's internal rotation vary with depth and latitude, as revealed by helioseismology?
• RQ2 Why does the solar core not rotate significantly faster than the radiative interior, contrary to theoretical expectations?
• RQ3 What mechanisms in the convection zone produce the observed differential rotation profile?
• RQ4 To what extent can numerical simulations of turbulent convection reproduce the Sun's observed rotation structure?
• RQ5 What role do magnetic fields and the tachocline play in enforcing near-uniform rotation in the deep interior?

Key findings

• The solar convection zone exhibits strong differential rotation, with equatorial rotation at ~2.91 microrad/s (25-day period) and polar rotation at ~2.02 microrad/s (36-day period).
• The radiative interior, especially outside the core, rotates nearly uniformly, with a sharp transition at the tachocline.
• Numerical simulations show that turbulent convection can reproduce the observed differential rotation, but only with appropriate boundary conditions and resolution.
• The contrast in rotation rate between low and high latitudes is about 130 nHz in the Sun, but simulations struggle to match this unless carefully tuned.
• Meridional circulation patterns in the near-surface layers show asymmetric, time-varying behavior, with changes observed over years.
• A very rapidly rotating core is ruled out unless it is very small, based on helioseismic constraints.