Subsurface Evolution of Active Region Flux Tubes

If the magnetic field seen in sunspots and active regions on the solar surface originates from a strong toroidal magnetic field generated by the dynamo mechanism at the base of the solar convection zone, then the question of how magnetic flux is transported through the convection zone and emerge into the solar atmosphere must be addressed. It is generally thought that magnetic flux rises buoyantly through the convection zone in the form of discrete flux tubes, and that the tubes should maintain reasonable cohesion in order that the emerging flux be organized as active regions, which display a well-defined order as described by Hale's polarity rule and Joy's law of active region tilts. For many years, my research has focused on the physics of buoyant magnetic flux tubes and their transport through the bulk of the solar convection zone. The following is a list of some of my reserach results. For a reaview on this subject please see my article in Living Reviews in Soalr Physics.

• Destabilization of magnetic flux stored at the base of the solar convection zone and the formation of buoyant flux tubes:

  Fan (2001, ApJ, 546, 509) studied the magnetic buoyancy instability (or the Parker instability) of a neutrally buoyant layer of horizontal, unidirectional magnetic field in hydrostatic equilibrium at the base of the solar convection zone. It is found that the non-linear growth of the undulatory Parker instability lead to the formation of buoyant arching flux tubes which rise cohesively through the distance of about 1 density scale height included in the simulation domain. The figure and movie 1 above show the evolution of the magnetic layer perturbed with an unstable undulatory mode. Movies 2 and 3 show (from two different perspective views) a simulation where the magnetic layer is perturbed with a localized velocity field.

  movie1

  movie2

• Dynamic evolution of buoyant magnetic flux tubes in a 3D convecting flow:

  Fan, Abbett, and Fisher (2003, ApJ 582, 1206) have carried out 3D numerical simulations of the dynamic evolution of uniformly buoyant, twisted horizontal magnetic flux tubes in a 3D stratified convective velocity field. Our calculations are relevant to understanding how stratified convection in the deep solar convection zone may affect the rise and the structure of buoyant flux tubes that are responsible for the emergence of solar active regions. It is found that in order for the magnetic buoyancy force of the tube to dominate the hydrodynamic force due to the convective downflows, the field strength B of the flux tube needs to be significantly higher than the field strength Beq in equipartition with the kinetic energy density of the strong downdrafts. For tubes of equipartition field strength, the evolution and the morphology of the tube is largely controlled by the local conditions of the convective flow. Sections of the tube in the paths of strong downdrafts are pinned down to the bottom despite their buoyancy, while the rise speed of sections within upflow regions is significantly boosted. Omega-shaped emerging tubes can form between downdrafts. On the other hand, tubes with 10 times the equipartition field strength are found to rise unimpeded by the downdrafts, and are not significantly distorted by the 3D convective flow.

  convective velocity field

  tube with B=Beq

  tube with B=10Beq

• The rise of kink unstable magnetic flux tube and the origin of delta-configuration sunspots:

  animation

  To investigate the origin of the so-called delta-configuration sunspots which are a class of active regions that do not obey the Hale polarity rule and are shown to be flare productive, Fan et al. (1998, ApJ, 505, L59; 1999, ApJ, 521, 460) have performed 3D MHD simulations of the rise of highly twisted, kink-unstable magnetic flux tubes through an adiabatically-stratified model solar convection zone (see the example in the above figure). It is found that the rising flux tube evolves into a highly kinked shape with a large change (> 90 degree) of tube orientation at the apex. The forth panel shows the magnetic field in a horizontal cross-section near the apex of the kinked tube. It shows a compact bipolar structure with inverted polarity order and sheared horizontal field along the neutral line. These properties are similar to those found in delta-spots.