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Studies of solar radio bursts play an important role in understanding the dynamics and acceleration processes behind solar space weather events, and the influence of solar magnetic activity on solar system planets. Similar low-frequency bursts detected from active M-dwarfs are expected to probe their space weather environments and therefore the habitability of their planetary companions. Active M-dwarfs produce frequent, powerful flares which, along with radio emission, reveal conditions within their atmospheres. However, to date, only one candidate solar-like coherent radio burst has been identified from these stars, preventing robust observational constraints on their space weather environment. During simultaneous optical and radio monitoring of the nearby dM5.5e star Proxima Centauri, we detected a bright, long-duration optical flare, accompanied by a series of intense, coherent radio bursts. These detections include the first example of an interferometrically detected coherent stellar radio burst temporally coincident with a flare, strongly indicating a causal relationship between these transient events. The polarization and temporal structure of the trailing long-duration burst enable us to identify it as a type IV burst. This represents the most compelling detection of a solar-like radio burst from another star to date. Solar type IV bursts are strongly associated with space weather events such as coronal mass ejections and solar energetic particle events, suggesting that stellar type IV bursts may be used as a tracer of stellar coronal mass ejections. We discuss the implications of this event for the occurrence of coronal mass ejections from Proxima Cen and other active M-dwarfs., Comment: 18 pages, 7 figures, 1 table. Published in the Astrophysical Journal

Modern mobile phones contain a three-axis microelectromechanical system (MEMS) gyroscope, capable of taking accurate measurements of the angular velocity along the three principal axes of the phone with a sampling rate of 100 Hz or better. If the phone is tossed in the air, then, neglecting air resistance, it is in free rotation (rotation in the absence of a torque) with respect to its centre of mass, and the phone's gyroscope can be used to record the rotational dynamics. This enables experimental investigation of free rotation. In this paper, we use a mobile phone to demonstrate the steady states for rotation of the phone about two of its principal axes, and the instability in rotation about the third corresponding to the intermediate moment of inertia. We also show the approximate conservation of angular momentum and rotational kinetic energy during motion in the air, and compare the data with numerical solution of Euler's equations for free rotation. Our results demonstrate the capability of smartphones for investigating free rotation, and should be of interest to college and university teachers developing "at home" physics labs for remote learning., Comment: 18 pages, 7 figures. Accepted for publication in the American Journal of Physics

The distributions of solar flare energies and waiting times have not been described simultaneously by a single physical model, yet. In this research, we investigate whether recent avalanche models can describe the distributions for both the released energies and waiting times of flares in an active region. Flaring events are simulated using the modified Lu and Hamilton model (Lu and Hamilton (1991), ApJ, 380, 89) and also the optimized model (Farhang et al. (2018), ApJ, 859, 41). Applying a probability balance equation approach, we study the statistics of the simulated flaring events and investigate the origin of the observed power law in the flare frequency-size distribution. The results indicate that the power law originates in the distribution of transition rates (the distribution of the probabilities of transitions between different energies) rather than the distribution of the energy of the active region. It is also observed that the waiting-time distribution of simulated flaring events follows a q-exponential function which approximates a simple Poisson distribution.

Since the early 1980s, decimetric spike bursts have been attributed to electron cyclotron maser emission (ECME) by the electrons that produce hard X-ray bursts as they precipitate into the chromosphere in the impulsive phase of a solar flare. Spike bursts are regarded as analogous to the auroral kilometric radiation (AKR), which is associated with the precipitation of auroral electrons in a geomagnetic substorm. Originally, a loss-cone-driven version of ECME, developed for AKR, was applied to spike bursts, but it is now widely accepted that a different, horseshoe-driven, version of EMCE applies to AKR. We explore the implications of the assumption that horseshoe-driven ECME also applies to spike bursts. We develop a 1D model for the acceleration of the electrons by a parallel electric field, and show that under plausible assumptions it leads to a horseshoe distribution of electrons in a solar flare. A second requirement for horseshoe-driven ECME is an extremely low plasma density, referred to as a density cavity. We argue that a coronal density cavity should develop in association with a hard X-ray burst, and that such a density cavity can overcome a long-standing problem with the escape of ECME through the second-harmonic absorption layer. Both the horseshoe distribution and the associated coronal density cavity are highly localized, and could not be resolved in the statistically large number of local precipitation regions needed to explain a hard X-ray burst. The model highlights the "number problem" in the supply of the electrons needed to explain a hard X-ray burst., Accepted for publication in Solar Physics

