Naoto Nishizuka

25 Years of Self-Organized Criticality: Solar and Astrophysics

Shortly after the seminal paper “Self-Organized Criticality: An explanation of 1/fnoise” by Bak et al. (1987), the idea has been applied to solar physics, in “Avalanches and the Distribution of Solar Flares” by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme.

Twisting solar coronal jet launched at the boundary of an active region

Aims. A broad jet was observed in a weak magnetic eld area at the edge of active region NOAA 11106 that also produced other nearby recurring and narrow jets. The peculiar shape and magnetic environment of the broad jet raised the question of whether it was created by the same physical processes of previously studied jets with reconnection occurring high in the corona. Methods. We carried out a multi-wavelength analysis using the EUV images from the Atmospheric Imaging Assembly (AIA) and magnetic elds from the Helioseismic and Magnetic Imager (HMI) both on-board the SDO satellite, which we coupled to a high-resolution, nonlinear force-free eld extrapolation. Local correlation tracking was used to identify the photospheric motions that triggered the jet, and time-slices were extracted along and across the jet to unveil its complex nature. A topological analysis of the extrapolated eld was performed and was related to the observed features. Results. The jet consisted of many dierent threads that expanded in around 10 minutes to about 100 Mm in length, with the bright features in later threads moving faster than in the early ones, reaching a maximum speed of about 200 km s 1 . Time-slice analysis revealed a striped pattern of dark and bright strands propagating along the jet, along with apparent damped oscillations across the jet. This is suggestive of a (un)twisting motion in the jet, possibly an Alfv

Fermi acceleration in plasmoids interacting with fast shocks of reconnection via fractal reconnection.

We propose the particle acceleration model coupled with multiple plasmoid ejections in a solar flare. Unsteady reconnection produces plasmoids in a current sheet and ejects them out to the fast shocks, where particles in a plasmoid are reflected upstream the shock front by magnetic mirror effect. As the plasmoid passes through the shock front, the reflection distance becomes shorter and shorter driving Fermi acceleration, until it becomes proton Larmor radius. The fractal distribution of plasmoids may also have a role in naturally explaining the power-law spectrum in nonthermal emissions.

THE ROLE OF A FLUX ROPE EJECTION IN A THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC SIMULATION OF A SOLAR FLARE

We investigated the dynamic evolution of a three-dimensional (3D) flux rope eruption and magnetic reconnection process in a solar flare by simply extending the two-dimensional (2D) resistive magnetohydrodynamic simulation model of solar flares with low β plasma to a 3D model. We succeeded in reproducing a current sheet and bi-directional reconnection outflows just below the flux rope during the eruption in our 3D simulations. We calculated four cases of a strongly twisted flux rope and a weakly twisted flux rope in 2D and 3D simulations. The time evolution of a weakly twisted flux rope in the 3D simulation shows behaviors similar to those of the 2D simulation, while a strongly twisted flux rope in the 3D simulation clearly shows a different time evolution from the 2D simulation except for the initial phase evolution. The ejection speeds of both strongly and weakly twisted flux ropes in 3D simulations are larger than in the 2D simulations, and the reconnection rates in 3D cases are also larger than in the 2D cases. This indicates positive feedback between the ejection speed of a flux rope and the reconnection rate even in the 3D simulation, and we conclude that the plasmoid-induced reconnection model can be applied to 3D. We also found that small-scale plasmoids are formed inside a current sheet and make it turbulent. These small-scale plasmoid ejections have a role in locally increasing the reconnection rate intermittently as observed in solar flares, coupled with a global eruption of a flux rope.

PARTICLE ACCELERATION IN PLASMOID EJECTIONS DERIVED FROM RADIO DRIFTING PULSATING STRUCTURES

We report observations of slowly drifting pulsating structures (DPSs) in the 0.8-4.5 GHz frequency range of the RT4 and RT5 radio spectrographs at Ondřejov Observatory, between 2002 and 2012. We found 106 events of DPSs, which we classified into four cases: (I) single events with a constant frequency drift (12 events), (II) multiple events occurring in the same flare with constant frequency drifts (11 events), (III) single or multiple events with increasing or decreasing frequency drift rates (52 events), and (IV) complex events containing multiple events occurring at the same time in a different frequency range (31 events). Many DPSs are associated with hard X-ray (HXR) bursts (15-25 keV) and soft X-ray (SXR) gradient peaks, as they typically occurred at the beginning of HXR peaks. This indicates that DPS events are related to the processes of fast energy release and particle acceleration. Furthermore, interpreting DPSs as signatures of plasmoids, we measured their ejection velocity, their width, and their height from the DPS spectra, from which we also estimated the reconnection rate and the plasma beta. In this interpretation, constant frequency drift indicates a constant velocity of a plasmoid, and an increasing/decreasing frequency drift indicates a deceleration/acceleration of a plasmoid ejection. The reconnection rate shows a good positive correlation with the plasmoid velocity. Finally we confirmed that some DPS events show plasmoid counterparts in Solar Dynamics Observatory/Atmospheric Imaging Assembly images.

