Solar flares and coronal mass ejections (CMEs), the most catastrophic eruptions in our solar system, have been known to affect terrestrial environments and infrastructure. However, because their triggering mechanism is still not sufficiently understood, our capacity to predict the occurrence of solar eruptions and to forecast space weather is substantially hindered. Even though various models have been proposed to determine the onset of solar eruptions, the types of magnetic structures capable of triggering these eruptions are still unclear. In this study, we solved this problem by systematically surveying the nonlinear dynamics caused by a wide variety of magnetic structures in terms of three-dimensional magnetohydrodynamic simulations. As a result, we determined that two different types of small magnetic structures favor the onset of solar eruptions. These structures, which should appear near the magnetic polarity inversion line (PIL), include magnetic fluxes reversed to the potential component or the nonpotential component of major field on the PIL. In addition, we analyzed two large flares, the X-class flare on December 13, 2006 and the M-class flare on February 13, 2011, using imaging data provided by the Hinode satellite, and we demonstrated that they conform to the simulation predictions. These results suggest that forecasting of solar eruptions is possible with sophisticated observation of a solar magnetic field, although the lead time must be limited by the time scale of changes in the small magnetic structures.

No author has a financial or proprietary interest in any material or method mentioned.

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We present a comparison of the Solar Dynamics Observatory (SDO) analysis of NOAA Active Region (AR) 11158 and numerical simulations of flux-tube emergence, aiming to investigate the formation process of the flareproductive AR. First, we use SDO/Helioseismic and Magnetic Imager (HMI) magnetograms to investigate the photospheric evolution and Atmospheric Imaging Assembly (AIA) data to analyze the relevant coronal structures. Key features of this quadrupolar region are a long sheared polarity inversion line (PIL) in the central δ-sunspots and a coronal arcade above the PIL. We find that these features are responsible for the production of intense flares including an X2.2-class event. Based on the observations, we then propose two possible models for the creation of AR 11158 and conduct flux emergence simulations of the two cases to reproduce this AR. Case 1 is the emergence of a single flux tube, which is split into two in the convection zone and emerges at two locations, while Case 2 is the emergence of two isolated but neighboring tubes. We find that, in Case 1, a sheared PIL and a coronal arcade are created in the middle of the region, which agrees with the AR 11158 observation. However, Case 2 never build a clear PIL, which deviates from the observation. Therefore, we conclude that the flare-productive AR 11158 is, between the two cases, more likely to be created from a single split emerging flux than two independent flux bundles.

Context. The anelastic approximation is often adopted in numerical calculations with low Mach numbers, such as those including stellar internal convection. This approximation requires so-called frequent global communication, because of an elliptic partial differential equation. Frequent global communication is, however, negative factor for the parallel computing performed with a large number of CPUs. Aims. We test the validity of a method that artificially reduces the speed of sound for the compressible fluid equations in the context of stellar internal convection. This reduction in the speed of sound leads to longer time steps despite the low Mach number, while the numerical scheme remains fully explicit and the mathematical system is hyperbolic, thus does not require frequent global communication. Methods. Two-and three-dimensional compressible hydrodynamic equations are solved numerically. Some statistical quantities of solutions computed with different effective Mach numbers (owing to the reduction in the speed of sound) are compared to test the validity of our approach. Results. Numerical simulations with artificially reduced speed of sound are a valid approach as long as the effective Mach number (based on the lower speed of sound) remains less than 0.7.

We report a detailed event analysis on the M6.6-class flare in the active region (AR) NOAA 11158 on 2011 February 13. AR 11158, which consisted of two major emerging bipoles, showed prominent activities including one X-and several M-class flares. In order to investigate the magnetic structures related to the M6.6 event, particularly the formation process of a flare-triggering magnetic region, we analyzed multiple spacecraft observations and numerical results of a flare simulation. We observed that, in the center of this quadrupolar AR, a highly sheared polarity inversion line (PIL) was formed through proper motions of the major magnetic elements, which built a sheared coronal arcade lying over the PIL. The observations lend support to the interpretation that the target flare was triggered by a localized magnetic region that had an intrusive structure, namely a positive polarity penetrating into a negative counterpart. The geometrical relationship between the sheared coronal arcade and the triggering region was consistent with the theoretical flare model based on the previous numerical study. We found that the formation of the trigger region was due to a continuous accumulation of the small-scale magnetic patches. A few hours before the flare occurrence, the series of emerged/advected patches reconnected with a preexisting fields. Finally, the abrupt flare eruption of the M6.6 event started around 17:30 UT. Our analysis suggests that, in a triggering process of a flare activity, all magnetic systems of multiple scales, not only the entire AR evolution but also the fine magnetic elements, are altogether involved. Subject headings: Sun: activity -Sun: flares -Sun: magnetic fields Recently, a systematic study of three-dimensional magnetohydrodynamic (MHD) simulations in terms of the flare-triggering mechanisms has been performed by Kusano et al. (2012). They modeled the preexisting coronal arcade overlying the PIL of an AR and a triggering field injected at the bottom boundary. By varying the shear angle of the coronal arcade and the azimuth angle of the injected flux, they systematically surveyed the conditions of the flare onset. As a result, it is found that there are two different types for the flare onset depending on the azimuth angle of the injected flux (Figure 1). One is the opposite-polarity (OP) case, where the injected bipole on the PIL has an opposite orientation to the overlying arcade (Panel a), and the other is the reversed-shear (RS) case, where the azimuth of the bipole is sheared in a reversed sense to the arcade (Panel b).

Frequencies of magnetic patch processes on supergranule boundary, namely flux emergence, splitting, merging, and cancellation, are investigated through an automatic detection. We use a set of line of sight magnetograms taken by the Solar Optical Telescope (SOT) on board Hinode satellite. We found 1636 positive patches and 1637 negative patches in the data set, whose time duration is 3.5 hours and field of view is 112" × 112". Total numbers of magnetic processes are followed: 493 positive and 482 negative splittings, 536 positive and 535 negative mergings, 86 cancellations, and 3 emergences. Total numbers of emergence and cancellation are significantly smaller than those of splitting and merging. Further, frequency dependences of merging and splitting processes on flux content are investigated. Merging has a weak dependence on flux content only with a powerlaw index of 0.28. Timescale for splitting is found to be independent of parent flux content before splitting, which corresponds to ∼33 minutes. It is also found that patches split into any flux contents with a same probability. This splitting has a power-law distribution of flux content with an index of −2 as a time independent solution. These results support that the frequency distribution of flux content in the analyzed flux range is rapidly maintained by merging and splitting, namely surface processes. We suggest a model for frequency distributions of cancellation and emergence based on this idea.