The structure of high-temperature flare plasma

In Paper I (Emslie, 1985) we derived scaling laws which relate peak loop temperature to injected non-thermal electron flux in electron-heated models of the flare corona. In this paper, we compare these predicted relationships with recent coordinated observations in hard X-rays and soft X-rays. Satisfactory agreement is found for large events, while for smaller events the plasma electron temperature determined by soft X-ray spectral fitting is too high. We discuss a possible resolution of this apparent discrepancy through careful examination of the method used to determine the temperature of the soft X-ray emitting plasma. It is concluded that temperatures determined by spectral fitting over a series of lines are not necessarily representative of the true temperature of the plasma, since the fitting technique is plagued by the same difficulties as a more straightforward technique involving a single spectral line or portion of continuum (Craig and Brown, 1976). The differences between actual and derived temperatures are sufficiently large to remove the above discrepancy between observations and modeling of electron-heated coronae.Presidential Young Investigator.     

Heat balance for the high-temperature component of a solar flare

Shortly after the occurrence of the impulsive spikes of the two-ribbon flare of May 21, 1980, a temperature analysis of the X-ray emitting flare plasma showed the presence of a low-temperature component [n = 15 × 10¹⁰ cm^#X2212;3; T = 20 × 10⁶ K] and a high-temperature component [n = 2 × 10¹⁰ cm^#X2212;3; T = 40 × 10⁶ K]. The mean free path of an electron in the hot component is comparable to the size of the source (≈ 10⁴ km). Heat losses from the hot source can therefore not be described with classical formulae. Theoretical arguments show that most likely the electron to ion temperature ratio T _e/T_i in the hot plasma is close to unity. This implies the presence of a hot ion component (T _i ≈ 40 × 10⁶ K) as well. Under these conditions (T _e ≈ T _i) heat flux limitation by electrostatic turbulence is ineffective. However, reduction of the heat flux is still possible due to the breakdown of classical theory. It is demonstrated that only non-classical current dissipation processes can sustain a hot source against cooling by a saturated heat flux. Investigation of the collisionality as a function of position along a magnetic loop shows that the breakdown of classical theory should be expected to occur first near the base of the loop. We conclude that the newly discovered hot source is important for the energy budget of the flare, even if the heat losses are considerably reduced. It is estimated that for the May 21, 1980 flare a total of about 10³¹ ergs were necessary to maintain the hot source against heat losses over the time period that it was observed (≈ 10 min).     

Beam-return current systems in nonthermal solar flare models

Previous investigations of return currents driven by suprathermal electron beams in solar flares have been based both conceptually and mathematically on analyses of electron beams in the laboratory environment. However, the physics of laboratory electron beams is fundamentally different from the physics of solar flare electron beams. Consider first the laboratory beam, which is injected into the plasma from an external source and is, therefore, modeled as a semi-infinite charged rigid rod. The longitudinal electrostatic field of such a charged rod has no preferred direction and therefore cannot drive a return current. Consequently, in the laboratory the return current is established inductively through the appearance of the changing magnetic field associated with the rising beam current, there being no offsetting displacement current term in such a geometry. It subsequently decays on the resistive time-scale; because of this decay, the net current of the system increases, and the lifetime of the electron beam becomes limited by self-pinching effects. Therefore, in the laboratory, the beam/return current system cannot reach a steady state.By contrast, the electron beam in the solar flare forms in situ and the longitudinal electrostatic field is produced by charge separation. Such an electrostatic field does have a preferred direction and so can drive a cospatial return current. Further, the magnetic field generated by the beam current is always close to being offset by either the magnetic field associated with the displacement current (E/t) or the electrostatically-driven return current; hence, inductive fields are never important. Thus, in the solar flare the return current is principally established by electrostatic fields; the return current is continuously driven and does not decay resistively. Thus, if the acceleration mechanism drives a steady beam current, then the beam/return current system rapidly achieves a steady state. We present in this paper analytic expressions for the approach to this state.Presidential Young Investigator.     

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.     

A classification scheme for solar flare models

We present a classification scheme for solar flare models that utilize magnetic free energycurrents. The classification scheme is geometry independent and delineates models into two categories: those models utilizing currents flowing parallel to B and those utilizing currents flowing perpendicular to B. This delineation of drivers allows us to specify what kinds of plasma-magnetic field configurations should be expected for a given current driver. Further, the delineation of drivers will allow us to identify both the strengths and the weaknesses of the various models.Based on invited talks given at the SERF Workshop (Aug. 13, 1979) and the IAU Meeting of Commission 10 (Aug. 15, 1979) held in Montreal.     

