[Paper Review] Bistability between equatorial and axial dipoles during magnetic field reversals

Christophe Gissinger, Ludovic Petitdemange+2 more|arXiv (Cornell University)|Mar 19, 2012

Geomagnetism and Paleomagnetism Studies18 references21 citations

TL;DR

This study demonstrates that equatorial symmetry breaking in geodynamo simulations induces a bistable regime between axial and equatorial dipole magnetic fields, enabling chaotic polarity reversals via transient equatorial dipole states. The mechanism explains Earth-like reversals as turbulent transitions mediated by a hemispherical equatorial dipole, with reversal frequency increasing with symmetry breaking strength (C).

ABSTRACT

Numerical simulations of the geodynamo in presence of an heterogeneous heating are presented. We study the dynamics and the structure of the magnetic field when the equatorial symmetry of the flow is broken. If the symmetry breaking is sufficiently strong, the m = 0 axial dipolar field is replaced by an hemispherical magnetic field, dominated by an oscillating m = 1 magnetic field. Moreover, for moderate symmetry breaking, a bistability between the axial and the equatorial dipole is observed. In this bistable regime, the axial magnetic field exhibits chaotic switches of its polarity, involving the equatorial dipole during the transition period. This new scenario for magnetic field reversals is discussed within the framework of the Earth's dynamo.

Motivation & Objective

• To investigate how equatorial symmetry breaking in the core flow influences magnetic field morphology and reversal dynamics.
• To determine whether a bistable regime between axial and equatorial dipole states can emerge under moderate symmetry breaking.
• To explore the role of the equatorial dipole as a transitional state during axial dipole reversals.
• To link reversal frequency to the degree of equatorial asymmetry in the thermal boundary condition.
• To assess the relevance of this mechanism for explaining the irregular, chaotic nature of Earth's geomagnetic reversals.

Proposed method

• Conduct 3D numerical simulations of a thermally convecting, electrically conducting Boussinesq fluid in a rotating spherical shell with inner and outer spheres.
• Apply a heterogeneous temperature boundary condition at the outer sphere: $ T_o = T_i - \Delta T(1 - C\cos\theta) $, where $ C $ controls symmetry breaking.
• Solve the coupled system of dimensionless Navier-Stokes, induction, and heat equations under divergence-free constraints for velocity and magnetic fields.
• Use fixed boundary conditions: no-slip for velocity, insulating for magnetic fields, and isothermal for temperature.
• Vary the symmetry-breaking parameter $ C $ from 0 to 0.25 while holding $ Ra = 120 $, $ Pm = 20 $, $ Pr = 1 $, $ Ek = 6 \times 10^{-3} $, and $ r_i/r_o = 0.3 $.
• Analyze magnetic field structure via azimuthally averaged magnetic energy and radial field components at the core-mantle boundary.

Experimental results

Research questions

• RQ1 Can equatorial symmetry breaking in the core flow lead to the emergence of a stable equatorial dipole magnetic field?
• RQ2 Does a bistable regime exist between axial and equatorial dipole states under moderate symmetry breaking?
• RQ3 Is the equatorial dipole state responsible for mediating chaotic polarity reversals in the axial dipole field?
• RQ4 How does the reversal frequency of the axial dipole depend on the degree of equatorial symmetry breaking?
• RQ5 Can this mechanism reproduce the bimodal, irregular reversal patterns observed in Earth's paleomagnetic record?

Key findings

• For $ C = 0.1 $, the magnetic field remains predominantly axial dipole, with weak non-axisymmetric components, indicating stability under weak symmetry breaking.
• At $ C > 0.1 $, the system transitions to a stable equatorial dipole state, with a hemispherical magnetic field structure in the fluid interior and a dominant $ m=1 $ mode at the boundary.
• A sharp transition in magnetic field morphology occurs at $ C \approx 0.12 $, with the axial dipole's basin of attraction shrinking as $ C $ increases.
• For $ C \approx 0.12 $, the axial dipole exhibits chaotic polarity reversals with rapid tilt switching from $ 0^\circ $ to $ 180^\circ $, consistent with Earth-like reversals.
• The equatorial dipole acts as a transitional state during reversals, with the magnetic field in the bulk being strongly hemispherical and rotating around the rotation axis.
• Reversal frequency increases with $ C $, peaking in the bistable regime before vanishing at $ C > 0.2 $, where only the equatorial dipole persists.