Kanya Kusano

Nonlinear Force‐free Field Modeling of a Solar Active Region around the Time of a Major Flare and Coronal Mass Ejection

Solar flares and coronal mass ejections are associated with rapid changes in field connectivity and are powered by the partial dissipation of electrical currents in the solar atmosphere. A critical unanswered question is whether the currents involved are induced by the motion of preexisting atmospheric magnetic flux subject to surface plasma flows or whether these currents are associated with the emergence of flux from within the solar convective zone. We address this problem by applying state-of-the-art nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA AR 10930 around the time of a powerful X3.4 flare. We compute 14 NLFFF models with four different codes and a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We discuss the relative merits of these models in a general critique of present abilities to model the coronal magnetic field based on surface vector field measurements. For our application in particular, we find a fair agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the ~1032 erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection.

Measurement of Magnetic Helicity Injection and Free Energy Loading into the Solar Corona

We develop a new methodology that can determine magnetic helicity flux as well as Poynting flux across the photosphere based on magnetograph observation. By applying this method, we study the injection mechanism of magnetic helicity and magnetic free energy into the solar corona. In order to derive the helicity and energy fluxes, first the velocity tangential to the solar surface is constructed by applying a correlation tracking technique on the magnetic observation, and second, the velocity component normal to the photosphere is derived from the condition that the magnetic evolution must be consistent with the induction equation. Through this procedure, we can determine the helicity and energy fluxes separately for the shear motion effect and for the flux emergence effect. Based on this new method, NOAA Active Region 8100 was analyzed from 1997 November 1 to 5 using data observed by the Solar and Heliospheric Observatory Michelson Doppler Interferometer and the vector magnetograph at the National Astronomical Observatory of Japan (NAOJ) in Tokyo. The results indicate that the photospheric shear motion and the flux emergence process have equally contributed to the helicity injection and have supplied magnetic helicity of opposite signs into this active region.

MAGNETIC FIELD STRUCTURES TRIGGERING SOLAR FLARES AND CORONAL MASS EJECTIONS

Solar flares and coronal mass ejections, 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 2006 December 13 and the M-class flare on 2011 February 13, 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 timescale of changes in the small magnetic structures.

Tests and Comparisons of Velocity-Inversion Techniques

Recently, several methods that measure the velocity of magnetized plasma from time series of photospheric vector magnetograms have been developed. Velocity fields derived using such techniques can be used both to determine the fluxes of magnetic energy and helicity into the corona, which have important consequences for understanding solar flares, coronal mass ejections, and the solar dynamo, and to drive time-dependent numerical models of coronal magnetic fields. To date, these methods have not been rigorously tested against realistic, simulated data sets, in which the magnetic field evolution and velocities are known. Here we present the results of such tests using several velocity-inversion techniques applied to synthetic magnetogram data sets, generated from anelastic MHD simulations of the upper convection zone with the ANMHD code, in which the velocity field is fully known. Broadly speaking, the MEF, DAVE, FLCT, IM, and ILCT algorithms performed comparably in many categories. While DAVE estimated the magnitude and direction of velocities slightly more accurately than the other methods, MEFs estimates of the fluxes of magnetic energy and helicity were far more accurate than any other methods. Overall, therefore, the MEF algorithm performed best in tests using the ANMHD data set. We note that ANMHD data simulate fully relaxed convection in a high-β plasma, and therefore do not realistically model photospheric evolution.

The super‐droplet method for the numerical simulation of clouds and precipitation: a particle‐based and probabilistic microphysics model coupled with a non‐hydrostatic model

A novel, particle-based, probabilistic approach for the simulation of cloud microphysics is proposed, which is named the super-droplet method (SDM). This method enables the accurate simulation of cloud microphysics with a less demanding cost in computation. SDM is applied to a warm-cloud system, which incorporates sedimentation, condensation/evaporation and stochastic coalescence. The methodology to couple super-droplets and a non-hydrostatic model is also developed. It is confirmed that the result of our Monte Carlo scheme for the stochastic coalescence of super-droplets agrees fairly well with the solutions of the stochastic coalescence equation. The behaviour of the model is evaluated using a simple test problem, that of a shallow maritime cumulus formation initiated by a warm bubble. Possible extensions of SDM are briefly discussed. A theoretical analysis suggests that the computational cost of SDM becomes lower than the spectral (bin) method when the number of attributes—the variables that identify the state of each super-droplet—becomes larger than some critical value, which we estimate to be in the range . Copyright

TWIST AND CONNECTIVITY OF MAGNETIC FIELD LINES IN THE SOLAR ACTIVE REGION NOAA 10930

Twist and connectivity of magnetic field lines in the flare-productive active region NOAA 10930 are investigated in terms of the vector magnetograms observed by the Solar Optical Telescope on board the Hinode satellite and the nonlinear force-free field (NLFFF) extrapolation. First, we show that the footpoints of magnetic field lines reconstructed by the NLFFF correspond well to the conjugate pair of highly sheared flare ribbons on the Ca II images, which were observed by Hinode as an X3.4 class flare on 2006 December 13. This demonstrates that the NLFFF extrapolation may be used to analyze the magnetic field connectivity. Second, we find that the twist of magnetic field lines anchored on the flare ribbons increased as the ribbons moved away from the magnetic polarity inversion line in the early phase of the flare. This suggests that magnetic reconnection might commence from a region located below the most strongly twisted field. Third, we reveal that the magnetic flux twisted more than a half turn and gradually increased during the last one day prior to the onset of the flare, and that it quickly decreased for two hours after the flare. This is consistent with the store-and-release scenario of magnetic helicity. However, within this active region, only a small fraction of the flux was twisted by more than one full turn and the field lines that reconnected first were twisted less than one turn. These results imply that the kink mode instability could hardly occur, at least before the onset of flare. Based on our results, we discuss the trigger process of solar flares.

