A Method for Estimating the Spatial Period of Energy Release in Solar Flares II

Energy release in solar flares occurs during the impulsive phase, which is a period of a few to about ten minutes, during which energy is injected into the flare region in bursts with durations of various time scales, from a few tens of seconds down to 0.1 s or even shorter. Non-thermal heating is observed during a short period, not longer than a few minutes, in the very first part of the impulsive phase; in average flares, with ambient particle densities not larger than a few times 1010 cm−3 it is due to thick-target electron beam injection, causing chromospheric ablation followed by convection. In flares with larger densities the heating is due to thermal fronts (Section 1). The average energy released in chromospheric regions is a few times 1030 erg, and an average number of 1038 electrons with E ≳ 15 keV is accelerated. In subsecond pulses these values are about 1035 electrons and about 1027 erg per subsecond pulse. The total energy released in flares is larger than these values (Section 2). Energization occurs gradually, in a series of fast non-explosive flux-thread interactions, on the average at levels about 104 km above the solar photosphere, a region permeated by a large number (≳ 10) of fluxthreads, each carrying electric currents of ≈ 1010–1011 A. The energy is fed into the flare by differential motions of magnetic fields driven by photospheric-chromospheric movements (Section 3). In contrast to these are the high-energy flares, characterized by the emission of gamma-radiation and/or very high-frequency (millimeter) radiobursts. Observations of such flares, of the flare neutron emission, as well as the observation of 3He-rich interplanetary plasma clouds from flares all point to a common source, identified with shortlived (∼ 0.1 s) superhot (≳ 108 K) flare knots, situated in chromospheric levels (Section 4). Pre-flare phenomena and the existence of homologous flares prove that flare energization can occur repeatedly in the same part of an active region: the consequent conclusions are that only seldom the full energy of an active region is exhausted in one flare, or that the flare energy is generated anew between homologous flares; this latter case looks more probable (Section 5). Flare energization requires the formation of direct electric fields, in value comparable with, or somewhat smaller than the Dreicer field (Section 6). Such fields originate by current-thread reconnection in a regime in which the current sheet is thin enough to let resistive instability originate (Section 7). Particle acceleration occurs ‘by fast reconnection in magnetic fields ≳ 100 G and electric fields exceeding about 0.3 times the Dreicer field at fairly low particle densities (≈ 1010 cm−3); for larger densities plasma heating is expected to occur (Section 8). Transport of accelerated particles towards interplanetary space demands a field-line configuration open to space. Such a configuration originates mainly after the gradual gamma-ray/proton flares, and particularly after two-ribbon flares; these flares belong to the dynamic flares in Sturrock and Svestka's flare classification. Acceleration to GeV energies occurs subsequently in shock waves, probably by first-order Fermi acceleration (Section 9).

We examine observational evidence concerning energy release in solar flares. We propose that different processes may be operative on four different time scales: (a) on the sub-second time scale of ‘sub-bursts’ which are a prominent feature of mm-wave microwave records; (b) on the few-seconds time scale of ‘elementary bursts’ which are a prominent feature of hard X-ray records; (c) on the few-minutes time scale of the impulsive phase; and (d) on the tens-of-minutes or longer time scale of the gradual phase. We propose that the concentration of magnetic field into ‘magnetic knots’ at the photosphere has important consequences for the coronal magnetic-field structure such that the magnetic field in this region may be viewed as an array of ‘elementary flux tubes’. The release of the free energy of one such tube may produce an elementary burst. The development of magnetic islands during this process may be responsible for the sub-bursts. The impulsive phase may be simply the composite effect of many elementary bursts. We propose that the gradual phase of energy release, with which flares typically begin and with which many flares end, involves a steady process of reconnection, whereas the impulsive phase involves a more rapid stochastic process of reconnection which is a consequence of mode interaction. In the case of two-ribbon flares, the late part of the gradual phase may be attributed to reconnection of a large current sheet which is being produced as a result of filament eruption. A similar process may be operative in smaller flares.

Aims. We derive constraints on energy release, transport and conversion processes in solar flares based on a detailed characterization of the physical parameters of both the thermal plasma and the accelerated nonthermal electrons based on X-ray observations. In particular, we address the questions of whether the energy required to heat the thermal plasma can be supplied by nonthermal particles, and how the energetics derived from X-rays compare to the total bolometric radiated energy.

