An electric-current description of solar flares

The presently prevailing theories of solar flares rely on the hypothetical presence of magnetic flux tubes beneath the photosphere and the two subsequent hypotheses, their emergence above the photosphere and explosive magnetic reconnection, converting magnetic energy carried by the flux tubes to solar flare energy. In this paper, we discuss solar flares from an entirely different point of view, namely in terms of power supply by a dynamo process in the photosphere. By this process, electric currents flowing along the magnetic field lines are generated and the familiar ‘force-free’ fields or the ‘sheared’ magnetic fields are produced. Upward field-aligned currents thus generated are carried by downward streaming electrons; these electrons can excite hydrogen atoms in the chromosphere, causing the optical Hα flares or ‘low temperature flares’. It is thus argued that as the ‘force-free’ fields are being built up for the magnetic energy storage, a flare must already be in progress.     

High energy particle acceleration in solar flares — observational evidence

The recent gamma ray and neutron observations made by the SMM Gamma Ray Spectrometer are reviewed. The implication these observations hold for understanding particle acceleration in solar flares are discussed. The data require that both electrons and ions must be accelerated together to relativistic energies and interact with matter in a time scale of seconds.     

The Alfvén-wave theory of solar flares

Evidence is discussed showing that a representative solar flare event comprises three or more separate but related phenomena requiring separate mechanisms. In particular it is possible to separate the most energetic effect (the interplanetary blast) from the thermal flare and from the rapid acceleration of particles to high energies. The phenomena are related through the magnetic structure characteristic of a composite flare event, being a bipolar surface field with most of its field lines ‘closed’. Of primary importance are helical twists on all scales, starting with the ‘flux rope’ of the spot pair which was fully twisted before it emerged. Subsequent untwisting by the upward propagation of an Alfvén twist wave provides the main flare energy.

1. The interplanetary blast model is based on subsurface, helically twisted flux ropes which erupt to form spots and then transfer their twists and energy by Alfvén-twist waves into the atmospheric magnetic fields. The blast is triggered by the prior-commencing flash phase or by a coronal wave.
2. The thermal flare is explained in terms of Alfvén waves travelling up numerous ‘flux strands’ (Figure 3) which have frayed away from the two flux ropes. The waves originate in interaction (collisions, bending, twisting, rubbing) between subsurface flux strands; the sudden flash is caused by a collision. The classical twin-ribbon flare results from the collision of a flux rope with a tight bunch of S-shaped flux strands.
3. The impulsive acceleration of electrons (hard X-ray, EUV, Hα and radio bursts) is tentatively attributed to magnetic reconnection between fields in two parallel, helically twisted flux strands in the low corona.
4. Flare (Moreton) waves in the corona have the same origin as the interplanetary blast. Sympathetic flares represent only the start of enhanced activity in a flare event already in the slow phase. Filament activation also occurs during the slow phase as twist Alfvén waves store their energy in the atmosphere.
5. Flare ejecta are caused by Alfvén waves moving up flux strands. Surges are attributed to packets of twist Alfvén waves released into bundles of flux strands; the waves become non-linear and drive plasma upwards. Spray-type prominences result from accumulations of Alfvén wave energy in dome-shaped fields; excessive energy density eventually explodes the field.

     

Polarization of hard X-rays from solar flares

The polarization of hard solar X-radiation (> 10 keV) is calculated on the assumption that electrons get a non-isotropic velocity distribution in the initial phase of a flare. The brems-strahlung generated by nonthermal electrons spiralling around magnetic field lines with discrete pitch angles is considerably polarized if observed at approximately right angles to the magnetic field. In the energy range from 10 to 50 keV the degree of polarization is not strongly dependent on the photon energy. For pitch-angle distributions of the form sin² and cos², the polarization has opposite signs; it decreases appreciably at high photon energies. The observation of X-ray polarization will be useful in deducing the physical conditions in flares.     

