The Emergence of Magnetic Flux into the Solar Corona
The global properties of active regions are governed, at least in part, by photospheric and sub-surface magnetic fields and flows, and some of the most intense episodes of activity may well be related to the dynamic process of magnetic flux emergence from the convective interior into the low-density solar corona. The detailed physics of the emergence of these magnetic structures through the many pressure scale heights of the solar photosphere, chromosphere, transition region, and low corona is not well understood, yet may be critically important in our effort to understand the formation of filaments and prominences, and may provide clues to the triggering mechanism behind spectacular explosive and eruptive events such as coronal mass ejections.
The bottom red box on the left shows the volume encompassed by a 3D MHD simulation (in the anelastic approximation) of an emerging, twisted active region flux tube rising though the solar interior toward the solar surface. The grey plane and the field lines above it show a coupled, fully compressible MHD simulation of the response of the solar corona to the emerging flux. The six images on the right hand side show comparisons between the MHD simulations of coronal evolution and a potential field extrapolation (the lighter the field line, the stronger the normal component of the magnetic field at the loop footpoint). The left column shows the MHD results, and the right column the potential field extrapolation. Each row shows a different amount of twist in the emerging active region flux tube, with the top row corresponding to no initial twist, and the bottom row to substantial twist (from Abbett and Fisher 2003).
To date, a complete dynamic simulation of the solar envelope that extends from the base of the convection zone into the low corona remains computationally prohibitive. However, there are several useful approaches one can take when attempting to numerically model the process of active region-scale flux emergence through the surface layers. One approach is to exclude a majority of the convection zone from the computational domain, and simulate the emergence of a magnetic structure through the highly stratified surface layers alone --- this expedites a calculation, but neglects any connection to the dynamics of the convective interior.
Another approach is to create a simple interface between two separate codes --- one that can efficiently model the high-beta plasma of the solar convection zone, and one that can model the low-beta solar corona (here, beta refers to the plasma beta: the ratio of gas to magnetic pressure). While the interface between the two codes can be tricky (possibly introducing physical and numerical inconsistencies into a given calculation), it is important to be able to understand how to properly couple the codes together if we are to achieve the goal of successfully driving simulations of the solar atmosphere with magnetic fields and flows obtained directly from observations of the solar photosphere (see "Research: Space Weather"). My first attempt at coupling a 3D dynamic sub-surface model of the solar convection zone to a 3D model of the solar atmosphere is described in: