A New Code for Nonlinear Force-Free Field Extrapolation of the Global Corona

Reliable measurements of the solar magnetic field are still restricted to the photosphere, and our present knowledge of the three-dimensional coronal magnetic field is largely based on extrapolation from photospheric magnetogram using physical models, e.g., the nonlinear force-free field (NLFFF) model as usually adopted. Most of the currently available NLFFF codes have been developed with computational volume like Cartesian box or spherical wedge while a global full-sphere extrapolation is still under developing. A high-performance global extrapolation code is in particular urgently needed considering that Solar Dynamics Observatory (SDO) can provide full-disk magnetogram with resolution up to $4096\times 4096$. In this work, we present a new parallelized code for global NLFFF extrapolation with the photosphere magnetogram as input. The method is based on magnetohydrodynamics relaxation approach, the CESE-MHD numerical scheme and a Yin-Yang spherical grid that is used to overcome the polar problems of the standard spherical grid. The code is validated by two full-sphere force-free solutions from Low & Lou's semi-analytic force-free field model. The code shows high accuracy and fast convergence, and can be ready for future practical application if combined with an adaptive mesh refinement technique.Comment: Accepted by ApJ, 26 pages, 10 figure

MHD simulation of rapid change of photospheric magnetic field during solar eruption caused by magnetic reconnection

It has been well observed that the horizontal component of the magnetic field at photosphere changes rapidly and irreversibly after solar eruptions. Specifically, the horizontal magnetic field near the polarity inversion line increases substantially, while that near the center of the magnetic polarity decreases. Such a phenomenon is considered as the dynamic feedback from the corona to the photosphere, but the underlying mechanism remains in debate. Here based on a recent magnetohydrodynamics (MHD) simulation of homologous eruptions initiated by magnetic reconnection, we analyzed the rapid changes of the horizontal magnetic field, the magnetic inclination angle, the Lorentz force and as well as the derivative variation of the horizontal magnetic field. The simulation reproduces a pattern of rapid evolution of the horizontal field during the eruptions in agreement with typical observations. Our analysis suggests the physical reasons for this phenomenon: 1) The magnetic field near the polarity inversion line becomes more horizontal after flares due to the compression of the downward outflow of flare reconnection, and accordingly the magnetic inclination angle decreases and the downward Lorentz force increases; 2) The magnetic field near the center of the magnetic polarities become more vertical mainly due to the expansion effect of the velocity divergence term, and as a result the magnetic inclination angle and the upward Lorentz force increase