Simulation Study of the Formation Mechanism of Sigmoidal Structure in the Solar Corona

The formation mechanism of sigmoidal structure in the solar coronal magnetic field is studied using the three-dimensional magnetohydrodynamic numerical simulations, based on the so-called reversed-shear flare model recently proposed by Kusano et al. The simulation results clearly indicate that magnetic reconnection driven by the resistive tearing mode instability growing on the magnetic shear inversion layer can cause the spontaneous formation of sigmoidal structure. Furthermore, it is also numerically demonstrated that the formation of the sigmoids can be followed by the explosive energy liberation, if the sigmoids contain sufficient magnetic flux. This implies that the reversed-shear flare model can provide a self-consistent explanation for the formation of sigmoids as well as for the onset of eruption, which is driven by magnetic reconnection above sigmoids. The geometric relationship between the sigmoidal structure and the minimum energy state predicted by J. B. Taylor in 1974 is examined. The result suggests that the sigmoidal formation could be understood as a manifestation of the minimum energy state, which has the excess magnetic helicity compared to the bifurcation criterion of the linear force-free field. The consistency with the observations of magnetic helicity is also discussed.

STUDY ON THE TRIGGERING PROCESS OF SOLAR FLARES BASED ON HINODE/SOT OBSERVATIONS

We investigated four major solar flare events that occurred in active regions NOAA 10930 (2006 December 13 and 14) and NOAA 11158 (2011 February 13 and 15) by using data observed by the Solar Optical Telescope on board the Hinode satellite. To reveal the trigger mechanism of solar flares, we analyzed the spatio-temporal correlation between the detailed magnetic field structure and the emission image of the Ca II H line at the central part of flaring regions for several hours prior to the onset of the flares. In all the flare events, we observed that the magnetic shear angle in the flaring regions exceeded 70°, as well as that characteristic magnetic disturbances developed at the centers of flaring regions in the pre-flare phase. These magnetic disturbances can be classified into two groups depending on the structure of their magnetic polarity inversion lines; the so-called opposite-polarity and reversed-shear magnetic field recently proposed by our group, although the magnetic disturbance in one event of the four samples is too subtle to clearly recognize the detailed structure. The result suggests that some major solar flares are triggered by rather small magnetic disturbances. We also show that the critical size of the flare-trigger field varies among flare events and briefly discuss how the flare-trigger process depends on the evolution of active regions.

Three-dimensional Simulation Study of Flux Rope Dynamics in the Solar Corona

The three-dimensional stability and the nonlinear dynamics of a flux rope embedded in a magnetic arcade are investigated using magnetohydrodynamic (MHD) simulations, with the goal of understanding the mechanism of filament eruption in the solar corona. The flux rope equilibrium proposed by Forbes in 1990 is adopted as the initial state of the three-dimensional simulation, and we find that the equilibrium is linearly unstable to the kink mode instability, when the system approaches the loss-of-equilibrium state. The three-dimensional simulation demonstrates that when the flux rope is long enough, it can escape from the arcade at an almost constant speed after the accelerated launching phase due to the kink instability. The continuous ascending of the flux rope is driven by the nonlinear growth of several kink modes. In the case of a short flux rope, however, the flux rope ascension fails at some height. This suggests that the flux rope eruption must proceed through the multiple stages, which are driven by the loss of stability in the launching phase and by the loss of equilibrium in the late ascending phase. Since the short rope could not come up to the critical height for the transition from the first to the second stage, the ascending must stop. The role of magnetic reconnection in the late ascending phase and the formation mechanism of density cavity, which corresponds to dimming region observed in CMEs, is also discussed using the simulation results.

Non-linear coupling effects on the relaxation process in the reversed field pinch

The relaxation process in the reversed field pinch has been studied extensively with three-dimensional magnetohydrodynamic simulations. It is found that the non-linear coupling between multiple helicity modes plays a leading role in the relaxation process. Specifically, the (m; n)=(0; 1) island is excited as a result of non-linear coupling between the linearly unstable m=l modes, with a toroidal mode number difference of one. The m=0 island is then subject to axisymmetric non-linear reconnection whereby reversed flux is effectively generated in the outer region. It should be noted that although the axisymmetric non-linear reconnection of m=0 island is the dominant relaxation process, helical non-linear reconnection of linearly unstable m=l modes also plays some role in the relaxation of the whole system. It is also found that through this multiple helicity relaxation process, Taylors minimum energy state is realized. The simulation results are generally consistent with experimental observations in the sustainment phase. This indicates that the multiple helicity relaxation process is of fundamental importance in the maintenance of the reversed field during the sustainment phase as well as in the self-reversal during the set-up phase. The relation between relaxation and aspect ratio has also been examined and it is found that the relaxation process is not strongly affected by the aspect ratio.