D. Shiota

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.

Predicting Observational Signatures of Coronal Heating by Alfvén Waves and Nanoflares

Alfv?n waves can dissipate their energy by means of nonlinear mechanisms, and constitute good candidates to heat and maintain the solar corona to the observed few million degrees. Another appealing candidate is nanoflare reconnection heating, in which energy is released through many small magnetic reconnection events. Distinguishing the observational features of each mechanism is an extremely difficult task. On the other hand, observations have shown that energy release processes in the corona follow a power-law distribution in frequency whose index may tell us whether small heating events contribute substantially to the heating or not. In this work we show a link between the power-law index and the operating heating mechanism in a loop. We set up two coronal loop models: in the first model Alfv?n waves created by footpoint shuffling nonlinearly convert to longitudinal modes which dissipate their energy through shocks; in the second model numerous heating events with nanoflare-like energies are input randomly along the loop, either distributed uniformly or concentrated at the footpoints. Both models are based on a 1.5-dimensional MHD code. The obtained coronae differ in many aspects; for instance, in the flow patterns along the loop and the simulated intensity profile that Hinode XRT would observe. The intensity histograms display power-law distributions whose indexes differ considerably. This number is found to be related to the distribution of the shocks along the loop. We thus test the observational signatures of the power-law index as a diagnostic tool for the above heating mechanisms and the influence of the location of nanoflares.

BUILDUP AND RELEASE OF MAGNETIC TWIST DURING THE X3.4 SOLAR FLARE OF 2006 DECEMBER 13

We analyze the temporal evolution of the three-dimensional magnetic structure of the flaring active region (AR) NOAA 10930 by using the nonlinear force-free fields extrapolated from the photospheric vector magnetic fields observed by the Solar Optical Telescope on board Hinode. This AR consisted mainly of two types of twisted magnetic field lines: one has a strong negative (left-handed) twist due to the counterclockwise motion of the positive sunspot and is rooted in the regions of both polarities in the sunspot at a considerable distance from the polarity inversion line (PIL). In the flare phase, dramatic magnetic reconnection occurs in those negatively twisted lines in which the absolute value of the twist is greater than a half-turn. The other type consists of both positively and negatively twisted field lines formed relatively close to the PIL between two sunspots. A strong Ca II image began to brighten in this region of mixed polarity, in which the positively twisted field lines were found to be injected within one day across the pre-existing negatively twisted region, along which strong currents were embedded. Consequently, the central region near the PIL contains a mix of differently twisted field lines and the strong currents may play a prominent role in flare onset.

NONLINEAR FORCE-FREE EXTRAPOLATION OF THE CORONAL MAGNETIC FIELD BASED ON THE MAGNETOHYDRODYNAMIC RELAXATION METHOD

We develop a nonlinear force-free field (NLFFF) extrapolation code based on the magnetohydrodynamic (MHD) relaxation method. We extend the classical MHD relaxation method in two important ways. First, we introduce an algorithm initially proposed by Dedner et al. to effectively clean the numerical errors associated with ? ? B . Second, the multigrid type method is implemented in our NLFFF to perform direct analysis of the high-resolution magnetogram data. As a result of these two implementations, we successfully extrapolated the high resolution force-free field introduced by Low & Lou with better accuracy in a drastically shorter time. We also applied our extrapolation method to the MHD solution obtained from the flux-emergence simulation by Magara. We found that NLFFF extrapolation may be less effective for reproducing areas higher than a half-domain, where some magnetic loops are found in a state of continuous upward expansion. However, an inverse S-shaped structure consisting of the sheared and twisted loops formed in the lower region can be captured well through our NLFFF extrapolation method. We further discuss how well these sheared and twisted fields are reconstructed by estimating the magnetic topology and twist quantitatively.

