The heating of the temperature minimum region in solar flares — A reassessment

As a sequel to the work by Machado et al. (1978), we discuss and evaluate the suggestions made by these authors on how to possibly reconcile the observed temperature enhancements at temperature-minimum levels in solar flares with some form of theoretical heating mechanism. After establishing the H^– LTE assumption used by Machado et al., we then consider EUV irradiation, and joule heating by steady currents, as heating mechanisms. We find that, unless there are strong inhomogeneities associated with either mechanism, neither can reasonably be reconciled with observations. It is concluded that detailed, high resolution (both spatial and temporal) measurements are necessary to further our understanding of the flare process at temperature-minimum levels.On leave from: Department of Astronomy, The University, Glasgow G12 8QQ, Scotland, U. K.     

Temperature minimum heating in solar flares by resistive dissipation of Alfvén waves

We examine the possibility that the strong heating produced at temperature-minimum levels during solar flares is due to resistive dissipation of Alfvén waves generated by the primary energy release process in the corona. It is shown how, for suitable parameters, these waves can carry their energy essentially undamped into the temperature-minimum layers and can then produce a degree of heating consistent with observations.Also Department of Applied Physics, Stanford University.     

On the regimes of heating during solar flares

We suggest a new differential method whereby we have detected the separation of a long-duration flare into intervals characterized by different regimes of plasma heating and cooling based on soft X-ray data. The rise phase of the flare is shown to consist of accelerated and decelerated heating regimes compared to an exponential law. Accelerated cooling takes place at the beginning of the decay phase, which is followed by decelerated one. The final part of the flare is a prolonged process of cooling according to a nearly exponential law.     

The structure of high-temperature solar flare plasma in non-thermal flare models

We solve the energy equation for the high-temperature (coronal) component of flare plasma for two models of energy input: (i) direct collisional heating by a beam of suprathermal electrons, and (ii) ohmic heating by the beam-neutralizing reverse current. We discuss the regimes where each case is applicable, and solve for the differential emission measure distribution of the coronal plasma in each case. Scaling laws between loop temperatures and injected electron fluxes are derived for both models; these are testable observationally through coordinated soft X-ray and hard X-ray observations, thus providing a method of discriminating between the two cases. We also readdress the question of the energetic importance of a return current which is below the instability threshold for generation of ion-acoustic plasma turbulence. We find that unless the ambient coronal density is very low ( 10⁹ cm ^–3), collisional heating will always dominate there, in agreement with the findings of previous authors. However, in the chromosphere/corona transition region, the relatively low temperature and correspondingly high plasma resistivity imply that reverse current ohmic heating can predominate the flare energetics, by up to an order of magnitude.Presidential Young Investigator.     

The coronal and transition region temperature structure of a solar active region

Using measurements of EUV and X-ray spectral lines we derive the differential emission measure vs electron temperature T from the transition region to the corona of an active region (10⁵ T <5 × 10⁶ K). The total emission measure and radiative losses are of order 3 × 10⁴⁸ cm^–3 and 4 × 10²⁶ ergss^–1 respectively. The emission measure at T > 10⁶ K (i.e. that mainly responsible for the X-ray emission) is about 75% of the total. We also examine the use of Mg x 625 Å as an indicator of coronal electron density. A set of theoretical energy balance models of coronal loops in which the loop divergence is a variable parameter is presented and compared with the observations. Particular attention is given to the limitations inherent in any such comparison.     

The heating of the solar transition region

The temperature curve in the solar chromosphere has puzzled astronomers for a long time.Referring to the structure of supergranular cells,we propose an in ductive heating model.It mainly includes the following three steps.(1) A small-scale dynamo exists in the supergranulation and produces alternating small-scale magnetic fluxes;(2) The supergranular flow distributes these small-scale fluxes according to a regular pattern;(3) A skin effect occurs in the alternating and regularly-distributed magnetic fields.The induced current is concentrated near the transition region and heats it by resistive dissipation.     