During eruptive flares, vector magnetograms show increasing horizontal magnetic field and downward Lorentz force in the Sun's photosphere around the polarity-inversion line. Such behavior has often been associated with the implosion conjecture and interpreted as the result of either momentum conservation while the eruption moves upward, or of the contraction of flare loops. We characterize the physical origin of these observed behaviors by analyzing a generic 3D MHD simulation of an eruptive flare. Even though the simulation was undesigned to recover the magnetic field and Lorentz force properties, it is fully consistent with them, and it provides key additional informations to understand them. The area where the magnetic field increases gradually develops between current ribbons, which spread away from each other and are connected to the coronal region. This area is merely the footprint of the coronal post-flare loops, whose contraction increases their shear field component and the magnetic energy density in line with the ideal induction equation. For simulated data, we computed the Lorentz force density map by applying the method used in observations. We obtained increase of the downward component of the Lorentz force density around the PIL -consistent with observations. However, this significantly differs from the Lorentz force density maps obtained directly from the 3D magnetic field and current. These results altogether question previous interpretations based on the implosion conjecture and momentum conservation with the CME, and rather imply that the observed increases in photospheric horizontal magnetic fields result from the reconnection-driven contraction of sheared flare-loops., Comment: 20 pages, 11 figures, accepted for publication in ApJ (April 19, 2019)

We review nonlinear force-free field (NLFFF) modeling of magnetic fields in active regions. The NLFFF model (in which the electric current density is parallel to the magnetic field) is often adopted to describe the coronal magnetic field, and numerical solutions to the model are constructed based on photospheric vector magnetogram boundary data. Comparative tests of NLFFF codes on sets of boundary data have revealed significant problems, in particular associated with the inconsistency of the model and the data. Nevertheless NLFFF modeling is often applied, in particular to flare-productive active regions. We examine the results, and discuss their reliability.

Rapid and stepwise changes of the magnetic field are often observed during flares but cannot be explained by models yet. Using a 45 min sequence of SDO/HMI 135 s fast-cadence vector magnetograms of the X1 flare on 2014-03-29 we construct, at each timestep, nonlinear force-free models for the coronal magnetic field. Observed flare-related changes in the line-of-sight magnetic field $B_{\rm LOS}$ at the photosphere and chromosphere are compared with changes in the magnetic fields in the models. We find a moderate agreement at the photospheric layer (the basis for the models), but no agreement at chromospheric layers. The observed changes at the photosphere and chromosphere are surprisingly different, and are unlikely to be reproduced by a force-free model. The observed changes are likely to require a change in the magnitude of the field, not just in its direction., Comment: accepted for publication in ApJ

Flares produce sudden and permanent changes in the horizontal photospheric magnetic field. In particular flares generally produce increased magnetic shear in the photospheric field along the neutral line. Recent observations show also that flares can produce sudden photospheric motion. We present a model for the observed changes as the response of the photosphere to a large-amplitude shear Alfv\'{e}n wave propagating down from the corona on either side of the neutral line. The Alfv\'{e}nic front is assumed to impact the photosphere close to the neutral line first, and then successively further away with time, such that the line of impact coincides with the flare ribbon. The wave introduces magnetic shear and velocity shear. The magnetic shear introduced at the photosphere has the same sign on either side of the neutral line, while the velocity shear has the opposite sign. We discuss the possibility that this process is responsible for particle acceleration in flares., Comment: 10 pages, 6 figures, accepted for publication in ApJ

The NOAA active region AR 11029 was a small but highly active sunspot region which produced 73 GOES soft X-ray flares. The flares appear to show a departure from the well known power-law frequency-size distribution. Specifically, too few GOES C-class and no M-class flares were observed by comparison with a power-law distribution (Wheatland in Astrophys. J. 710, 1324, 2010). This was conjectured to be due to the region having insufficient magnetic energy to power large events. We construct nonlinear force-free extrapolations of the coronal magnetic field of active region AR 11029 using data taken on 24 October by the SOLIS Vector-SpectroMagnetograph (SOLIS/VSM), and data taken on 27 October by the Hinode Solar Optical Telescope SpectroPolarimeter (Hinode/SP). Force-free modeling with photospheric magnetogram data encounters problems because the magnetogram data are inconsistent with a force-free model, and we employ a recently developed `self-consistency' procedure which addresses this and accommodates uncertainties in the boundary data (Wheatland and Regnier in Astrophys. J. 700, L88, 2009). We calculate the total energy and free energy of the self-consistent solution and find that the free energy was 4x10^29 erg on 24 October, and 7x10^31 erg on 27 October. An order of magnitude scaling between RHESSI non-thermal energy and GOES peak X-ray flux is established from a sample of flares from the literature and is used to estimate flare energies from observed GOES peak X-ray flux. Based on the scaling, we conclude that the estimated free energy of AR 11029 on 27 October when the flaring rate peaked is sufficient to power M-class or X-class flares, and hence the modeling does not appear to support the hypothesis that the absence of large flares is due to the region having limited energy.

