Non-thermal processes in large solar flares

We analyze particle acceleration processes in large solar flares, using observations of the August, 1972, series of large events. The energetic particle populations are estimated from the hard X-ray and γ-ray emission, and from direct interplanetary particle observations. The collisional energy losses of these particles are computed as a function of height, assuming that the particles are accelerated high in the solar atmosphere and then precipitate down into denser layers. We compare the computed energy input with the flare energy output in radiation, heating, and mass ejection, and find for large proton event flares that:

1. The ～10–10² keV electrons accelerated during the flash phase constitute the bulk of the total flare energy.
2. The flare can be divided into two regions depending on whether the electron energy input goes into radiation or explosive heating. The computed energy input to the radiative quasi-equilibrium region agrees with the observed flare energy output in optical, UV, and EUV radiation.
3. The electron energy input to the explosive heating region can produce evaporation of the upper chromosphere needed to form the soft X-ray flare plasma.
4. Very intense energetic electron fluxes can provide the energy and mass for interplanetary shock wave by heating the atmospheric gas to energies sufficient to escape the solar gravitational and magnetic fields. The threshold for shock formation appears to be ～10³¹ ergs total energy in >20 keV electrons, and all of the shock energy can be supplied by electrons if their spectrum extends down to 5–10 keV.
5. High energy protons are accelerated later than the 10–10² keV electrons and most of them escape to the interplanetary medium. The energetic protons are not a significant contributor to the energization of flare phenomena. The observations are consistent with shock-wave acceleration of the protons and other nuclei, and also of electrons to relativistic energies.
6. The flare white-light continuum emission is consistent with a model of free-bound transitions in a plasma with strong non-thermal ionization produced in the lower solar chromosphere by energetic electrons. The white-light continuum is inconsistent with models of photospheric heating by the energetic particles. A threshold energy of ～5×10³⁰ ergs in >20 keV electrons is required for detectable white-light emission.

The highly efficient electron energization required in these flares suggests that the flare mechanism consists of rapid dissipation of chromospheric and coronal field-aligned or sheet currents, due to the onset of current-driven Buneman anomalous resistivity. Large proton flares then result when the energy input from accelerated electrons is sufficient to form a shock wave.     

The emission and propagation of ∼ 40keV solar flare electrons

Observations of prompt 40 keV solar flare electron events by the IMP series of satellites in the period August, 1966 to December, 1967 are tabulated along with prompt energetic solar proton events in the period 1964–1967. The interrelationship of the various types of energetic particle emission by the sun, including relativistic energy electrons reported by Cline and McDonald (1968) are investigated. Relativistic energy electron emission is found to occur only during proton events. The solar optical, radio and X-ray emission associated with these various energetic particle emissions as well as the propagation characteristics of each particle species are examined in order to study the particle acceleration and emission mechanisms in a solar flare. Evidence is presented for two separate particle acceleration and/or emission mechanisms, one of which produces 40 keV electrons and the other of which produces solar proton and possibly relativistic energy electrons. It is found that solar flares can be divided into three categories depending on their energetic particle emission: (1) small flares with no accompanying energetic phenomena either in particles, radio or X-ray emission; (2) small flares which produce low energy electrons and which are accompanied by type III and microwave radio bursts and energetic ( 20 keV) X-ray bursts; and (3) major solar flare eruptions characterized by energetic solar proton production and type II and IV radio bursts and accompanied by intense microwave and X-ray emission and relativistic energy electrons.     

On proton and electron acceleration by shock waves during large solar flares

The data on optical, X-ray and gamma emission from proton flares, as well as direct observations of flare-associated phenomena, show energetic proton acceleration in the corona rather than in the flare region. In the present paper, the acceleration of protons and accompanying relativistic electrons is accounted for by a shock wave arising during the development of a large flare. We deal with a regular acceleration mechanism due to multiple reflection of resonance protons and fast electrons from a collisionless shock wave front which serves as a moving mirror. The height of the most effective acceleration in the solar corona is determined. The accelerated particle energy and density are estimated. It is shown in particular that a transverse collisionless shock wave may produce the required flux of protons with energy of 10 MeV and of relativistic electrons of 1–10 MeV.The proposed scheme may also serve as an injection mechanism when the protons are accelerated up to relativistic energies by other methods.     

