7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Extrapolating the solar magnetic field as a magnetohydrostatic equilibrium
Xiaoshuai Zhu1, Thomas Wiegelmann2
1
National Space Science Center, Chinese Academy of Sicence2
Max Planck Institute for Solar System Researche-mail: zhuxiaoshuai@nssc.ac.cn

Modeling the three-dimensional (3D) magnetic fields ofthe solar active region in multiple layers is very
important in studies of solar activities. Since only themagnetic field in the photosphere can be measured
accurately and routinely, the main approach of themagnetic field modeling is to extrapolate the magnetic
field from photospheric magnetograms. A basic
assumption of the modeling in the past several decades
was to completely neglect all plasma effects and to
perform the so-called force-free field (FFF)
extrapolations. The FFF extrapolation has been proved to
be a great success in recovering 3D magnetic field in thesolar corona. While the force-free assumption is welljustified in the corona where plasma is very sparse so themagnetic field dominates the corona, it is not the case in
the photosphere and chromosphere. In these lower
atmosphere, a magnetohydrostatic (MHS) equilibrium
which takes into account plasma forces, such as pressure
gradient and gravitational force, is considered to be more
appropriate. The corresponding MHS extrapolation has
been developing rapidly during the past several years.
Both analytical and numerical methods have beendeveloped to model the MHS equilibrium. In an
analytical approach, one has to assume a horizontal
electric current which is perpendicular with gravitational
force [1]. To model twisted magnetic configuration, Low[2]further introduced a linear-force-free electric currentcomponent. In the general MHS case, three kinds ofmethods have been proposed to solve the MHS equations.
They are: MHD relaxation method [3,4], Grad-Rubin
method [5], and optimization method [6]. Each of them has
been tested with either analytical or numerical reference

solution (Figure 1). Furthermore, the MHD relaxation
method and the optimization method have been used to
study solar activities by extrapolating the observed
magnetograms.
Recently, an MHS version of preprocessing of thevector magnetogam has been proposed to make themagnetogram consistent with the MHS assumption. TheMHS preprocessing is an extension of the widely applied
FFF preprocessing. Moreover, by recognizing that thenon-force-free layer is very thin in the solar atmosphere,
the MHS extrapolation is combined with the nonlinear
FFF extrapolation to improve the computational
efficiency dramatically.
The MHS extrapolations require high spatial
resolution boundary conditions as input to resolve thefine structures in the solar lower atmosphere. Such
hig-resolutin measurements (e.g., with SST, DKIST) areimproving rapidly, which offer great opportunities tofurther develop the MHS modeling.

References[1] Low, B. 1985, ApJ, 293, 31[2] Low, B. 1991, ApJ, 370, 427[3] Zhu, X., et al. 2013, ApJ, 768, 119[4] Miyoshi, T., et al. 2020, ApJS, 247, 6[5] Gilchrist, S., et al. 2016, SoPh, 291,3583[6] Zhu, X., & Wiegelmann, T. 2018, ApJ, 866, 130

Figure 1 Left: Comparison of the reference (white), MHS (yellow), and NLFFF (blue) field lines. Right: Comparison of referenceand MHS pressure (density).