Evolution of the high-temperature plasma in the 15 June 1973 flare

The analysis of the high temperature plasma in Fe xxiii–xxiv in the 15 June 1973 flare is presented. The observations were obtained with the NRLXUV spectroheliograph on Skylab. The results are: (1) There was preheating of the active region in which the flare occurred. In particular, a large loop in the vicinity of the flaring region showed enhanced brightness for many hours before the flare. The loop disappeared when the flare occurred, and returned in the postflare phase, as if the energy flux which had been heating the large loop was blocked during the flare and restored after the flare was gone. The large magnetic fields did not change significantly. (2) The flare occurred in low-lying loop or loops. The spatial distribution of flare emission shows that there was a temperature gradient along the loop. (3) The high temperature plasma emitting Fe xxiii and xxiv had an initial upward motion with a velocity of about 80 km s^–1. (4) There was large turbulent mass motion in the high temperature plasma with a random velocity of 100 to 160 km s^–1. (5) The peak temperature of the hot plasma, determined from the Fe xxiii and xxiv intensity ratio, was 14 × 10⁶ K. It decreased slightly and then, for a period of 4 min, remained at 12.6 × 10⁶ K before dropping sharply to below 10 × 10⁶ K. The density of the central core of the hot plasma, determined from absolute intensity of Fe xxiv 255 Å line, was of the order of 10¹¹ cm^–3.The persistence of the high level of turbulence and of the high temperature plateau in the decaying phase of the flare indicates the presence of secondary energy release. From the energy balance equation the required energy source is calculated to be about 3 to 7 ergs cm^–3 s^–1.Ball Brothers Research Corporation.     

Stochastic forces on electrons in the solar flare plasma

A Langevin equation for electrons in the plasma of a solar flare with electrostatic lower-hybrid-drift turbulence is developed from first principles and in consistency with the kinetic theory in the polarization approximation. The waves are assumed to be excited by small density gradients causing drift velocities below the thermal ion velocity. First utilizable expressions for the space-time spectral density of the wave energy are given, and estimates of the mean wave force on an electron as well as of the intensity of the stochastic wave force are made. It seems that almost electrostatic lower-hybrid-drift waves could contribute to electron chaotization in solar flare plasmas.Presented at the CESRA-Workshop on Coronal Magnetic Energy Release at Caputh near Potsdam in May 1994.     

Magnetic reconnection in high-temperature plasma of solar flares

Quasi-steady high-temperature current sheets are an energy source during the main or hot phase of solar flares. Such sheets are shown to be stabilized with respect to the tearing instability by a small transverse component of magnetic field existing in the sheets.     

Relationship between CME dynamics and solar flare plasma

The relationship between the velocity of CMEs and the plasma temperature of the associated X-ray solar flares is investigated.The velocity of CMEs increases with plasma temperature(R=0.82)and photon index below the break energy(R=0.60)of X-ray flares.The heating of the coronal plasma appears to be significant with respect to the kinetics of a CME from the reconnection region where the flare also occurs.We propose that the initiation and velocity of CMEs perhaps depend upon the dominant process of conversion of the magnetic field energy of the active region to heating/accelerating the coronal plasma in the reconnected loops.Results show that a flare and the associated CME are two components of one energy release system,perhaps,magnetic field free energy.     

The dependence of solar flare energetics on flare volumes

Solar X-ray flare images from Skylab and data from full Sun detectors were used in a statistical analysis to determine the relationship between flare volumes and flare energetics. Data from the rise phases of 45 flares were used in the analysis. For each event the diameter D, length L, and volume V of the flare loops were determined and then compared to the thermal energy, rate of increase of thermal energy, and rise time of the soft X-ray flux. The latter three quantities were all found to be positively correlated with D, L, and V. However, the thermal energy per unit volume and rate of increase of thermal energy per unit volume decrease with increasing volume. No correlation was found between emission measure Y and volume V, indicating that the electron density tends to be smaller for larger flare volumes. We find a larger dynamic range for V than for Y, hence knowledge of V is more critical than that of Y for calculating the thermal energy of the X-ray emitting structure, which is proportional to Y ^0.5 V ^0.5. Using certain assumptions, the results were compared to several flare models. The classical neutral sheet model, the sheared loop model of Spicer and even models using the magnetic field in a passive role for the energy release were all found to be consistent with the results.     

Magnetic reconnection in a high-temperature plasma of solar flares

A simple self-consistent model of a high-temperature turbulent current sheet (HTCS) is considered. The anomalous character of plasma conductivity in a sheet is assumed to be due to gradient instabilities. The possibility of a low threshold of their excitation is demonstrated by an example of temperature-drift instability.Application of the HTCS model to the hot or main phase of a solar flare is discussed. The model consistently explains many observed properties of this phase.     

