We investigate the statistical properties of Ellerman bombs in the dynamic emerging flux region NOAA Active Region 8844, underneath an expanding arch filament system. High-resolution chromospheric H filtergrams (spatial resolution 0>8), as well as photospheric vector magnetograms (spatial resolution 0>5) and Dopplergrams, have been acquired by the balloon-borne Flare Genesis Experiment. H observations reveal the first '' seeing-free '' data set on Ellerman bombs and one of the largest samples of these events. We find that Ellerman bombs occur and recur in preferential locations in the low chromosphere, either above or in the absence of photospheric neutral magnetic lines. Ellerman bombs are associated with photospheric downflows, and their loci follow the transverse mass flows on the photosphere. They are small-scale events, with typical size 1>8 Â 1>1 , but this size depends on the instrumental resolution. A large number of Ellerman bombs are probably undetected, owing to limited spatial resolution. Ellerman bombs occur in clusters that exhibit fractal properties. The fractal dimension, with an average value $1.4, does not change significantly in the course of time. Typical parameters of Ellerman bombs are interrelated and obey power-law distribution functions, as in the case of flaring and subflaring activity. We find that Ellerman bombs may occur on separatrix, or quasi-separatrix, layers, in the low chromosphere. A plausible triggering mechanism of Ellerman bombs is stochastic magnetic reconnection caused by the turbulent evolution of the low-lying magnetic fields and the continuous reshaping of separatrix layers. The total energies of Ellerman bombs are estimated in the range (10 27 , 10 28 ) ergs, the temperature enhancement in the radiating volume is $2 Â 10 3 K, and the timescale of radiative cooling is short, of the order of a few seconds. The distribution function of the energies of Ellerman bombs exhibits a power-law shape with an index $À2.1. This suggests that Ellerman bombs may contribute significantly to the heating of the low chromosphere in emerging flux regions.

No abstract

We report here on the present state-of-the-art in algorithms used for resolving the 180 • ambiguity in solar vector magnetic field measurements. With present observations and techniques, 268 T.R. METCALF ET AL. some assumption must be made about the solar magnetic field in order to resolve this ambiguity. Our focus is the application of numerous existing algorithms to test data for which the correct answer is known. In this context, we compare the algorithms quantitatively and seek to understand where each succeeds, where it fails, and why. We have considered five basic approaches: comparing the observed field to a reference field or direction, minimizing the vertical gradient of the magnetic pressure, minimizing the vertical current density, minimizing some approximation to the total current density, and minimizing some approximation to the field's divergence. Of the automated methods requiring no human intervention, those which minimize the square of the vertical current density in conjunction with an approximation for the vanishing divergence of the magnetic field show the most promise.

Solar flares produce radiation which can have an almost immediate effect on the near-Earth environment, making it crucial to forecast flares in order to mitigate their negative effects. The number of published approaches to flare forecasting using photospheric magnetic field observations has proliferated, with varying claims about how well each works. Because of the different analysis techniques and data sets used, it is essentially impossible to compare the results from the literature. This problem is exacerbated by the low event rates of large solar flares. The challenges of forecasting rare events have long been recognized in the meteorology community, but have yet to be fully acknowledged by the space weather community. During the interagency workshop on "all clear" forecasts held in Boulder, CO in 2009, the performance of a number of existing algorithms was compared on common data sets, specifically line-of-sight magnetic field and continuum intensity images from MDI, with consistent definitions of what constitutes an event. We demonstrate the importance of making such systematic comparisons, and of using standard verification statistics to determine what constitutes a good prediction scheme. When a comparison was made in this fashion, no one method clearly outperformed all others, which may in part be due to the strong correlations among the parameters used by different methods to characterize an active region. For M-class flares and above, the set of methods tends towards a weakly positive skill score (as measured with several distinct metrics), with no participating method proving substantially better than climatological forecasts.

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, MEF's estimates of the fluxes of magnetic energy and helicity were far more accurate than any other method's. 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-plasma, and therefore do not realistically model photospheric evolution.

Shortly after the seminal paper "Self-Organized Criticality: An explanation of 1/f noise" 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

Magnetic helicity is a conserved quantity of ideal magneto-hydrodynamics characterized by an inverse turbulent cascade. Accordingly, it is often invoked as one of the basic physical quantities driving the generation and structuring of magnetic fields in a variety of astrophysical and laboratory plasmas. We provide here the first systematic comparison of six existing methods for the estimation of the helicity of magnetic fields known in a finite volume. All such methods are reviewed, benchmarked, and compared with each other, and specifically tested for accuracy and sensitivity to errors. To that purpose, we consider four groups of numerical tests, ranging from solutions of the three-dimensional, force-free equilibrium, to magneto-hydrodynamical numerical simulations. Almost all methods are found to produce the same value of magnetic helicity within few percent in all tests. In the more solar-relevant and realistic of the tests employed here, the simulation of an eruptive flux rope, the spread in the computed values obtained by all but one method is only 3 %, indicating the reliability and mutual consistency of such methods in appropriate parameter ranges. However, methods show differences in the sensitivity to numerical resolution and to errors in the solenoidal property of the input fields. In addition to finite volume methods, we also briefly discuss a method that estimates helicity from the field lines' twist, and one that exploits the field's value at one boundary and a coronal minimal connectivity instead of a pre-defined three-dimensional magnetic-field solution.

We propose a forecasting approach for solar flares based on data from Solar Cycle 24, taken by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) mission. In particular, we use the Spaceweather HMI Active Region Patches (SHARP) product that facilitates cut-out magnetograms of solar active regions (AR) in the Sun in near-realtime (NRT), K. Florios cflorios@aueb.gr I. Kontogiannis K. Florios et al.taken over a five-year interval (2012 -2016). Our approach utilizes a set of thirteen predictors, which are not included in the SHARP metadata, extracted from line-of-sight and vector photospheric magnetograms. We exploit several Machine Learning (ML) and Conventional Statistics techniques to predict flares of peak magnitude >M1 and >C1, within a 24 h forecast window. The ML methods used are multi-layer perceptrons (MLP), support vector machines (SVM) and random forests (RF). We conclude that random forests could be the prediction technique of choice for our sample, with the second best method being multi-layer perceptrons, subject to an entropy objective function. A Monte Carlo simulation showed that the best performing method gives accuracy ACC=0.93(0.00), true skill statistic TSS=0.74(0.02) and Heidke skill score HSS=0.49(0.01) for >M1 flare prediction with probability threshold 15% and ACC=0.84(0.00), TSS=0.60(0.01) and HSS=0.59(0.01) for >C1 flare prediction with probability threshold 35%.