Polarization structure of a solar flare region at 9.5 mm wavelength

Polarization structure of an active region that produced a minor flare around 1900 UT on September 28, 1971 was measured at 9.5 mm wavelength using the 85-ft telescope of the Naval Research Laboratory Maryland Point Observatory. The angular resolution of the telescope at this wavelength is 1.6. The flare region underwent changes both in the degree of polarization as well as in its polarization structure before and after the start of the flare. These changes in the degree of polarization correspond to a decrease of longitudinal magnetic field of about 200 G at the chromospheric levels where the 9.5 mm radiation originates. Observations on the polarization structure of active regions for several days before and after September, 1971 are also presented.     

The structure of the solar flare stream magnetic field

The structure of the interplanetary magnetic field within the flare streams as well as associated variations of the geomagnetic disturbancy are considered. It is shown that in the main body of the flare stream the magnetic field is determined by the configuration of the large scale magnetic field on the Sun at the flare region. Within the head part of the flare stream the magnetic field represents by itself the compressed field of the background solar wind and hence is determined by the distribution of the super large scale solar magnetic field outside the flare region.A certain asymmetry in the parameters of the magnetic field within the streams associated with geoeffective and non-effective flares is shown to exist.     

The eruption of active region filaments and its relation to the triggering of a solar flare

The formation and eruption of active region filaments is supposed to be caused by the increase of a concentrated current embedded in the active region background magnetic field of an active region according to the theory of Van Tend and Kuperus (1978).The onset of a filament eruption is due to either changes in the background magnetic field or the increase of the filament current intensity. Both processes can be caused by the emergence of new magnetic flux as well as by the motion of the photospheric footpoints of the magnetic field lines. It is shown that if the background field evolves from a potential field to a nearly force-free field the vertical equilibrium of the current filament is not affected, but large forces are generated along the filament axis. This is identified as the cause of filament activation and the increase in filament turbulence during the flare build-up phase. Depending on the evolution of the background field and the current filament, two different scenarios for flare build-up and filament eruption are distinguished.This work was done while one of the authors (M.K.) was participating in the CECAM workshop on Physics of Solar Flares held at Orsay, France, in June 1979.     

Location of the electron acceleration region in solar flares

Observations of impulsive solar flare X-rays 10 keV by the OGO-5 satellite and the measurements of energetic solar electrons made with the Explorer-35 and Explorer-41 (IMP-5) satellites during the period March 1968–September 1969 have been analyzed in order to determine the ion density in the X-ray source region as well as the location of the electron acceleration region in the solar atmosphere. If we assume that the efficiency of escape of the accelerated electrons into interplanetary space is 10^–3, the observations are found to be consistent with the following interpretation: (i) the ion density in the X-ray source region varies from event to event and lies between 10⁹ and 10¹¹ ions cm^–3 for those events in which the impulsive X-ray emission could be detected; (ii) for those events in which no impulsive emission was detected above threshold, the ion density in the X-ray source was < 10⁹ ions cm^–3; (iii) at least in some small solar flares the region where the electrons are accelerated during the flash phase is located in the lower corona.     

Kernel heating and ablation in the impulsive phase of two solar flares

At the very start of the impulsive phase of two solar flares the temperature derived from medium-energy ( 16 keV) X-ray countrates was observed to rise abruptly, by several times 10⁷ K above the temperature derived from low-energy X-ray ( 7 keV) countrates. The difference between the two temperatures relaxed to zero thereafter, quasi-exponentially, with a characteristic time of 1.5 min. This differential temperature variation appears to mimique the differences between the ionic kinetic and the electron temperatures derived from spectral observations (Figures 1 and 2).These observations are explained in a quantitatively supported model of the flare kernel (Figure 4) in which the kernel is heated by electron beams from above. The low-energy electrons are stopped above the kernel and only the medium and high energy electrons penetrate down to the top of the chromosphere, causing heating of the chromospheric gas to about 50 MK, and ablation (evaporation), leading to the abrupt formation of a superhot flare kernel and a likely superhot dome above it (Figure 4), through which gas rises up and spreads out convectively, while cooling down in approximately the same time (45 s). The heating process lasts only for a few minutes. The difference between the Doppler temperature and the electron temperature derived from line intensity ratios or from low energy countrate ratios is ascribed to truncation of the tail of the electron energy distribution in the kernel. The kernel is about 2500 km deep; H emission is radiated by a thin layer at its basis.     

