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Large-Scale Numerical Simulation of the Sunspot-Forming Region of the Sun

Reseach group of Hiroaki Isobe (His current address is the Dept. of Earth and Planeraty Science, Univ. Tokyo), Takehiro Miyagoshi, and Kazunari Shibata (Kyoto Univ.) and Takaaki Yokoyama (Tokyo Univ.) carried out large-scale numerical simulation of the sunspot-forming region (also called emerging flux region) of the Sun using the Earth Simulator, and succeeded to re-produce the filamentary strucutre that are often observed in such region. On the basis of the simulation results, they propose a new model for the filament formation and coronal heating in the solar atmosphere. This result has been published in Nature on 2005 March 24 (vol. 434, p478).


Sunspots are formed from a bundle of magnetic flux that emerges from solar interior into the upper atmosphere. The regions where sunspots are formed are called emerging flux regions. Solar observers have found that explosive phenomena such as solar flares and jets often occur in emerging flux regions. Understanding the mechanism of these magnetic activities is one of the most important problems in solar physics and astrophysics. Also, such magnetic activities have significant influence on the Earth and our life. For example, coronal mass ejections associated with solar flares interact with the magnetosphere of the Earth, and the disturbance of the magnetosphere causes the aurora activities, disturbance of the communication sattellites, and damaging of electric plants. The high energy particles from solar flares and interplanetary shock waves also damage space crafts and health of astronauts. The emerging flux regions are the ultimate origin of such solar-terrestrial disturbances.



Figure 1 is the H alpha (emission from Hydrogen atom) image of an emerging flux region, taken by the Domeless Solar Telescope at the Hida Observatory, Kyoto University. The lower-left dark spot is the sunpot. The white region are called plage, where heating of the chromosphere occurs. The large plage (upper-right) cover another sunspot that has the opposite polarity. The characteristics of the emerging flux region is the dark and narrow filaments that connect the sunspots (plages) with opposite polarities. They are called arch filament system and believed to trace the structure of the magnetic field. Using the Earth Simulator, we have carried out the numerical simulations of such emerging flux region with the highest resolution ever achieved, and succeeded to reproduce the arch filament system and fine sturcture in coronal heating and flares for the first time.



Figure 2 shows the three-dimensional visualization of the simulation result. The gray illuminated surfaces are the isosurface of the mass density of the plasma (surfaces of the constant mass density). The blue lines and color on the side in the figure shows magnetic field lines and temperature distributions, respectively. The semi-circular magnetic field near the center of the figure is the emerging magnetic field. Narrow filaments at the top of the emerging magnetic field are clearly seen. These filametns correspond to the arch filament system observed in the H alpha image. By carefully examining the simulation result we have found that the mechanism of the formation of the filamentary structure is the magnetic Rayleigh-Taylor instablity. The magnetic Rayleigh-Taylor instability is a kind of instability in magnetized plasmas. When heavy fluid (such as chromospheric gas) is supported by the light magnetic field against gravity, such top-heavy configuration becomes unstable and the gas falls between the magnetic field, forming the interlocking, filamentary sturucture.



An important cosequense of the filament formation by the magnetic Rayleigh-Taylor instability is the fomation of many small-scale electric current in the emerging flux. Figure 3 shows the distribution of the electiric current. The color on two cross sections is the electric current density; red is strong and blue is weak. The arch filament (gray) and magnetic field lines are also shown. The electric currents are induced by the deformation of the magnetic field by the Rayleigh-Taylor instability, hence the small-scale current sheets are formed in the periphery of the arch filaments, where magnetic field is strongly deformed. We propose that such small-scale electric current may serve for the coronal heating, whose mechanism is one of the biggest puzzles of the Sun.



When the emerging magnetic field interact and reconnect with the overlying coronal field, the plasma is heated and accelerated, that is, flares and jets occur. As the development of the filametntary structure in the emerging magnetic field, fine structures also appear in flares and jets, which are actually often observed. An example is shown in figure 4. The left panel shows the structure of jets from the emerging flux region in our simulation, and the right panel shows an H alpha image of a jet observed near the solar limb by the Domeless Solar Telescope at the Hida Observatory. Because the plasma heating and acceleration occur at the top of the emergig flux where filament formation simultaneously occurs, the resultant structure of jets and flares also exhibits fine structure. Since such fine structure is always observed in solar flares and jets, we conjecture that similar mechanism, i.e., plasma heating and acceleration by the reconnection of the interchanging (filament-forming) magnetic field, is quite universal process in the explosive phenomena in the solar corona and other space plasma (such as the magnetosphere of the Earth).


In summary, on the basis of the result of the large-scale numerical simulation, we propose a new model for the filament formation, coronal heating, and formation of fine structure in the solar flares. We hope that observations by the new telescope SMART at the Hida Observatory and the upcoming solar-observation satellite Solar-B will be able to test our model, and also will reveal further interesting and puzzling feature of the Sun.

(Hiroaki Isobe)