← Back to Research    English | 日本語

In the solar corona, the magnetic pressure is dominant and thus the plasma β (=8πp/B^2), which is the ratio between the gas pressure p and the magnetic pressure B^2/8π, is sufficiently small. In such circumstance, the gas pressure can be neglected and the equilibrium is achieved when the Lorentz force vanishes, i.e., the magnetic tension and the magnetic pressure are balanced.

JxB=0       (1)

In order to reproduce the magnetic fields in active regions, we have to numerically solve the nonlinear equation (1) based on the magnetic field at the photosphere.

Where and when is free magnetic energy stored?

Some solar flares occur in an X-shaped quadrupolar field configuration. To understand how magnetic energy is stored in such a region, we applied NLFFF modeling to a time series of vector magnetic field maps of the active region NOAA 11967, which produced three X-shaped M-class flares on 2014 February 2. The maps were taken with the Solar Optical Telescope on board Hinode and the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory.

The reconstructed three-dimensional evolution shows that sufficient free energy had already been stored more than 10 hours before the first M-class flare, and that this storage was confined to a localized region. Within that same region, quasi-separatrix layers (QSLs) started to develop gradually from 9 hours before the flare. One of the flare ribbons that appeared in the first M-class flare was co-spatial with the QSL location, which suggests that the formation of QSLs is an important step in the energy release process.

These QSLs do not appear in the potential field calculation, meaning that they were created by the non-potential component of the field. Their formation was associated with the transverse photospheric motion of pre-emerged flux together with the emergence of new flux. In other words, a flare requires not only stored free energy but also the formation of QSLs in the non-potential field.

→ Y. Kawabata, S. Inoue, and T. Shimizu, The Astrophysical Journal, 842, 106, 2017

How much does the initial guess affect the extrapolation?

NLFFF extrapolation is an iterative calculation that starts from an initial guess of the three-dimensional field. Most previous studies used the potential field as that guess. We instead adopted linear force-free fields with several different values of the constant force-free alpha, which allows us to examine how unique the extrapolated field really is.

The dependence on the initial condition is smaller where the magnetic field is strong. Consequently the field at lower heights (below about 10 Mm) is relatively robust: solutions started from different initial conditions agree with a correlation coefficient above 0.9. This holds even though the Lorentz force is concentrated at those same low heights.

→ Y. Kawabata, S. Inoue, and T. Shimizu, The Astrophysical Journal, 895, 105, 2020

← Back to Research