Fine structure of a solar flare region at 3.7 and 11.1 cm wavelengths

On June 9, 1973, a flare associated burst was observed with the NRAO 3-element interferometer at 3.7 and 11.1 cm wavelength. The burst was of gradual rise and fall type. Comparing the fringe amplitudes at 3.7 cm to the visibility computed for model flare regions we found that the precursor data are best fitted by a region of 3 in size while at the time of the peak, the flare appears to have a size of 2. During the post-maximum phase a size of 5 is the best estimate. Similar computations have been done for 11.1 cm data. The peak brightness temperatures are 1.2 × 10⁹ K and 1.65 × 10⁸ K at 3.7 and 11.1 cm respectively. Such high temperatures would imply that a significant fraction of the burst radiation has a non-thermal origin.     

Collisional and return current heating functions for beam-heated models of solar flares

In beam-heated models of solar flares, the bulk of the energy deposited in the flare atmosphere resides in the low-energy end of the electron spectrum. Since the shape of the spectrum at low energy is not well determined observationally, various forms of low-energy cut-off have been assumed in theoretical modelling. Certain results of such modelling may depend strongly on the assumed spectrum. We derive the heating distributions for various spectra, both for collisional energy loss and for Ohmic dissipation of the return current, and show that none of the spectra are fully satisfactory, according to the criteria that for both collisional and Ohmic heating, the heating rate should be bounded, continuous, and smooth, and have a tractable functional form. A simple form of electron spectrum is suggested, which satisfies these criteria.     

X-ray heating of a low-temperature region in chromospheric flares

Part of the proper X-ray emission of a flare is absorbed in the chromosphere and heats the region which creates an optical (in particular Hα) flare emission. The heating of chromosphere by X-ray emission may be responsible for the diffuse halo around the flare kernels. The optical emission of flare kernels, whose main sources of heating are energetic particles and/or thermal fluxes, may be also increased. By simple model calculations the present paper discusses the possibility of such effects for the large flare of 1972 August 7.     

A high-energy solar flare burst complex and the physical properties of its source region

We discuss a solar flare microwave burst complex, which included a major structure consisting of some 13 spikes of 60 ms FWHM each, observed 21 May, 1984 at 90 GHz (3 mm). It was associated with a simultaneous very hard X-ray burst complex. We suggest that the individual spikes of both bursts were caused by the same electron population: the X-bursts by their bremsstrahlung, and the microwave bursts by their gyrosynchrotron emission. This latter conclusion is based on the evidence that the radio turnover frequency was 150 GHz. It follows that the emission sources were characterized by an electron density of about 10¹¹ cm^–3, a temperature of 5 × 10⁸ K and a magnetic field of about 1400–2000 G. They had a size of about 350 km; if the energy release is caused by reconnection the sources of primary instability could have been smaller and in the form of thin sheets with reconnection speed at a fraction of the Alfvén velocity and burst-like energy injections of 10²⁷ erg during about 50 ms each. The energized plasma knots lost their injection energy by saturated convective flux (collisionless conduction) in about 30 ms.     