Vector magnetogram data show that (1) regions of large current flow, I ∼ 10<SUP>12</SUP> A, correlate with the footpoints of flaring coronal loops, and (2) the currents flow up in a region of one magnetic polarity and down in a region of opposite magnetic polarity. It is argued that these properties imply that the currents cannot be generated by shearing or other motions near the photo sphere, and must close deep in the solar atmosphere. It is also argued that the line-tying assumption is inappropriate on timescales of 1 day or longer on which coronal magnetic structures evolve and that an appeal to line tying incorrectly implies that coronal currents close near the photo sphere. The observed shearing of coronal magnetic structures is attributed to the emergence of current-carrying magnetic flux tubes. <P />Energy release in a solar flare is discussed with emphasis on the nonlocal nature of changes in the stored magnetic energy. Energy release occurs in two stages, with nondissipative, local conversion of stored energy into a Poynting flux at Alfvénic fronts, and conversion into particle energy in localized energy release site. The nonlocal nature of the energy release process is described in terms of a circuit model with temporally varying parameters. The power release, IV, occurs at constant total current I ∼ 10<SUP>12</SUP> A, due to a large inductive voltage, V ∼10<SUP>10</SUP> V, and involves changes in the current profile or current path, described by a changing coronal inductance, L, with a coronal resistance, R<SUB>c</SUB> determined by Ldot + R<SUB>c</SUB> = 0. Three ways in which the net inductance can decrease are discussed: like currents moving apart, the current path shortening, and unlike currents moving closer together. Simple models for an erupting filament show that magnetic energy release can drive the eruption only if the current in the filament drains away into a current path lower in the corona. Relocation of the current to a lower height should cause the shearing near the neutral line to increase as a result of a flare, as has been reported recently.

The well-known Chandrasekhar-Prendergastmagnetostatic solution for a sphericalmagnetic vortex with axial symmetry squeezed externally by a potential magnetic field is of considerable interest both for describing the magnetic field of a star as a whole and for modeling solar active phenomena (flares, coronal spiders, etc.). This solution is generalized to the case of a uniform gravity field. In contrast to the Chandrasekhar-Prendergast model, the dependence of the plasma density in the spherical vortex on magnetic flux appears in the new solution. This expands considerably the class of magnetoplasma equilibria being analyzed and allows new scenarios for energy release in solar flares and coronal spiders to be proposed.

Context. The primary energy release in solar flares is almost certainly due to magnetic reconnection, making this a strong candidate as a mechanism for particle acceleration. While particle acceleration in 2D geometries has been widely studied, investigations in 3D are a recent development. Two main classes of reconnection regimes at a 3D magnetic null point have been identified: fan and spine reconnection Aims. Here we investigate particle trajectories and acceleration during reconnection at a 3D null point, using a test particle numerical code, and compare the efficiency of the fan and spine regimes in generating an energetic particle population. Methods. We calculated the time evolution of the energy spectra. We discuss the geometry of particle escape from the two configurations and characterise the trapped and escaped populations. Results. We find that fan reconnection is less efficent than spine reconnection in providing seed particles to the region of strong electric field where acceleration is possible. The establishment of a steady-state spectrum requires approximately double the time in fan reconnection. The steady-state energy spectrum at intermediate energies (protons 1 keV to 0.1 MeV) is comparable in the fan and spine regimes. While in spine reconnection particle escape takes place in two symmetric jets along the spine, in fan reconnection no jets are produced and particles escape in the fan plane, in a ribbon-like structure.

Extended review of selected papers which deal with the problem of flare heating in solar coronal loops is presented. Discussed methods of the analysis of flare heating based on the X-ray observations have been worked out using the Palermo-Harvard hydrodynamic code. The case is presented when the assumption of the uniform heating across the loop is made. The existence of multiple elementary heating episodes is postulated as well. Next the possibility of the non-uniform heating across the loop is assumed and its manifestation in the X-ray observations is investigated. The application of proposed methods of the analysis to the observations of solar flares in X-rays is presented.

Magnetic field annihilation in resistive viscous incompressible plasmas is analyzed. Anisotropic viscous transport is modeled by the dominant terms in the Braginskii viscous stress tensor. An analytical solution for steady-state magnetic merging, driven by vortical plasma flows in two dimensions, is derived. Resistive and viscous energy dissipation rates are calculated. It is shown that, except in the limiting case of zero vorticity, viscous heating can significantly exceed Joule heating at the merging site. The results strongly suggest that viscous dissipation can provide a significant fraction of the total energy release in solar flares, which may have far-reaching implications for flare models.