A stochastic model for the energy of a flaring solar active region is presented, generalising and extending the approach of Wheatland & Glukhov (1998). The probability distribution for the free energy of an active region is described by the solution to a master equation involving deterministic energy input and random jump transitions downwards in energy (solar flares). It is shown how two observable distributions, the flare frequency-energy distribution and the flare waiting-time distribution, may be derived from the steady-state solution to the master equation, for given choices for the energy input and for the rates of flare transitions. An efficient method of numerical solution of the steady-state master equation is presented. Solutions appropriate for flaring, involving a constant rate of energy input and power-law distributed jump transition rates, are numerically investigated. The flare-like solutions exhibit power-law flare frequency-energy distributions below a high energy rollover, set by the largest energy the active region is likely to have. The solutions also exhibit approximately exponential (i.e. Poisson) waiting-time distributions, despite the rate of flaring depending on the free energy of the system., 24 pages, 6 figures. Accepted for publication in the Astrophysical Journal

Prediction of solar flares is an important task in solar physics. The occurrence of solar flares is highly dependent on the structure and the topology of solar magnetic fields. A new method for predicting large (M and X class) flares is presented, which uses machine learning methods applied to the Zernike moments of magnetograms observed by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) for a period of six years from 2 June 2010 to 1 August 2016. Magnetic field images consisting of the radial component of the magnetic field are converted to finite sets of Zernike moments and fed to the Support Vector Machine (SVM) classifier. Zernike moments have the capability to elicit unique features from any 2-D image, which may allow more accurate classification. The results indicate whether an arbitrary active region has the potential to produce at least one large flare. We show that the majority of large flares can be predicted within 48 hours before their occurrence, with only 10 false negatives out of 385 flaring active region magnetograms, and 21 false positives out of 179 non-flaring active region magnetograms. Our method may provide a useful tool for prediction of solar flares which can be employed alongside other forecasting methods., Comment: This paper has been accepted for publication in The Astrophysical Journal

There is a variety of observational evidence for solar flare sympathy, i.e., the triggering of a flare in one active region by a flare in another region. Models for solar flare statistics, however, usually ignore sympathy by assuming that flares occur as independent events. In this paper, we argue that statistical flare models should be robust to the effects of sympathetic flaring. Further, we investigate the consequences of flare sympathy for a specific model of flare statistics, the M. S. Wheatland and I. J. D. Craig (Astrophys. J.595, 458, 2003) model. The original treatment describes an assembly of reconnecting structures (labelled separators) that flare independently according to simple rules consistent with magnetohydrodynamic flare models. This description is modified by allowing a flare at one separator to increase the probability of flaring at all other separators for a period of time following the flare, by an amount proportional to the energy of the flare. Simulations illustrate the transition of the model from weak to strong sympathy. In the limit of weak sympathy, the model reproduces observed flare frequency–energy and waiting-time distributions.

Solar flare sympathy is the triggering of a flare in one active region by a flare in another. Statistical tests for flare sympathy have returned varying results. However, existing tests have relied on flaring rates in active regions being constant in time, or else have attempted to model the rate variation, which is a difficult task. A simple test is described which is independent of flaring rates. The test generalizes the approach of L. Fritzova-Svestkova, R.C. Chase, and Z. Svestka [Solar Phys. 48, 275, 1976], and examines the distribution of flare coincidences in pairs of active regions as a function of coincidence interval τ. The test is applied to available soft X-ray and Hα flare event listings. The soft X-ray events exhibit a deficit of flare coincidences for τ≤;20 min, which is most likely due to an event-selection effect whereby the increased soft X-ray emission due to one flare prevents a second flare being identified. The Hα events show an excess of flare coincidences for τ≤; 10 min, suggesting flare sympathy. The number of Hα event pairs occurring within 10 min of one another is higher than that expected on the basis of random coincidence by a fraction 0.12± 0.02. Nearby active regions (spatial separation