10–100 keV electron acceleration and emission from solar flares

We present an analysis of spacecraft observations of non-thermal X-rays and escaping electrons for 5 selected small solar flares in 1967. OSO-3 multi-channel energetic X-ray measurements during the non-thermal component of the solar flare X-ray bursts are used to derive the parent electron spectrum and emission measure. IMP-4 and Explorer-35 observations of > 22 keV and > 45 keV electrons in the interplanetary medium after the flares provide a measure of the total number and spectrum of the escaping particles. The ratio of electron energy loss due to collisions with the ambient solar flare gas to the energy loss due to bremsstrahlung is derived. The total energy loss due to collisions is then computed from the integrated bremsstrahlung energy loss during the non-thermal X-ray burst. For > 22 keV flare electrons the total energy loss due to collisions is found to be 10⁴ times greater than the bremsstrahlung energy loss and 10² times greater than the energy loss due to escaping electrons. Therefore the escape of electrons into the interplanetary medium is a negligible energetic electron loss mechanism and cannot be a substantial factor in the observed decay of the non-thermal X-ray burst for these solar flares.We present a picture of electron acceleration, energy loss and escape consistent with previous observations of an inverse relationship between rise and decay times of the non-thermal X-ray burst and X-ray energy. In this picture the acceleration of electrons occurs throughout the 10–100 sec duration of the non-thermal X-ray burst and determines the time profile of the burst. The average energy of the accelerated electrons first rises and then falls through the burst. Collisions with the ambient gas provide the dominant energetic electron loss mechanism with a loss time of 1 sec. This picture is consistent with the ratio of the total number of energetic electrons accelerated in the flare to the maximum instantaneous number of electrons in the flare region. Typical values for the parameters derived from the X-ray and electron observations are: total energy in > 22 keV electrons total energy lost by collisions = 10^28–29 erg, total number of electrons accelerated above 22 keV = 10³⁶, total energy lost by non-thermal bremsstrahlung = 10²⁴erg, total energy lost in escaping > 22 keV electrons = 10²⁶erg, total number of > 22 keV electrons escaping = 10^33–34.The total energy in electrons accelerated above 22 keV is comparable to the energy in the optical or quasi-thermal flare, implying a flare mechanism with particle acceleration as one of the dominant modes of energy dissipation.The overall efficiency for electron escape into the interplanetary medium is 0.1–1% for these flares, and the spectrum of escaping electrons is found to be substantially harder than the X-ray producing electrons.Currently at Tokyo Astronomical Observatory, Mitaka, Tokyo, Japan.     

First phase acceleration mechanisms and implications for hard X-ray burst models in solar flares

Requirements for the number of nonthermal electrons which must be accelerated in the impulsive phase of a flare are reviewed. These are uncertain by two orders of magnitude depending on whether hard X-rays above 25 keV are produced primarily by hot thermal electrons which contain a small fraction of the flare energy or by nonthermal streaming electrons which contain > 50% of the flare energy. Possible acceleration mechanisms are considered to see to what extent either X-ray production scenario can be considered viable. Direct electric field acceleration is shown to involve significant heating. In addition, candidate primary energy release mechanisms to convert stored magnetic energy into flare energy, steady reconnection and the tearing mode instability, transfer at least half of the stored energy into heat and most of the remaining energy to ions. Acceleration by electron plasma waves requires that the waves be driven to large amplitude by electrons with large streaming velocities or by anisotropic ion-acoustic waves which also require streaming electrons for their production. These in turn can only come from direct electric field acceleration since it is shown that ion-acoustic waves excited by the primary current cannot amplify electron plasma waves. Thus, wave acceleration is subject to the same limitations as direct electric field acceleration. It is concluded that at most 0.1% of the flare energy can be deposited into nonthermal streaming electrons with the energy conversion mechanisms as they have been proposed and known acceleration mechanisms. Thus, hard X-ray production above 10 keV primarily by hot thermal electrons is the only choice compatible with models for the primary energy release as they presently exist.     