A dynamo theory of solar flares

It is proposed that the solar flare phenomenon can be understood as a manifestation of the electrodynamic coupling process of the photosphere-chromosphere-corona system as a whole. The system is coupled by electric currents, flowing along (both upward and downward) and across the magnetic field lines, powered by the dynamo process driven by the neutral wind in the photosphere and the lower chromosphere. A self-consistent formulation of the proposed coupling system is given. It is shown in particular that the coupling system can generate and dissipate the power of 10²⁹ erg s^#X2212;1 and the total energy of 10³² erg during a typical life time (10³ s) of solar flares. The energy consumptions include Joule heat production, acceleration of current-carrying particles along field lines, magnetic energy storage and kinetic energy of plasma convection. The particle acceleration arises from the development of field-aligned potential drops of 10–150 kV due to the loss-cone constriction effect along the upward field-aligned currents, causing optical, X-ray and radio emissions. The total number of precipitating electrons during a flare is shown to be of order 10³⁷–10³⁸.     

Magnetohydrodynamic modelling of interplanetary disturbances between the Sun and Earth

A time-dependent, nonplanar, two-dimensional magnetohydrodynamic computer model is used to simulate a series, separately examined, of solar flare-generated shock waves and their subsequent disturbances in interplanetary space between the Sun and the Earth's magnetosphere. The ‘canonical’ or ansatz series of shock waves include initial velocities near the Sun over the range 500 to 3500 km s^?1. The ambient solar wind, through which they propagate, is taken to be a steady-state homogeneous plasma (that is, independent of heliolongitude) with a representative set of plasma and magnetic field parameters. Complete sets of solar wind plasma and magnetic field parameters are presented and discussed. Particular attention is addressed to the MHD model's ability to address fundamental operational questions vis-à-vis the long-range forecasting of geomagnetic disturbances. These questions are: (i) will a disturbance (such as the present canonical series of solar flare shock waves) produce a magnetospheric and ionospheric disturbance, and, if so, (ii) when will it start, (iii) how severe will it be, and (iv) how long will it last? The model's output is used to compute various solar wind indices of current interest as a demonstration of the model's potential for providing ‘answers’ to these questions.     

Helmholtz instability in stratified shear flows with magnetic fields

The stability characteristics of a Helmholtz velocity profile in a stratified Boussinesq fluid in the presence of a rigid boundary is studied. A jump in the magnetic field is introduced at a level different from the velocity discontinuity. New unstable modes in addition to the Kelvin-Helmholtz mode are found. The wavelengths of these unstable modes are close to the wavelengths of internal Alfvén gravity waves in the atmosphere.     

Reverse-current effect in present-day models of solar flares: Theory and high-accuracy observations

We propose an accurate analytical model for the source of hard X-ray emission from a flare in the form of a “thick target” with a reverse current to explain the results of present-day observations of solar flares onboard the GOES, Hinode, RHESSI, and TRACE satellites. The model, one-dimensional in coordinate space and two-dimensional in velocity space, self-consistently takes into account the fact that the beam electrons lose the kinetic energy of their motion along the magnetic field almost without any collisions under the action of the reverse-current electric field. Some of the electrons return from the emission source to the acceleration region without losing the kinetic energy of their transverse motion. Based on the observed hard X-ray bremsstrahlung spectrum, the model allows the injection spectrum of accelerated electrons to be reconstructed with a high accuracy. As an example, we consider the white-light flare of December 6, 2006, which was observed with a high spatial resolution in the optical wavelength range at the main maximum of hard X-ray emission. Within the framework of our model, we show that to explain the hard X-ray spectrum, the flux density of the energy transferred by electrons with energies above 18 keV was ～3 × 10¹³ erg cm^?2 s^?1. This exceeds the habitual values typical of the classical model of a thick target without a reverse current by two orders of magnitude. The electron density in the beam is also very high: ～10¹¹ cm^?3. A more careful consideration of plasma processes in such dense electron beams is needed when the physical parameters of a flare are calculated.     

