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We performed a magnetohydrodynamic (MHD) simulation using a nonlinear force-free field (NLFFF) in solar active region 11158 to clarify the dynamics of an X2.2-class solar flare. We found that the NLFFF never shows the drastic dynamics seen in observations, i.e., it is in stable state against the perturbations. On the other hand, the MHD simulation shows that when the strongly twisted lines are formed at close to the neutral line, which are produced via tether-cutting reconnection in the twisted lines of the NLFFF, consequently they erupt away from the solar surface via the complicated reconnection. This result supports the argument that the strongly twisted lines formed in NLFFF via tether-cutting

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We have investigated the variation of magnetic helicity over a span of several days around the times of 11 X-class flares which occurred in seven active regions (NOAA 9672, 10030, 10314, 10486, 10564, 10696, and 10720) using the magnetograms taken by the Michelson Doppler Imager (MDI ) on board the Solar and Heliospheric Observatory (SOHO). As a major result we found that each of these major flares was preceded by a significant helicity accumulation, (1:8Y16) ; 10 42 Mx 2 over a long period (0.5 to a few days). Another finding is that the helicity accumulates at a nearly constant rate, (4:5Y 48) ; 10 40 Mx 2 hr À1 , and then becomes nearly constant before the flares. This led us to distinguish the helicity variation into two phases: a phase of monotonically increasing helicity and the following phase of relatively constant helicity. As expected, the amount of helicity accumulated shows a modest correlation with timeintegrated soft X-ray flux during flares. However, the average helicity change rate in the first phase shows even stronger correlation with the time-integrated soft X-ray flux. We discuss the physical implications of this result and the possibility that this characteristic helicity variation pattern can be used as an early warning sign for solar eruptions.

We study the three-dimensional magnetic structure of solar active region 11158, which produced one X-class and several M-class flares on 2011 February

We clarify a relationship of the dynamics of a solar flare and a growing Coronal Mass Ejection (CME) by investigating the dynamics of magnetic fields during the X2.2-class flare taking place in the solar active region 11158 on 2011 February 15, based on simulation results obtained from Inoue et al. (2014a). We found