Wheatland and Litvinenko (2001) presented a model for dynamical energy balance in the flaring solar corona which predicts a time lag between flare occurrence and the supply of energy to the corona (`driving'). They also suggested that an observed net lag between flare numbers and sunspot numbers over cycles 21 and 22 might provide support for the model. Temmer, Veronig, and Hanslmeier (2003) examined data for five individual solar cycles (19–23) and confirmed a lag between flare and sunspot numbers for odd solar cycles, but found no lag for even cycles. Following the suggestion of Temmer, Veronig, and Hanslmeier, the energy balance model is here extended to incorporate 22-year driving consistent with the phenomenological Gnevyshev—Ohl rule. The model is found to exhibit a greater lag for the smaller (even) cycles, in contradiction with the findings of Temmer, Veronig, and Hanslmeier. A modification to the model is investigated in which the flaring rate is proportional to the free energy and to the driving rate for small driving rates, but is proportional only to the free energy for large driving rates. The modified model can in principle account for the observations.

A model to account for observed solar flare statistics in terms of a superposition of independent random flaring elements (assumed to be sites of magnetic reconnection in the coronal magnetic field and hence termed '' separators '') is described. A separator of length l is assumed to flare as a Poisson process in time, with a rate � ðlÞ inversely proportional to the Alfven transit time for the structure. It is shown that a relationship E / l � between the mean energy of events E at a separator and the separator length implies a relationship E / � � between individual waiting timesand energies E of events at the separator. The most plausible � ¼ 2 model is found to be compatible with simple pictures for magnetohydrodynamic energy storage prior to magnetic reconnection in a current sheet with anomalous (turbulent) resistivity. Formal inversion of the observed flare frequency-energy distribution is shown to imply a distribution Pðl Þ/ l � 1 of the separator lengths in active regions. A simulation confirms the basic results of the model. It is also demonstrated that a model comprising time-dependent separator numbers N ¼ NðtÞ can reproduce an observed power-law tail in the flare waiting- time distribution, for large waiting times.

The distribution of times Δt between coronal mass ejections (CMEs) in the Large Angle and Spectrometric Coronagraph (LASCO) CME catalog for the years 1996–2001 is examined. The distribution exhibits a power-law tail ∼(Δt)γ with an index γ≈−2.36±0.11 for large waiting times (Δt>10 hours). The power-law index of the waiting-time distribution varies with the solar cycle: for the years 1996–1998 (a period of low activity), the power-law index is γ≈−1.86±0.14, and for the years 1999–2001 (a period of higher activity), the index is γ≈−2.98±0.20. The observed CME waiting-time distribution, and its variation with the cycle, may be understood in terms of CMEs occurring as a time-dependent Poisson process. The CME waiting-time distribution is compared with that for greater than C1 class solar flares in the Geostationary Operational Environmental Satellite (GOES) catalog for the same years. The flare and CME waiting-time distributions exhibit power-law tails with very similar indices and time variation.

The ability of magnetic reconnection solutions to explain statistical flare data is discussed. It is assumed that flares occur at well-defined, isolated sites within an active region, determined by the null points and separators of the coronal magnetic field (Craig, 2001). Statistical flare observations then derive from a multiplicity of independent sites, flaring in parallel, that produce events of widely varying output (Wheatland, 2002). Given that the `separator length' at an individual site controls the event frequency and the mean energy release, it is shown that the observed frequency-energy spectrum N(E)can be inverted to yield a source function that relates directly to the distribution of separator lengths. It is also pointed out that, under the parallel flaring model, inferred waiting-time distributions are naturally interpreted as a superposition of individual point processes. Only a modest number of flaring separators is required to mimic a Poisson process.

A model is presented to explain the observed frequency distribution of flare energies, based on independent flaring at a number of distinct topological structures (separators) within active-region magnetic fields. The model is a modification and generalization of a recent model due to Craig (2001), and reconciles that model with the observed flare waiting-time distribution, and the observed absence of a flare waiting-time versus energy relationship. The basic assumptions of the model are that flares of energy E∼\(\left( \ell \right)\)2 occur at separators of length \(\left( \ell \right)\), and that the frequency of flaring at a separator is defined by the Alfven transit time of the structure. To reproduce the observed distribution of flare energies the model requires a probability distribution P(\(\left( \ell \right)\))∼\(\left( \ell \right)\)−1 of separator lengths \(\left( \ell \right)\) within active regions. This prediction of the model is in principle testable. A theoretical origin for this distribution is also discussed.

