3D Magnetic Configuration of Solar Active Regions
Example of the Active Region 8151

Introduction

To fill the lack of measurements of the solar coronal magnetic field, we reconstruct the 3D magnetic field on the corona from photospheric observations. Using vector magnetograms as boundary condition, we determine the non-constant-alpha force-free magnetic configuration of a given active region (Amari et al., Solar Phys., 174, 129; Amari et al., A&A, 351, 1051). The active region 8151 observed on February 1998 exhibits a system of coronal loops and a sigmoid before an eruptive event and its associated slow CME.

Non-constant-alpha Force-free Magnetic Field

The vector magnetograms are obtained by IVM (Mees Solar Observatory, Hawai) on Feb 11, 1998. On the photosphere, the boundary conditions are the vertical component of the magnetic field B_z (Fig.1 top left) and the distribution of alpha (Fig.1 bottom) for B_z >0 or B_z<0. The latter photospheric condition is deduced from the vertical density of electric current J_z (Fig.1 top right) provided by the tranverse components of the magnetic field (J_z = (rot B)_z = alpha B).

The non-constant-alpha force-free field is computed for the active region 8151 (see Fig.2): three characteristic flux tubes are plotted.

Fig.1: Magnetic Data from IVM (Mees Solar Observatory, Hawaii)

Fig.2: Non-constant-alpha Magnetic Field of AR8151

Comparison with Coronal Features

Fig.3 is a comparison between the non-constant-alpha force-free field and the coronal structures observed either by SXT/Yohkoh for the sigmoid or by EIT/SOHO for the system of coronal loops. See the best agreement between the three charateristic flux tubes and the obsevations.

Fig.3: Non-constant-alpha Force-free Field vs. Coronal Observations (top right: SXT/Yohkoh, bottom right: FeIX/X EIT/SOHO)

Fig.4: Comparison between the three models: current-free, constant-alpha force-free and non-constant-alpha force-free

Potential Field, Constant-alpha Force-free Field and Non-constant-alpha Force-free Field

In Fig.4, we compare three magnetohydrostatic models: the current-free field (alpha = 0, Fig.4 left), the constant-alpha force-free field (alpha = 7.63 10^-2 Mm^-1, Fig.4 center) and the non-constant-alpha force-free field (Fig.4 right). For each model, the flux tubes (1), (2) and (3) have the same footpoints in the positive polarity (red). See the topoligic and geometrical changes between the different models.

Conclusion

Using non-constant-alpha force-free field reconstruction, we are able to determine the 3D magnetic configuration of an active region. In the frame of the MURI project, we propose to apply this method in order to study the time evolution of active regions and to study the mechanism of the related eruptive event.

MURI-MSU Nugget December 2001