A PLASMA β TRANSITION WITHIN A PROPAGATING FLUX ROPE

We present a 2.5 dimensional magnetohydrodynamic simulation of a magnetic flux rope (FR) propagating in the heliosphere and investigate the cause of the observed sharp plasma ? transition. Specifically, we consider a strong internal magnetic field and an explosive fast start, such that the plasma ? is significantly lower in the FR than in the sheath region that is formed ahead. This leads to an unusual FR morphology in the first stage of propagation, while the more traditional view (e.g., from space weather simulations like Enlil) of a pancake-shaped FR is observed as it approaches 1?AU. We investigate how an equipartition line, defined by a magnetic Weber number, surrounding a core region of a propagating FR, can demarcate a boundary layer where there is a sharp transition in the plasma ?. The substructure affects the distribution of toroidal flux, with the majority of the flux remaining in a small core region that maintains a quasi-cylindrical structure. We quantitatively investigate a locus of points where the kinetic energy density of the relative inflow field is equal to the energy density of the transverse magnetic field (i.e., effective tension force). The simulation provides compelling evidence that at all heliocentric distances the distribution of toroidal magnetic flux away from the FR axis is not linear, with 80% of the toroidal flux occurring within 40% of the distance from the FR axis. Thus, our simulation displays evidence that the competing ideas of a pancaking structure observed remotely can coexist with a quasi-cylindrical magnetic structure seen in situ.

Improvement of solar-cycle prediction: Plateau of solar axial dipole moment

Aims. We report the small temporal variation of the axial dipole moment near the solar minimum and its application to the solar cycle prediction by the surface flux transport (SFT) model. Methods. We measure the axial dipole moment using the photospheric synoptic magnetogram observed by the Wilcox Solar Observatory (WSO), the ESA/NASA Solar and Heliospheric Observatory Michelson Doppler Imager (MDI), and the NASA Solar Dynamics Observatory Helioseismic and Magnetic Imager (HMI). We also use the surface flux transport model for the interpretation and prediction of the observed axial dipole moment. Results. We find that the observed axial dipole moment becomes approximately constant during the period of several years before each cycle minimum, which we call the axial dipole moment plateau. The cross-equatorial magnetic flux transport is found to be small during the period, although the significant number of sunspots are still emerging. The results indicates that the newly emerged magnetic flux does not contributes to the build up of the axial dipole moment near the end of each cycle. This is confirmed by showing that the time variation of the observed axial dipole moment agrees well with that predicted by the SFT model without introducing new emergence of magnetic flux. These results allows us to predict the axial dipole moment in Cycle 24/25 minimum using the SFT model without introducing new flux emergence. The predicted axial dipole moment of Cycle 24/25 minimum is 60--80 percent of Cycle 23/24 minimum, which suggests the amplitude of Cycle 25 even weaker than the current Cycle 24. Conclusions. The plateau of the solar axial dipole moment is an important feature for the longer prediction of the solar cycle based on the SFT model.

Predicting observational signatures of coronal heating by Alfvén waves and nanoflares

Alfvenwavescandissipatetheirenergybymeansof nonlinearmechanisms,andconstitutegoodcandidatestoheat and maintain the solar corona to the observed few million degrees. Another appealing candidate is nanoflare re- connection heating, in which energy is released through many small magnetic reconnection events. Distinguishing the observational features of each mechanism is an extremely difficult task. On the other hand, observations have shown that energy release processes in the corona follow a power-law distribution in frequency whose index may tell uswhethersmallheatingeventscontributesubstantiallytotheheatingornot.Inthisworkweshowalinkbetweenthe power-law index and the operating heating mechanism in a loop. We set up two coronal loop models: in the first model Alfven waves created by footpoint shuffling nonlinearly convert to longitudinal modes which dissipate their energy throughshocks;inthesecondmodelnumerousheatingeventswithnanoflare-likeenergiesareinputrandomlyalongthe loop, either distributed uniformly or concentrated at the footpoints. Both models are based on a 1.5-dimensional MHD code. The obtained coronae differ in many aspects; for instance, in the flow patterns along the loop and the simulated intensity profile that HinodeXRTwould observe. The intensity histograms display power-law distributions whose indexes differ considerably. This number is found to be related to the distribution of the shocks along the loop. We thus test the observational signatures of the power-law index as a diagnostic tool for the above heating mechanisms and the influence of the location of nanoflares.