The observed distribution of waiting times Δt between X-ray solar flares of greater than C1 class listed in the Geostationary Operational Environmental Satellite (GOES) catalog exhibits a power-law tail ∼(Δt)γ for large waiting times (Δt>10 hours). It is shown that the power-law index γ varies with the solar cycle. For the minimum phase of the cycle the index is γ=−1.4±0.1, and for the maximum phase of the cycle the index is −3.2±0.2. For all years 1975–2001, the index is −2.2±0.1. We present a simple theory to account for the observed waiting-time distributions in terms of a Poisson process with a time-varying rate λ(t). A common approximation of slow variation of the rate with respect to a waiting time is examined, and found to be valid for the GOES catalog events. Subject to this approximation the observed waiting-time distribution is determined by f(λ), the time distribution of the rate λ. If f(λ) has a power-law form ∼λα for low rates, the waiting time-distribution is predicted to have a power-law tail ∼(Δt)−(3+α) (α>−3). Distributions f(λ) are constructed from the GOES data. For the entire catalog a power-law index α=−0.9±0.1 is found in the time distribution of rates for low rates (λ

Assuming only that flares derive their energy from a coronal source and that flaring is the dominant mechanism for depleting that source, the global coronal response time (time for flares to remove available coronal energy) is about 9 months. A detailed model for dynamic energy balance in the solar corona over the solar cycle is presented to describe how the magnetic free energy in the solar corona varies in response to changes in the supply of energy to the system and to changes in the flaring rate. The model predicts that both the flaring rate and the free energy of the system should lag behind the driving of the system because of the coronal response time (the detailed model gives a lag of ~11 months). This effect may account for hysteresis phenomena between certain solar activity indices. A specific example is presented in support of the model. Analysis of time series of monthly sunspot numbers and monthly numbers of soft X-ray flares over the years 1976-1999 indicates a tendency for flare numbers to lag behind sunspot numbers by ~6 months.

Dimensional considerations are used to analyze the distribution of times between solar flares (the flare waiting-time distribution). An analytical estimate for the mean flaring rate λ0 is obtained, based on the idea that the rate reflects a balance between the processes of energy input into the corona and energy dissipation by flaring. The estimate is shown to be in good agreement with observations of flares by Geostationary Operational Environmental Satellite detectors. The analytic result is confirmed using the master equation (probability balance equation) formalism. Analysis of time variation leads to a differential equation describing how the free energy in the corona changes when the rates of driving of the system and of flaring vary. This equation may be used to describe the global energy balance in the corona over the solar cycle.

A test of the hypothesis that flares derive their energy from large scale current systems inferred from active region vector magnetograms is proposed. The test involves a statistical comparison of the flarerelated change in coronal magnetic energy (based on the magnetohydrodynamic virial theorem) and an independent measure of the energy of the flare. A simulation suggests that — assuming the hypothesis is correct—the test requires around 50 flares with energy greater than 5×1023 J to return a significant result. Existing archives of vector magnetograms should provide sufficient data for such a study.

A loop flare that occurred on 22 April 1993 near the disk center is examined using the Yohkoh Hard X-ray Telescope (HXT). We specifically looked into the faint early phase of the flare prior to the start of the strong impulsive phase. The pre-impulsive phase, though weak in intensity, is expected to contain essential clues to the mechanism of loop flares according to the causality principle, but it has not received attention previously, probably due to the insufficient dynamic range and cadence of observations by the instruments on earlier satellites. Observations with Yohkoh/HXT can clarify what occurs in this phase. This flare, like many other flares of this type, shows a relatively weak emission with a smooth and gradual increase during this pre-impulsive phase, followed by impulsive bursts, and then turns into a smooth decay phase without impulsive bursts. First, we found that the spectrum for the initial smooth rise part is consistent with a thin-thermal source at a temperature around 80 MK. Imaging of this phase in the HXT/L and M bands shows a single source between the footpoint sources that will come up in the impulsive phase following this phase, suggesting that this hyperhot source is located at a high part of the loop between the footpoints, since this flare takes a form of a loop. Furthermore, as we go up to the earliest times of the flare before this `hyperhot' source phase, two fainter sources are found near the footpoint sources that will appear later in the impulsive phase. The spectra of these sources at this earliest time of the flare, in contrast to the `hyperhot' source, cannot be determined from the HXT because the instrument was not in flare mode, and HXT/M1, M2, and H-band data are, unfortunately, not available at this very initial time. We can guess, however, that they are also of thermal character because the time profile is smooth without any spikes just as in the following `hyperhot' thermal phase, and in the post-impulsive `superhot' thermal phase coming up much later. These findings suggest that there is an important, and probably dynamic, early phase in loop flares that has been unnoticed in the still dark pre-impulsive phase, because the very early footpoint sources change into the loop top source in a matter of 20–30 s, comparable to the dynamic Alfven time scale. Some implications of our new findings are discussed.