Analysis Of The Disappearing Filament And Flare Of 7 May 1992

By using Yohkoh soft X-ray data, H filtergrams, and radio data, the activation of the disappearing filament and the flare eruption on 7 May 1992 have been studied. Main conclusions are as follows: (1) the emergence of new magnetic flux tends to affect the pre-existing X-ray loops, which usually appear in arcades spanning H filament, changing the magnetic environment of the filament, and then enhance the current in the filament. Therefore newly emerging flux plays a fundamental role in the destabilization of this filament. (2) According to the H data and the rising motion of the filament, the corresponding current variation in the filament has been calculated. It seems that the current interruption may be a possible trigger mechanism for this filament disappearance. (3) The magnetic field strength and the energy flux of energetic electrons in the source region of microwave bursts have been estimated by using the microwave spectrum. During the main phase, the mean magnetic strength and the energy flux of energetic electrons are about 300–400 G and 1×1011 erg cm–2 s –1, respectively. (4) The energy provided by reconnection of the current sheet and the total energy of the current filament are estimated and we show that there is enough energy stored in the filament to feed the 7 May, 1992 flare.     

Evidence for prolonged acceleration based on a detailed analysis of the long-duration solar gamma-ray flare of June 15, 1991

Gamma-ray emission extending to energies greater than 2 GeV and lasting at least for two hours as well as 0.8–8.1 MeV nuclear line emission lasting 40 min were observed with very sensitive telescopes aboard the GAMMA and CGRO satellites for the well-developed post-flare loop formation phase of the 3B/X12 flare on June 15, 1991. We undertook an analysis of optical, radio, cosmic-ray, and other data in order to identify the origin of the energetic particles producing these unusual gamma-ray emissions. The analysis yields evidence that the gamma-rays and other emissions, observed well after the impulsive phase of the flare, appear to be initiated by prolonged nonstationary particle acceleration directly during the late phase of the flare rather than by a long-term trapping of energetic electrons and protons accelerated at the onset of the flare. We argue that such an acceleration, including the acceleration of protons up to GeV energies, can be caused by a prolonged post-eruptive energy release following a coronal mass ejection (CME), when the magnetic field above the active region, strongly disturbed by the CME eruption, relaxes to its initial state through magnetic reconnection in the coronal vertical current sheet.     

Energetics of two-ribbon solar flares

A theory of two-ribbon solar flares is presented which identifies the primary energy release site with the tops of the flare loops. The flare loops are formed by magnetic reconnection of a locally opened field configuration produced by the eruption of a pre-flare filament. Such eruptions are commonly observed about 15 min prior to the flare itself. It is proposed that the flare loops represent the primary energy release site even during the earliest phase of the flare, i.e., the flare loops are in fact the flare itself.Based upon the supposition that the energy release at the loop tops is in the form of Joulean dissipation of magnetic energy at the rising reconnection site, a quantitative model of the energy release process is developed based upon an analytic reconnecting magnetic field geometry believed to represent the basic process. Predicted curves of energy density vs time are compared with X-ray observations taken aboard Skylab for the events of 29 July, 13 August, and 21 August in 1973. Considering the crudity of the model, the comparisons appear reasonable. The predicted field strengths necessary to produce the observed energy density curves are also reasonable, being in the range 100–1000 G.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the relation between solar-flare gamma-ray emission and proton escape into interplanetary space