Gamma-ray and microwave evidence for two phases of acceleration in solar flares

Relativistic electrons in large solar flares produce gamma-ray continuum by bremsstrahlung and microwave emission by gyrosynchrotron radiation. Using observations of the 1972, August 4 flare, we evaluate in detail the electron spectrum and the physical properties (density, magnetic field, size, and temperature) of the common emitting region of these radiations. We also obtain information on energetic protons in this flare by using gamma-ray lines. From the electron spectrum, the proton-to-electron ratio, and the time dependences of the microwave emission, the 2.2 MeV line and the gamma-ray continuum, we conclude that in large solar flares relativistic electrons and energetic nuclei are accelerated by a mechanism which is different from the mechanism which accelerates 100 keV electrons in flares.Research supported by NASA Grant 21-002-316 at the University of Maryland, College Park.     

On the polarization and anisotropy of solar X-radiation during flares

Starting from the idea that the electrons accelerated during a solar flare have originally a preferred direction, the angular distribution and the polarization of bremsstrahlung below 10 Å is calculated taking into account the influence of the magnetic field. The energy distribution of the nonthermal electrons is based on X-ray spectra measured by the Leicester group during flares in 1962 and 1967. In addition to the case of a fixed angle between the electron velocity and the magnetic field, an angular distribution of the form sin ⁿ is considered. The results may be used to test flare models. Recent measurements of the polarization of solar X-radiation yield the expected order of magnitude.Paper presented to the Int. Symp. on Solar-Terr. Phys., Leningrad, May 1970.     

Observation of chromospheric evaporation during the solar maximum mission

A sample of flares detected in 1980 with the Bent Crystal Spectrometer and the Hard X-Ray Burst Spectrometer on the Solar Maximum Mission satellite has been analysed to study the upward motions of part of the soft X-ray emitting plasma. These motions are inferred from the presence of secondary blue-shifted lines in the Ca XIX and Fe XXV spectral regions during the impulsive phase of disk flares. Limb flares do not show such blue-shifted lines indicating that the direction of the plasma motion is mainly radial and outward. The temporal association of these upward motions with the rise of the thermal phase and with the impulsive hard X-ray burst, as well as considerations of the plasma energetics, favour the interpretation of this phenomenon in terms of chromospheric evaporation. The two measureable parameters of the evaporating plasma, emission measure and velocity, depend on parameters related to the energy deposition and to the thermal phase. The evaporation velocity is found to be correlated with the spectral index of the hard X-ray flux and with the rise time of the thermal emission measure of the coronal plasma. The emission measure of the rising plasma is found to be correlated with the total energy deposited by the fast electrons in the chromosphere by collisions during the impulsive phase and with the maximum emission measure of the coronal plasma.     

Energy changes of cosmic rays in the interplanetary region

A clarification and discussion of the energy changes experienced by cosmic rays in the interplanetary region is presented. It is shown that the mean time rate of change of momentum of cosmic rays reckoned for a fixed volume in a reference frame fixed in the solar system is 〈p〉 =p V·G/3 (p=momentum,V is the solar wind velocity andG=cosmic-ray density gradient). This result is obtained in three ways:

1. by a rearrangement and reinterpretation of the cosmic-ray continuity equation;
2. by using a scattering analysis based on that of Gleeson and Axford (1967);
3. by using a special scattering model in which cosmic-rays are trapped in ‘magnetic boxes’ moving with the solar wind.

The third method also gives the rate of change of momentum of particles within a moving ‘magnetic box’ as 〈p〉_ad = ?p ?·V/3, which is the adiabatic deceleration rate of Parker (1965). We conclude that ‘turnaround’ energy change effects previously considered separately are already included in the equation of transport for cosmic rays.     