Rates of flaring in individual active regions on the Sun during the period 1981–1999 are examined using United States Air Force/Mount Wilson (USAF/MWL) active-region observations together with the Geostationary Operational Environmental Satellite (GOES) soft X-ray flare catalog. Of the flares in the catalog above C1 class, 61.5% are identified with an active region. Evidence is presented for obscuration, i.e. that the increase in soft X-ray flux during a large flare decreases the likelihood of detection of soft X-ray events immediately following the large flare. This effect means that many events are missing from the GOES catalog. It is estimated that in the absence of obscuration the number of flares above C1 class would be higher by (75±23) %. A second observational selection effect – an increased tendency for larger flares to be identified with an active region – is also identified. The distributions of numbers of flares produced by individual active regions and of mean flaring rate among active regions are shown to be approximately exponential, although there are excess numbers of active regions with low flare numbers and low flaring rates. A Bayesian procedure is used to analyze the time history of the flaring rate in the individual active regions. A substantial number of active regions appear to exhibit variation in flaring rate during their transit of the solar disk. Examples are shown of regions with and without rate variation, illustrating the different distributions of times between events (waiting-time distributions) that are observed. A piecewise constant Poisson process is found to provide a good model for the observed waiting-time distributions. Finally, applications of analysis of the rate of flaring to understanding the flare mechanism and to flare prediction are discussed.

It is well known that the size (peak count rate of emission, or inferred energy) distribution of —ares observed on the Sun follows a power law. However, the distributions that are constructed include —ares from diUerent active regions that have a variety of physical properties. In this paper cumulative peak count rate distributions are constructed for individual active regions using events listed in the WATCH solar X-ray burst catalog. The individual distributions are found to be consistent with the distribution constructed from events in all active regions named in the catalog. This result suggests that the —are power-law size distribution re—ects an intrinsic property of the —are mechanism and is not a product of the distributions of physical parameters between active regions. The result is consistent with the ava- lanche model for —ares and more generally argues against macroscopic —are models. Subject headings: MHDSun: activitySun: coronaSun: —ares

Some models for flare statistics predict or assume that there is a relationship between the times between flares and the energy of flares. This question is examined observationally using the WATCH solar X-ray burst catalogue. A rank correlation test applied to the data finds strong evidence for a correlation between the time since the last event, tb, and the size (peak count rate) of an event, and for a correlation between the time to the next event, ta, and the size of an event. A more sophisticated statistical test, taking into account a probable bias in event selection, does not support the hypothesis that event size depends on tb or ta.

A waiting-time distribution is constructed for 8 yr of solar flare hard X-ray bursts observed by the ICE/ISEE 3 spacecraft. The observed distribution is compared with a simulated waiting-time distribution produced by a time-dependent Poisson process constructed using rates estimated from the observations. The observed distribution shows an overabundance of short waiting times (10 s-10 minutes) in comparison with the simulation. This result implies that the hard X-ray bursts are not independent events. The implications of this result for the existence of sympathetic flaring and to models of flare statistics are discussed, and the result is compared with previous determinations of waiting-time distributions for solar hard X-ray events.

The Rosner & Vaiana model for flares is generalized to allow for flares that do not deplete all free energy from the system, a step that overcomes a number of objections to the original model. We obtain a probability balance equation, or master equation, describing the free energy E of an active region subject to a prescribed growth rate, Ė, and a prescribed distribution, α(E), of stochastic decay events. We argue that the solution appropriate to flares involves an energy-independent growth rate and a power-law form for α(E), which may be the result of an underlying avalanche process. The resulting model produces power-law flare frequency distributions below a high-energy rollover corresponding to the largest energy the system is likely to attain, which is set by the balance between the rate of growth and the rate of stochastic decay. There is a close correspondence between the resulting model and the avalanche model for flares.

The radial variation of temperature in the inner corona is examined using long-exposure Yohkoh images of two regions of diffuse (quiet) corona. The results indicate a steady radial increase of temperature for both regions, out to 0.7 and 0.95 solar radii above the limb. We find that the filter-ratio data for the two regions is well fitted in each case by integration over the line of sight of a spherically symmetric model atmosphere in hydrostatic equilibrium and with a temperature profile due to a conserved inward heat flux. An Abel inversion process is also applied to the data, and this gives results consistent with the spherically symmetric, conserved-heat flux model. These results imply that the nonthermal energy responsible for heating these regions of the quiet corona is being deposited beyond the observed range of heights. However, the diffuse regions we examined are believed to be partly closed-field regions, and so, the radial models require careful interpretation. We discuss the implications for coronal heating in these regions.