It is shown that escaping of solar flare energetic protons into interplanetary space as well as their relation to the flare gamma-ray emission depend on the parameter = 8p/B ₀ ² , where p is the pressure of hot plasma and energetic particles and B ₀ is the magnetic field in a flaring loop. If 1, the bulk of the energetic protons escape to the loss cone because of diffusion due to small-scale Alfvén-wave turbulence, and precipitate into the footpoints of the flaring loop. The flare then produces intense gamma-ray line emission and a weak flux of high energy protons in interplanetary space. If >_*0.3-1.0, then fast eruption of hot plasma and energetic particles out of the flaring loop occurs, this being due to the flute instability or magnetic-field-plasma nonequilibrium. The flare then produces a comparatively weak gamma-radiation and rather intense proton fluxes in interplanetary space. We predict a modulation of the solar flare gamma-ray line emission with a period 1 s during the impulsive phase that is due to the MHD-oscillations of the energy release volume. The time lag of the gamma-ray peaks with respect to the hard X-ray peaks during a simultaneous acceleration of electrons and protons can be understood in terms of strong diffusion.     

Evolvement of microwave spike bursts in a solar flare on 2006 December 13

Solar radio spikes are one of the most intriguing spectral types of radio bursts. Their very short lifetimes, small source size and super-high brightness temperature indicate that they should be involved in some strong energy release, particle acceleration and coherent emission processes closely related to solar flares. In particular, for the microwave spike bursts, their source regions are much close to the related flaring source region which may provide the fundamental information of the flaring process. In this work,we identify more than 600 millisecond microwave spikes which recorded by the Solar Broadband Radio Spectrometer in Huairou(SBRS/Huairou) during an X3.4 solar flare on 2006 December 13 and present a statistical analysis about their parametric evolution characteristic. We find that the spikes have nearly the same probability of positive and negative frequency drifting rates not only in the flare rising phase, but also in the peak and decay phases. So we suppose that the microwave spike bursts should be generated by shockaccelerated energetic electrons, just like the terminational shock(TS) wave produced by the reconnection outflows near the loop top. The spike bursts occurred around the peak phase have the highest central frequency and obviously weak emission intensity, which imply that their source region should have the lowest position with higher plasma density due to the weakened magnetic reconnection and the relaxation of TS during the peak phase. The right-handed polarization of the most spike bursts may be due to the TS lying on the top region of some very asymmetrical flare loops.     

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.

     

Energies of Electrons Accelerated in Turbulent Reconnecting Current Sheets in Solar Flares

Yohkoh observations strongly suggest that electron acceleration in solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Unfortunately, models for particle acceleration in reconnecting current sheets predict electron energy gains in terms of the reconnection electric field and the thickness of the sheet, both of which are extremely difficult to measure. It can be shown, however, that application of Ohm's law in a turbulent current sheet, combined with energy and Maxwell's equations, leads to a formula for the electron energy gain in terms of the flare power output, the magnetic field strength, the plasma density and temperature in the sheet, and its area. Typical flare parameters correspond to electron energies between a few tens of keV and a few MeV. The calculation supports the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a large-scale turbulent current sheet above the soft X-ray flare loops.     

Energetics of a double flare on November 8, 1980

Here we complete an energy balance analysis of a double impulsive hard X-ray flare. From spatial observations, we deduce both flares probably occur in the same loop within the resolution of the data. For the first flare, the energy in the fast electrons (assuming a thick-target model) is comparable to the convective up-flow energy, suggesting that these are related successive modes of energy storage and transfer. The total energy lost through radiation and conduction, 2.0 × 10²⁸ erg, is comparable to the energy in fast electrons 2.5 × 10²⁸ erg. For the second flare, the energy in the fast electrons is more than one order of magnitude greater than the energy of the convective up-flow. Total energy losses are within a factor of two lower than the calculated fast electron energy. We interpret the observations as showing that the first flare occurred in a small loop with fast electrons heating the chromosphere and resulting in chromospheric evaporation increasing the density in the loop. For the second flare most of the heating occurred at the electron acceleration site. The two symmetrical components of the Ca xix resonance line and a high velocity down-flow of 115 km s ^–1 observed at the end of the second hard X-ray burst are consistent with the flare eruption (reconnection) region being high in the flare loop. The estimated altitude of the acceleration site is 5500 km above the photosphere.     