Beam-driven return current instability and anomalous plasma heating in solar flares

We consider the problem of ion-acoustic wave generation, and resultant anomalous Joule heating, by a return current driven unstable by a small-area thick-target electron beam in solar flares. With a prescribed beam current evolution, j _b (t) (and, therefore, a prescribed return current j _p (t) = –j _b (t)), and using an approximate local treatment with a two component Maxwellian plasma, and neglecting energy losses, we demonstrate the existence of two quite distinct types of ion-acoustic unstable heating regimes. First, marginally stable heating occurs when the onset of instability occurs at electron-ion temperature ratios T _e /T _i > 4.8. Secondly, there exists a catastrophic heating regime for which marginally stable evolution is impossible, when the onset of instability occurs at T _e /T _i < 4.8.For the marginally stable case, we solve the electron and ion heating equations numerically and find that rapid anomalous Ohmic heating occurs in a substantial plasma volume. This large hot plasma emits thermal bremsstrahlung hard X-rays ( 20 keV) comparable to, or exceeding, the nonthermal bremsstrahlung which would have been emitted by the beam in a conventional thick target, large area, collisional scenario without anomalous effects. This means that, contrary to the usual assumption, onset of return current instability need not turn off hard X-ray production by a beam, though changing its source from direct to indirect. Indeed with small beam areas, this indirect mechanism can result in a higher hard X-ray bremsstrahlung efficiency than in a conventional collisional thick target.The catastrophic heating regime, for which we expect much larger wave levels, is discussed qualitatively, and preliminary results cited of an alternative approach, incorporating an equation directly describing the electrostatic wave energy level. Which of these two regimes will pertain in any particular case depends (discontinuously) on the beam and atmospheric parameters and we suggest that this effect may manifest itself in the distinctive temporal behaviour of X-ray flares.     

Role of nonthermal electrons in the heating of solar atmosphere during flares

Evolution of electron energy distributions have been studied by combining small-angle scattering with analytical treatment of large-angle collision using the Monte-Carlo technique. By use of these, the distributions and energy loss have been calculated as functions of column density, the heating functions have been calculated at different depths of the solar atmosphere. From the heating functions, an increase in temperature produced by the electrons at different column densities has been computed. It is found that rise in temperature increases with an increase in incident electron energy.     

Investigation of non-uniform heating during the decay phase of solar flares

We have analysed X-ray spectra of 13 solar flares as obtained by the Bent Crystal Spectrometer (BCS) on the Solar Maximum Mission. In particular, we have examined the observed ratio of T _Fe/T _Ca where T _Fe and T _Ca are the temperatures obtained from the Fexxv and Caxix spectra, respectively. In order to simplify the investigation we have analysed only flares which reach quasi-steady-state during the decay. It turned out that the observed ratios cannot be explained by a model consisting of a single, uniformly heated loop, with a constant or variable cross-sectional area. We propose that this problem may be solved by introducing some distribution of the heating function across the flaring loop. This model has been tested by detailed calculations.     

Energy build-up and release mechanisms in solar and auroral flares

The 80 and 160 MHz radioheliograph observations of a flare-associated outburst in June 1973 reveal three distinctive type IV continuum sources: a flare continuum, an isolated moving continuum and a storm continuum, in that time sequence. The observed characteristics of the three sources and their relations in space and time are described. The observed characteristics and the interrelations between the three continuum sources are explained in terms of energetic electrons trapped and accelerated in, and ejecta moving through, an arch-like magnetic field. It is also suggested that the isolated moving source - in the present event and in similar ones - is probably quite independent of the MHD shock wave which is responsible for the preceding type II burst.     

Impulsive phase heating and a coronal explosion in a solar flare

The flare of 12 November 1980, 0250 UT, in Active Region 2779 (NOAA classification) was studied by using X-ray images obtained with the Hard X-Ray Imaging Spectrometer aboard NASA's Solar Maximum Mission. In a ten-minute period, between about 0244 and 0254 UT, some five short-lived impulsive bursts occurred. We found that the so-called hard bursts ( 15 keV) are also detectable in low energy images. During that 10 min period - the impulsive phase - the heat input into the flare and the total number of energetic electrons increased practically exponentially, to reach their maximum values at 0254 UT. At the end of that period, when the thermal energy content of the flare was largest, a burst was observed, for the first time, to spread in a broad southern direction from an initially small area with a speed of about 50 km s^–1. We have called this phenomenon a coronal explosion.Fokker Aircraft Industries, Schiphol, The Netherlands.