The above observations and analysis lead us to believe that, (1) rapid and substantial changes of current helicity distribution in an area or in its vicinity probably lead to flare eruptions; (2) active regions in which average current helicity has a significant change show more flare activity than typical active regions; (3) no clear correlation between the peak values of current helicity and flare kernels; (4) the rate of variation of current helicity may better characterize the non-potentiality of active region magnetic fields - perhaps it can provide us with more information than other parameters, such as angular shear or vertical current.
We know that the magnetic helicity in the solar atmosphere comes mainly from the deeper layers of the Sun, and is accumulated during the course of magnetic activity. The accumulation will increase the magnetic complexity and magnetic free energy in the lower corona, and lead to flare eruptions. Taylor (1974) predicted that as a magnetized plasma relaxes, its magnetic field will evolve toward a force-free state, conserving total magnetic helicity. If Taylor's postulate is applicable for the solar atmosphere, the magnetic energy stored in the solar atmosphere evolves toward small spatial scales and dissipates much faster than magnetic helicity, which cascades toward larger spatial scales. However, this conservation of magnetic helicity is only in a global sense, it may be redistributed locally between magnetic systems as a result of reconnection. Such a helicity exchange may lead to instability in a system with higher helicity. Therefore, solar flares may be understood in the framework of current helicity change processes. Of course, photospheric shear motions besides reconnection may also cause gradual buildup of twist in active regions. Which of these two processes prevails on the Sun? This is beyond the scope of this paper.
In fact, many solar observations (e.g., the soft X-ray images and chromospheric filaments) imply that twist is found in magnetic structures that show a tendency to erupt. In the present paper, we try to discuss how the non-potential structures of photospheric magnetic fields in active regions change before and after flares, from the viewpoint of helicity. The results obtained here are preliminary since we do not have 3-dimensional observation data and study changes of current helicity distribution only in the photosphere. Although the helicity approach has not yet been widely applied in the study of flares, we think that the study of the influence of flares on helicity is very important for understanding the magnetic field structure and dynamic processes in the solar atmosphere. One should further research this topic, using a much larger sample.
Acknowledgements
We are indebted to Dr. Tongjiang Wang for helpful software and discussion. We also thank the referee for suggestions for improving the paper. This work was supported by the National Nature Science Foundation of China under grant 19791090.
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