A current ribbon model for energy storage and release with application to the flare of 7 January 1992

Observations of the flare on 7 January 1992 are interpreted using a topological model of the magnetic field. The model, developed here, applies a theory of three-dimensional reconnection to the inferred magnetic field configuration for 7 January. In the model field a new bipole ( 10²¹ Mx) emerges amidst pre-existing active region flux. This emergence gives rise to two current ribbons along the boundaries (separators) separating the distinct, new and old, flux systems. Sudden reconnection across these boundary curves transfers 3 ×10²⁰ Mx of flux from the bipole into the surrounding flux. The model also predicts the simultaneous (sympathetic) flaring of the two current ribbons. This explains the complex two-loop structure noted in previous observations of this flare. We subject the model predictions to comparisons with observations of the flare. The locations of current ribbons in the model correspond closely with those of observed soft X-ray loops. In addition the footpoints and apexes of the ribbons correspond with observed sources of microwave and hard X-ray emission. The magnitude of energy stored by the current ribbons compares favorably to the inferred energy content of accelerated electrons in the flare.     

On the reconciliation of simultaneous microwave imaging and hard X-ray observations of a solar flare

We have compared microwave imaging data for a small flare with simultaneous hard X-ray spectral observations. The X-ray data suggest that the power-law index of the energy distribution of the radiating electrons is 5.3 (thick-target) which differs significantly from the estimate ( = 1.4) from a homogeneous optically-thin gyrosynchrotron model which fits the radio observations well. In order to reconcile these results, we explore a number of options. We investigate a double power-law energy spectrum for the energetic electrons in the flare, as assumed by other authors: the power law is steep at low energies and much flatter at the higher energies which produce the bulk of the microwaves. The deduced break energy is about 230 keV if we tentatively ignore the X-ray emission from the radio-emitting electrons: however, the emission of soft photons by the flat tail strongly contributes to the observed hard X-ray range and would flatten the spectrum there. A thin-target model for the X-ray emission is also inconsistent with radio data. An inhomogeneous gyrosynchrotron model with a number of free parameters and containing an electron distribution given by the thick-target X-ray model could be made to fit the radio data.     

Hard X-ray imaging evidence of nonthermal and thermal burst components

We analyze hard X-ray imaging observations of three flares, showing widely different characteristics, in order to try and discriminate the relative efficiency of heating and acceleration in the primary energy release. Using a simplified approach, we compute the hard X-ray distribution and energy deposition due to accelerated electrons, with beam and ambient plasma parameters appropriate for each of the observed events. The results are convolved with the Hard X-Ray Imaging Spectrometer (HXIS) instrumental response and compared with observations. We find that: (a) Many observations are compatible with thick target processes, and with the possibility that flares may have high (>20%) acceleration efficiency. (b) Single hard X-ray sources should be very common in the data available at present (HXIS and HINOTORI), as it is the case, as well as a transition from chromospheric footpoints to single source structures. The latter cannot then be directly interpreted as thermal sources. (c) In the particular case of a limb flare, associated with a rather weak high energy burst, we show that the spatial and spectral behavior of the hard X-ray emission is incompatible with pure nonthermal processes. We thus propose that the observed emission was principally due to the strong heating intrinsic to a reconnection process within the region of interaction between two magnetic structures which are seen in the soft X-ray data. (d) We also study the heating effect of a beam, due to Coulomb losses, during its passage through the flare loops. In some cases, rather large and localized temperature increases can be expected to appear within short timescales ( 1 s), leading to a combination of nonthermal plus thermal output in the hard X-ray spectrum, which renders virtually impossible the determination of the underlying beam parameters. We finally discuss the extent to which our conclusions are valid, considering the instrumental limitations as well as the simple physical treatment that we apply.     