Energy of microwave-emitting electrons and hard X-ray/microwave source model in solar flares

We present a new method of estimating the energy of microwave-emitting electrons from the observed rate of increase of the microwave flux relative to the hard X-ray flux measured at various energies during the rising phase of solar flares. A total of 22 flares observed simultaneously in hard X-rays (20–400 keV) and in microwaves (17 GHz) were analyzed in this way and the results are as follows:

1. The observed energy of X-rays which vary in proportion to the 17 GHz emission concentrates mostly below 100 keV with a median energy of 70 keV. Since the mean energy of electrons emitting 70 keV X-rays is ?130 keV or ?180 keV, depending on the assumed hard X-ray emission model (thin-target and thick-target, respectively), this photon energy strongly suggests that the 17 GHz emission comes mostly from electrons with an energy of less than a few hundred keV.
2. Correspondingly, the magnetic field strength in the microwave source is calculated to be 500–1000 G for the thick-target case and 1000–2000 G for the thin-target case. Finally, judging from the values of the source parameters required for the observed microwave fluxes, we conclude that the thick-target model in which precipitating electrons give rise to both X-rays and microwaves is consistent with the observations for at least 16 out of 22 flares examined.

     

Plasma motions in the solar loop of emerging magnetic flux

The results of analyzing variations in the line-of-sight (LOS) velocities in the solar loop at photospheric and chromospheric levels in the region of emerging magnetic flux for the evolving active region NOAA 11024 are reported. The analysis combines the data of multiwave spectropolarimetric observations that were carried out on July 4, 2009, (Tenerife, Spain) using THEMIS solar telescope and the data obtained with GOES, SOHO, and STEREO cosmic satellites. A complex sequence of active events has been studied: formation of the Ellerman bomb, B1 X-ray microflare, and four chromospheric surges that were formed as a result of magnetic reconnection caused by new emerging magnetic flux. The Ellerman bomb was formed in the vicinity of a growing pore. Variations in the velocity V _LOS of the EB had an oscillation character for chromosphere and photosphere. Before the microflare, the average velocities of the upward and downward plasma fluxes in one leg of the magnetic loop were nearly the same—26 km/s. During the microflare, the velocity V _LOS of the ascending and descending flows increased up to ?33 and 50 km/s, respectively. Variations in line-of-sight velocity of a plasma in the second leg of the magnetic loop correlated well with variations of V _LOS in the region of microflare, but they occurred 1.5 minutes later. During the time of observations, four chromospheric ejections of matter were formed and three of them occurred in the region of Ellerman’s bomb formation. Sharp variations in the soft X-ray intensity occurred during these ejections. At photospheric level, variations in the line-of-sight velocity of plasma in the legs of the loop occurred in the opposite direction. In the region of the first leg, velocity V _LOS diminished from ?1.8 to ?0.4 km/s, while the velocity increased from ?0.6 to ?2.6 km/s in the region of the second leg.     

Catalogue of ${>}\,55$ MeV Wide-longitude Solar Proton Events Observed by SOHO,ACE, and the STEREOs at ≈1${\approx}\,1$ AU During 2009 – 2016

Based on energetic particle observations made at \({\approx}\,1\) AU, we present a catalogue of 46 wide-longitude (\({>}\,45^{\circ}\)) solar energetic particle (SEP) events detected at multiple locations during 2009?–?2016. The particle kinetic energies of interest were chosen as \({>}\,55\) MeV for protons and 0.18?–?0.31 MeV for electrons. We make use of proton data from the Solar and Heliospheric Observatory/Energetic and Relativistic Nuclei and Electron Experiment (SOHO/ERNE) and the Solar Terrestrial Relations Observatory/High Energy Telescopes (STEREO/HET), together with electron data from the Advanced Composition Explorer/Electron, Proton, and Alpha Monitor (ACE/EPAM) and the STEREO/Solar Electron and Proton Telescopes (SEPT). We consider soft X-ray data from the Geostationary Operational Environmental Satellites (GOES) and coronal mass ejection (CME) observations made with the SOHO/Large Angle and Spectrometric Coronagraph (LASCO) and STEREO/Coronagraphs 1 and 2 (COR1, COR2) to establish the probable associations between SEP events and the related solar phenomena. Event onset times and peak intensities are determined; velocity dispersion analysis (VDA) and time-shifting analysis (TSA) are performed for protons; TSA is performed for electrons. In our event sample, there is a tendency for the highest peak intensities to occur when the observer is magnetically connected to solar regions west of the flare. Our estimates for the mean event width, derived as the standard deviation of a Gaussian curve modelling the SEP intensities (protons \({\approx}\,44^{\circ}\), electrons \({\approx}\,50^{\circ}\)), largely agree with previous results for lower-energy SEPs. SEP release times with respect to event flares, as well as the event rise times, show no simple dependence on the observer’s connection angle, suggesting that the source region extent and dominant particle acceleration and transport mechanisms are important in defining these characteristics of an event. There is no marked difference between the speed distributions of the CMEs related to wide events and the CMEs related to all near-Earth SEP events of similar energy range from the same time period.     