Solar Flare Prediction Model with Three Machine-learning Algorithms using Ultraviolet Brightening and Vector Magnetograms

We developed a flare prediction model using machine learning, which is optimized to predict the maximum class of flares occurring in the following 24 h. Machine learning is used to devise algorithms that can learn from and make decisions on a huge amount of data. We used solar observation data during the period 2010-2015, such as vector magnetogram, ultraviolet (UV) emission, and soft X-ray emission taken by the Solar Dynamics Observatory and the Geostationary Operational Environmental Satellite. We detected active regions from the full-disk magnetogram, from which 60 features were extracted with their time differentials, including magnetic neutral lines, the current helicity, the UV brightening, and the flare history. After standardizing the feature database, we fully shuffled and randomly separated it into two for training and testing. To investigate which algorithm is best for flare prediction, we compared three machine learning algorithms: the support vector machine (SVM), k-nearest neighbors (k-NN), and extremely randomized trees (ERT). The prediction score, the true skill statistic (TSS), was higher than 0.9 with a fully shuffled dataset, which is higher than that for human forecasts. It was found that k-NN has the highest performance among the three algorithms. The ranking of the feature importance showed that the previous flare activity is most effective, followed by the length of magnetic neutral lines, the unsigned magnetic flux, the area of UV brightening, and the time differentials of features over 24 h, all of which are strongly correlated with the flux emergence dynamics in an active region.

HARD X-RAY AND MICROWAVE EMISSIONS FROM SOLAR FLARES WITH HARD SPECTRAL INDICES

We analyze 10 flare events that radiate intense hard X-ray (HXR) emission with significant photons over 300 keV to verify that the electrons that have a common origin of acceleration mechanism and energy power-law distribution with solar flares emit HXRs and microwaves. Most of these events have the following characteristics. HXRs emanate from the footpoints of flare loops, while microwaves emanate from the tops of flare loops. The time profiles of the microwave emission show delays of peak with respect to those of the corresponding HXR emission. The spectral indices of microwave emissions show gradual hardening in all events, while the spectral indices of the corresponding HXR emissions are roughly constant in most of the events, though rather rapid hardening is simultaneously observed in some for both indices during the onset time and the peak time. These characteristics suggest that the microwave emission emanates from the trapped electrons. Then, taking into account the role of the trapping of electrons for the microwave emission, we compare the observed microwave spectra with the model spectra calculated by a gyrosynchrotron code. As a result, we successfully reproduce the eight microwave spectra. From this result, we conclude that the electrons that have a common acceleration and a common energy distribution with solar flares emit both HXR and microwave emissions in the eight events, though microwave emission is contributed to by electrons with much higher energy than HXR emission.

A LABORATORY EXPERIMENT OF MAGNETIC RECONNECTION: OUTFLOWS, HEATING, AND WAVES IN CHROMOSPHERIC JETS

Hinode observations have revealed intermittent recurrent plasma ejections/jets in the chromosphere. These are interpreted as a result of non-perfectly anti-parallel magnetic reconnection, i.e. component reconnection, between a twisted magnetic flux tube and the pre-existing coronal/chromospheric magnetic field, though the fundamental physics of component reconnection is unrevealed. In this paper, we experimentally reproduced the magnetic configuration and investigated the dynamics of plasma ejections, heating and wave generation triggered by component reconnection in the chromosphere. We set plasma parameters as in the chromosphere (density 10^14 cm^-3, temperature 5-10 eV, i.e. (5-10)x10^4 K, and reconnection magnetic field 200 G) using argon plasma. Our experiment shows bi-directional outflows with the speed of 5 km/s at maximum, ion heating in the downstream area over 30 eV and magnetic fluctuations mainly at 5-10 us period. We succeeded in qualitatively reproducing chromospheric jets, but quantitatively we still have some differences between observations and experiments such as jet velocity, total energy and wave frequency. Some of them can be explained by the scale gap between solar and laboratory plasma, while the others probably by the difference of microscopy and macroscopy, collisionality and the degree of ionization, which have not been achieved in our experiment.

New developments in rotating and linear motion mechanisms used in contamination sensitive space telescopes

We have been developing a rotating mechanism and a linear motion mechanism for their usage in contamination sensitive space telescopes. They both are needed for ~1.4 meter optical telescope and its focal plane instrument onboard SOLAR-C, the next-generation spaceborne solar observatory following Hinode. Highly reliable long life performance, low outgassing properties, and low level of micro-vibration are required along with their scientific performance. With the proto-type mechanisms, the long life performance and outgassing properties of the mechanisms have been evaluated in vacuum chambers. The level of micro-vibration excited during the operations of the rotating mechanism was measured by operating it on the Kestler table. This paper provides the overall descriptions of our mechanism developments.

Deep Flare Net (DeFN) Model for Solar Flare Prediction

We developed a solar flare prediction model using a deep neural network (DNN), named Deep Flare Net (DeFN). The model can calculate the probability of flares occurring in the following 24 h in each active region, which is used to determine the most likely maximum classes of flares via a binary classification (e.g., >=M class versus =C class versus =10^7 K) and the X-ray and 131 A intensity data 1 and 2 h before an image. For operational evaluation, we divided the database into two for training and testing: the dataset in 2010-2014 for training and the one in 2015 for testing. The DeFN model consists of deep multilayer neural networks, formed by adapting skip connections and batch normalizations. To statistically predict flares, the DeFN model was trained to optimize the skill score, i.e., the true skill statistic (TSS). As a result, we succeeded in predicting flares with TSS=0.80 for >=M-class flares and TSS=0.63 for >=C-class flares. Note that in usual DNN models, the prediction process is a black box. However, in the DeFN model, the features are manually selected, and it is possible to analyze which features are effective for prediction after evaluation.