A Quantitative Model of Energy Release and Heating by Time-dependent,Localized Reconnection in a Flare with Thermal Loop-top X-ray Source

We present a quantitative model of the magnetic energy stored and then released through magnetic reconnection for a flare on 26 February 2004. This flare, well observed by RHESSI and TRACE, shows evidence of non-thermal electrons for only a brief, early phase. Throughout the main period of energy release there is a super-hot (T?30 MK) plasma emitting thermal bremsstrahlung atop the flare loops. Our model describes the heating and compression of such a source by localized, transient magnetic reconnection. It is a three-dimensional generalization of the Petschek model, whereby Alfvén-speed retraction following reconnection drives supersonic inflows parallel to the field lines, which form shocks: heating, compressing, and confining a loop-top plasma plug. The confining inflows provide longer life than a freely expanding or conductively cooling plasma of similar size and temperature. Superposition of successive transient episodes of localized reconnection across a current sheet produces an apparently persistent, localized source of high-temperature emission. The temperature of the source decreases smoothly on a time scale consistent with observations, far longer than the cooling time of a single plug. Built from a disordered collection of small plugs, the source need not have the coherent jet-like structure predicted by steady-state reconnection models. This new model predicts temperatures and emission measure consistent with the observations of 26 February 2004. Furthermore, the total energy released by the flare is found to be roughly consistent with that predicted by the model. Only a small fraction of the energy released appears in the super-hot source at any one time, but roughly a quarter of the flare energy is thermalized by the reconnection shocks over the course of the flare. All energy is presumed to ultimately appear in the lower-temperature (T?20 MK) post-flare loops. The number, size, and early appearance of these loops in TRACE’s 171 Å band are consistent with the type of transient reconnection assumed in the model.     

Acceleration through X-type coalescence in a small energetic flare

We studied the acceleration conditions in the small but fairly energetic flare of May 21, 1984 at 1326 UT. The most pronounced aspect of this flare was a series of 13 microwave/X-ray spikes, each lasting for about 0.1 s. A previous study has shown that each of these was due to a series of successive sudden formations of small plasma knots of high-energy particles. Each of these knots lost its energy in about 50 ms. In the present study we show that these knots can originate by the process of X-type (3-D) flux tube coalescence. The predicted rise time (30 to 50 ms) and energy are in good agreement with the observationally derived parameters.     

Ion-cyclotron instability and electron acceleration in coronal loops

Quasi-electrostatic electron and ion-cyclotron instabilities are studied. The result indicates that the higher harmonic ion cyclotron instabilities (ICI) can be excited while the fast ions produced from reconnection are injected into a coronal loop. Part of the energetic ions can be dragged out of the magnetic mirror turning points and a negative plasma potential is generated. The plasma potential may directly accelerate the electrons up to the relativistic velocity within a short time. This acceleration is similar to the processes occurring in the magnetic mirror devices of controlled thermonuclear fusion. The spectrum and flux of accelerated electrons have also been obtained. Some observational results during the solar flare might be explained by this acceleration mechanism.     

White light events as photospheric flares

We consider the possibility that white light flares are due to heating of the photosphere by a flux of energetic ions and electrons impinging on it from above. Particles with energy in the range 10 MeV to 1 BeV release most of their energy to the ambient gas at about optical depth unity in the photosphere. This increase in energy produces a temperature perturbation of several hundred degrees in the layer and results in a re-radiation of the energy with a radiative relaxation time of several seconds. The consequences of this model are applied to a study of the great flare of May 23, 1967 and to the very fast event of August 11, 1954. Large numbers of very energetic electrons or protons must be produced in the first few minutes of the primary flare event if our interpretation (or one based on synchrotron emission) is correct.After this paper had been submitted and accepted for publication we received from Dr. vestka a copy of his paper, The Phase of Particle Acceleration in the Flare Development, which was then already in proof. (It appeared in Solar Phys. 13, 471.) A number of the arguments contained in our paper, which we had previously presented in abstract form (Najita and Orrall, 1969) and in part in a dissertation (Najita, 1969), are independently discussed by Dr. vestka who was unaware of our earlier work. Although the ground covered by his and our paper touches in places we have left our paper as originally submitted and believe that this independent agreement supports the conclusions of both.