Heating and cooling of the thermal X-ray plasma in solar flares

Characteristic times for heating and cooling of the thermal X-ray plasma in solar flares are estimated from the time profile of the thermal X-ray burst and from the temperature, emission measure and over-all length scale of the flare-heated plasma at thermal X-ray maximum. The heating is assumed to be due to magnetic field reconnection, and the cooling is assumed to be due to heat conduction and radiation. Temperatures and emission measures derived from UCSD OSO-7 X-ray flare observations are used, and length scales are obtained from Big Bear large-scale Hα filtergrams for 17 small (subflare to Class 1) flares. The empirical values obtained for the characteristic times imply (1) that flares are produced by magnetic field reconnection, (2) that conduction cooling of the thermal X-ray plasma dominates radiative cooling and (3) that reconnection heating and conduction cooling of the thermal X-ray plasma are approximately in balance at thermal X-ray maximum. This model in combination with the data gives estimates for the electron number density (10¹⁰–10¹¹ cm^?3) and the magnetic field strength (10–100 G) in the thermal X-ray plasma and for the total thermal energy generated in a subflare (≈ 10³⁰ erg for an Hα area ≈ 1 square degree) which agree with previous observational and theoretical estimates obtained by others.     

Predicting Flares and Solar Energetic Particle Events: The FORSPEF Tool

A novel integrated prediction system for solar flares (SFs) and solar energetic particle (SEP) events is presented here. The tool called forecasting solar particle events and flares (FORSPEF) provides forecasts of solar eruptive events, such as SFs with a projection to occurrence and velocity of coronal mass ejections (CMEs), and the likelihood of occurrence of an SEP event. In addition, the tool provides nowcasting of SEP events based on actual SF and CME near real-time data, as well as the SEP characteristics (e.g. peak flux, fluence, rise time, and duration) per parent solar event. The prediction of SFs relies on the effective connected magnetic field strength (\(B_{\mathrm{eff}}\)) metric, which is based on an assessment of potentially flaring active-region (AR) magnetic configurations, and it uses a sophisticated statistical analysis of a large number of AR magnetograms. For the prediction of SEP events, new statistical methods have been developed for the likelihood of the SEP occurrence and the expected SEP characteristics. The prediction window in the forecasting scheme is 24 hours with a refresh rate of 3 hours, while the respective prediction time for the nowcasting scheme depends on the availability of the near real-time data and ranges between 15?–?20 minutes for solar flares and 6 hours for CMEs. We present the modules of the FORSPEF system, their interconnection, and the operational setup. Finally, we demonstrate the validation of the modules of the FORSPEF tool using categorical scores constructed on archived data, and we also discuss independent case studies.     

Non-radial oscillations and convective instability of a polytrope with a toroidal magnetic field

We examine the non-radial modes of oscillation, belonging to spherical harmonics of ordersl=1 andl=3, of a gaseous polytrope with a toroidal magnetic field. We find that a toroidal magnetic field increases the growth rate of convective instability for deformations belonging to the spherical harmonicl=1 whereas it decreases the growth rate of convective instability for deformations belonging to the harmonicsl=2 andl=3. The frequencies of the ‘acoustic’ mode and the ‘Kelvin’ mode are decreased by the presence of the toroidal magnetic field.