The shapes of solar coronal loops are sensitive to the presence of electrical currents that are the carriers of the nonpotential energy available for impulsive activity. We use this information in a new method for modeling the coronal magnetic field of AR 11158 as a nonlinear force-free field (NLFFF). The observations used are coronal images around time of major flare activity on 2011/02/15, together with the surface line-of-sight magnetic field measurements. The data are from the Helioseismic and Magnetic Imager and Atmospheric Imaging Assembly (HMI and AIA, respectively) onboard the Solar Dynamics Observatory (SDO). The model fields are constrained to approximate the coronal loop configurations as closely as possible, while also subject to the force-free constraints. The method does not use transverse photospheric magnetic field components as input, and is thereby distinct from methods for modeling NLFFFs based on photospheric vector magnetograms. We validate the method using observations of AR 11158 at a time well before major flaring, and subsequently review the field evolution just prior to and following an X2.2 flare and associated eruption. The models indicate that the energy released during the instability is about $1\times10^{32}$ erg, consistent with what is needed to power such a large eruptive flare. Immediately prior to the eruption the model field contains a compact sigmoid bundle of twisted flux that is not present in the post-eruption models, which is consistent with the observations. The core of that model structure is twisted by $\approx0.9$ full turns about its axis., ApJ, in press

Avalanche models of solar flares successfully reproduce the power-law distribution of flare frequency as a function of energy. However, the model distributions have been produced for a single numerical grid, representing a single active region on the Sun. Here we convolve the distribution owing to an avalanche grid with each of two observationally determined active region size distributions. The resulting energy distributions are power laws (with index α ≈ 1.5) below about 1031 ergs, but they gradually steepen with energy. The resulting distributions are compared with a flare energy distribution derived from International Cometary Explorer satellite observations. Qualitative agreement is found between the model and observed distributions, although the observations favor a simple power-law model distribution with a somewhat steeper index (≈1.71).

Zaitsev and Stepanov (1991, 1992) proposed a mechanism for energy release in solar flares that involves the intrusion of dense prominence material into a coronal loop. The resulting non-steady state conditions are claimed to increase the resistance of the loop by 8–10 orders of magnitude. It is shown here that the dramatic increase in resistance calculated by Zaitsev and Stepanov depends on a gross overestimate of the of the magnitude of the magnetic force in the loop prior to the flare trigger. A more realistic estimate of the increase due to the mechanism suggests that it is by no more than about four orders of magnitude. As a consequence, the ‘prominence-loading‘ mechanism does not provide a tenable flare model.

A simple model is presented to account for theYohkoh flare observations of Feldmanet al. (1994), and Masuda (1994). Electrons accelerated by the flare are assumed to encounter the dense, small regions observed by Feldmanet al. at the tops of impulsively flaring coronal magnetic loops. The values of electron density and volume inferred by Feldmanet al. imply that these dense regions present an intermediate thick-thin target to the energised electrons. Specifically, they present a thick (thin) target to electrons with energy much less (greater) thanE c , where 15 keV

A time-dependent model for the energy of a flaring solar active region is presented based on a stochastic jump-transition model (Wheatland and Glukhov 1998; Wheatland 2008; Wheatland 2009). The magnetic free energy of the model active region varies in time due to a prescribed (deterministic) rate of energy input and prescribed (random) flare jumps downwards in energy. The model has been shown to reproduce observed flare statistics, for specific time-independent choices for the energy input and flare transition rates. However, many solar active regions exhibit time variation in flare productivity, as exemplified by NOAA active region AR 11029 (Wheatland 2010). In this case a time-dependent model is needed. Time variation is incorporated for two cases: 1. a step change in the rates of flare jumps; and 2. a step change in the rate of energy supply to the system. Analytic arguments are presented describing the qualitative behavior of the system in the two cases. In each case the system adjusts by shifting to a new stationary state over a relaxation time which is estimated analytically. The new model retains flare-like event statistics. In each case the frequency-energy distribution is a power law for flare energies less than a time-dependent rollover set by the largest energy the system is likely to attain at a given time. For Case 1, the model exhibits a double exponential waiting-time distribution, corresponding to flaring at a constant mean rate during two intervals (before and after the step change), if the average energy of the system is large. For Case 2 the waiting-time distribution is a simple exponential, again provided the average energy of the system is large. Monte Carlo simulations of Case~1 are presented which confirm the analytic estimates. The simulation results provide a qualitative model for observed flare statistics in active region AR 11029., Comment: 25 pages, 9 figures