The magnetic field is the main, and probably only source of energy for many of nonsteady phenomena in cosmic and laboratory plasmas [200].In particular, events of this type in the solar atmosphere include flares,coronal transients, and plasma ejections into the interplanetary space (e.g.,[335, 280]). At the same time, the magnetic field dissipation in a high-conductivity plasma and the magnetic field energy conversion into other forms constitute a well-known problem of solar physics [94, 281]. The problem has proved to be especially urgent when applied to the so-called ‘hot’ or ‘main’ phase of solar flares. It is in the high-temperature plasma where the bulk of the flare energy is released within the hot phase time [ 167,165].

The role of magnetic field shear in solar flares

Flare-like events similar to those observed on the Sun occur on many different types of stars, particularly on late K and M dwarfs. Although the physical mechanisms responsible for these events remain largely unknown, it is likely that the flare energy derives from dissipation of magnetic fields as is the case for solar flares. We review the basic observational facts that suggest an analogy between solar and stellar flares and we discuss how the different physical conditions occurring on stars may affect the application of current solar-type models to the stellar case. We show that, in spite of a qualitative agreement found between model predictions and observations, there is still no convincing evidence that stellar flares are simply scaled-up versions of solar flares. Major advances in the observations of stellar flares are required before this fundamental question can be safely addressed.

Chromospheric flare ribbons are believed to result from coronal magnetic energy released by reconnection and propagating down to the cooler, lower atmosphere. They offer an opportunity to study flare reconnection using chromospheric observations at a spatial and temporal resolution higher than typically available by direct coronal observation. Transient downflows, known as chromospheric condensations (CCs), often occur at the leading edge of a ribbon as a prompt response to the energy input. These have properties that have recently been shown to relate to the coronal energy release process driving them. We use a set of IRIS observations of flare ribbons, made at high cadence in the sit-and-stare mode, to identify and analyze a sample of 134 CC episodes. Among this sample, 132 episodes have at least one time frame that exhibited a double-Gaussian profile. Clear CC appears to occur in only about one fifth of all ribbon pixels, indicating that flare energy release is necessary but not sufficient for producing the characteristic form of CC. We find that condensation pixels form clusters averaging 1 arcsec in extent, all undergoing similar and concurrent time evolution. This suggests that coronal reconnection and associated energy release occur in localized patches whose spatial extent maps to around 1 arcsec in the chromosphere.

We present a technique for automatic determination of flare-ribbon separation and the energy released during the course of two-ribbon flares. We have used chromospheric H$\alpha$ filtergrams and photospheric line-of-sight magnetograms to analyse flare-ribbon separation and magnetic-field structures, respectively. Flare-ribbons were first enhanced and then extracted by the technique of "region growing", i.e., a morphological operator to help resolve the flare-ribbons. Separation of flare-ribbons was then estimated from magnetic polarity reversal line using an automatic technique implemented into Interactive Data Language (IDL\tm) platform. Finally, the rate of flare-energy release was calculated using photospheric magnetic-field data and the corresponding separation of the chromospheric H$\alpha$ flare-ribbons. This method could be applied to measure the motion of any feature of interest (e.g., intensity, magnetic, Doppler) from a given point of reference.

Solar white-light flares (WLFs) are solar flares exhibiting enhanced emission in the optical continuum. They are critical for understanding energy release and transport mechanisms in solar flares and for conducting comparative studies with stellar WLFs. However, the scarcity of accurately and reliably measured optical continuum light curves for solar WLFs significantly hampers related studies. Based on the optimized solar WLF identification method, we construct a dataset of optical continuum light curves for 70 solar WLFs using 6173 {\AA} continuum intensity images from the Solar Dynamics Observatory. Moreover, for each solar WLF event, we also provide the location of the white-light emission enhancement signals and key parameters including bolometric energies and durations derived from both the traditional fixed-temperature blackbody model and the refined variable-temperature blackbody model. This dataset will serve as a valuable resource for future statistical investigations of solar WLFs and for comparative studies between solar and stellar flares.

Distinctive spatial configuration of a class ofmicrowave flaring sources