Active region 11029 was a small, highly flare-productive solar active region observed at a time of extremely low solar activity. The region produced only small flares: the largest of the $>70$ Geostationary Observational Environmental Satellite (GOES) events for the region has a peak 1--$8{\AA}$ flux of $2.2\times 10^{-6} {\rm W} {\rm m}^{-2}$ (GOES C2.2). The background-subtracted GOES peak-flux distribution suggests departure from power-law behavior above $10^{-6} {\rm W} {\rm m}^{-2}$, and a Bayesian model comparison strongly favors a power-law plus rollover model for the distribution over a simple power-law model. The departure from the power law is attributed to this small active region having a finite amount of energy. The rate of flaring in the region varies with time, becoming very high for two days coinciding with the onset of an increase in complexity of the photospheric magnetic field. The observed waiting-time distribution for events is consistent with a piecewise-constant Poisson model. These results present challenges for models of flare statistics and of energy balance in solar active regions., Comment: 29 pages, 5 figures, 1 table

International audience; 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.

[1] A Bayesian approach to solar flare prediction has been developed which uses only the event statistics of flares already observed. The method is simple and objective and makes few ad hoc assumptions. It is argued that this approach should be used to provide a baseline prediction for certain space weather purposes, upon which other methods, incorporating additional information, can improve. A practical implementation of the method for whole-Sun prediction of Geostationary Observational Environment Satellite (GOES) events is described in detail and is demonstrated for 4 November 2003, the day of the largest recorded GOES flare. A test of the method is described on the basis of the historical record of GOES events (1975–2003), and a detailed comparison is made with U.S. National Oceanic and Atmospheric Administration (NOAA) predictions for 1987–2003. Although the NOAA forecasts incorporate a variety of other information, the present method outperforms the NOAA method in predicting mean numbers of event days for both M-X and X events. Skill scores and other measures show that the present method is slightly less accurate at predicting M-X events than the NOAA method but substantially more accurate at predicting X events, which are important contributors to space weather.

A test of a new Bayesian approach to solar flare prediction (Wheatland 2004a) is presented. The approach uses the past history of flaring together with phenomenological rules of flare statistics to make a prediction for the probability of occurrence of a large flare within an interval of time, or to refine an initial prediction (which may incorporate other information). The test of the method is based on data from the Geostationary Observational Environmental Satellites (GOES), and involves whole-Sun prediction of soft X-ray flares for 1976-2003. The results show that the method somewhat over-predicts the probability of all events above a moderate size, but performs well in predicting large events., 4 pages, 2 figures, Astronomical Society of Australia meeting in Brisbane, July 2004; revised version

A number of methods of flare prediction rely on classification of physical characteristics of an active region, in particular optical classification of sunspots, and historical rates of flaring for a given classification. However these methods largely ignore the number of flares the active region has already produced, in particular the number of small events. The past history of occurrence of flares (of all sizes) is an important indicator to future flare production. We present a Bayesian approach to flare prediction, which uses the flaring record of an active region together with phenomenological rules of flare statistics to refine an initial prediction for the occurrence of a big flare during a subsequent period of time. The initial prediction is assumed to come from one of the extant methods of flare prediction. The theory of the method is outlined, and simulations are presented to show how the refinement step of the method works in practice., 17 pages, 3 figures

It was recently pointed out that the distribution of times between solar flares (the flare waiting-time distribution) follows a power law, for long waiting times. Based on 25 years of soft X-ray flares observed by Geostationary Operational Environmental Satellite (GOES) instruments it is shown that 1. the waiting-time distribution of flares is consistent with a time-dependent Poisson process, and 2. the fraction of time the Sun spends with different flaring rates approximately follows an exponential distribution. The second result is a new phenomenological law for flares. It is shown analytically how the observed power-law behavior of the waiting times originates in the exponential distribution of flaring rates. These results are argued to be consistent with a non-stationary avalanche model for flares., Comment: 7 pages, 3 figures, accepted by ApJ Letters

During the interval 3–15 May 1992, an extended region of diffuse, stable corona crossed the north-east limb of the Sun. During this passage, the soft X-ray telescope on Yohkoh obtained a number of high-quality pairs of images, closely spaced in time, through the two thinnest analysis filters. Our first step was to average the measurements at each radial position over an azimuthal sector about 25 degrees wide. These averaged measurements were represented, at each radial position, by an emission measure and a temperature (derived from the ratio of the signals from the two filters).