The spatial structure of a solar flare in soft X-rays and centimetric wavelengths

High-resolution images of the decay phase of a soft X-ray flare observed by the S-054 experiment on Skylab are compared with interferometric scans of the radio burst obtained simultaneously at 2.8 cm (Felli et al., 1975). The spatial resulution of the radio instrument in one direction, although lower than the X-ray telescope resolution, is high enough for a detailed comparison. The comparison clarifies the relationship between the sources of soft X-ray and thermal radio emission in solar flares. The X-ray emission is localized in a loop-like structure which appears spatially coincident with the rapidly varying component of the radio burst. The more stable components of the radio source, which do not appear to contribute substantially to X-ray emission, are found to be spatially associated with the extremes of the X-ray loop. A model of plasma-filled loops is suggested which accounts for the emissions in both spectral ranges and for their spatial location and temporal development.On leave from Osservatorio Astrofisico di Arcetri, Florence, Italy.     

Magnetic nulls and topology in a class of solar flare models

We study the magnetic field-line topology in a class of solar flare models with four magnetic dipoles. By introducing a series of symmetry-breaking perturbations to a fully symmetric potential field model, we show that isolated magnetic nulls generally exist above the photosphere. These nulls are physically important because they determine the magnetic topology above the photosphere. In some special cases, there may be a single null above the photosphere with quasi two-dimensional properties. For such a model, aquasi null line connects the null to the photosphere. In the limit of small non-ideal effects, boundary layers and current sheetsmay develop along the quasi null line and the associated separatrix surfaces. Field lines can then reconect across the quasi null line, as in two-dimensional reconnection. In a more general force-free case, the field contains a pair of nulls above the photosphere, with a field line (theseparator) connecting the two nulls. In the limit of small non-ideal effects, boundary layers and current sheets develop along the separator and the associated separatrix surfaces. The system exhibits three-dimensional reconnection across the separator, over which field lines exchange identity. The separatrices are related to preferable sites of energy release during solar flares.     

Magnetic reconnection in a high-temperature plasma of solar flares

Dispersion relations for the resistive tearing instability are analytically found in the hydromagnetic approximation for a current sheet with a small normal component of the magnetic field. A strong stabilizing influence of the normal component on the development of the tearing instability is shown to exist. These results are also obtained from physical considerations, and so a simple interpretation of the stabilization effect of the normal component is given. The results of the present paper are compared with those of previous works on the topic, and the previous negative results are explained.     

Magnetic reconnection in a high-temperature plasma of solar flares

Simple self-consistent models for non-neutral current sheets are considered. Characteristics of high-temperature turbulent current sheets (HTCS) with a small transverse component of magnetic field are determined for conditions in the solar corona. The energy output of such an HTCS is much larger than that of a neutral sheet. This makes it possible to consider the HTCS as an energy source not only in long-lived X-ray loops but also in flaring loops during the not or main phase of a flare. In this case, the magnetic reconnection velocity agrees with the observed velocity of the loop rise. Thus, these phenomena can be interpreted as a result of magnetic reconnection, for example, between new flux emerging from under the photosphere and an old magnetic field.The role of a longitudinal magnetic field in a current sheet is less important for HTCS. As a result of the compression of a longitudinal field, there appears an electric current circulating around the sheet. This current may induce strong Joule heating, if the compression is large. This additional heating is realized because of the annihilation of the main component, not the longitudinal component of magnetic field. The effect is small for HTCS, but may be significant for preflare current sheets.     

Heating of the solar flare plasma by high energy electrons

Heating of the ambient plasma by high energy electrons in solar flares is discussed. It is shown that for large flares the heating is enough to produce a thermal plasma of a temperature up to a few times of 10⁷K rapidly in the initial phase of the flares. Thus thermal bremsstrahlung in addition to non-thermal bremsstrahlung should be considered for the X-ray emission of solar flares in the initial phase.NAS-NRC Resident Research Associate.     

Diagnostics of solar flare and evaporated plasma using mm-wave emission

Pulsations of mm-wave emission with a period of about 5 s, which occurred during the impulsive phase of the flare of June 22, 1989, are investigated. It has been shown that these pulsations can be driven by Alfvénic oscillations of a flare loop excited due to upward motion of the chromospheric evaporated plasma. A method is proposed to determine the density and temperature of the evaporated plasma as well as the flare loop magnetic field and loop length in terms of Alfvénic oscillations of the loop and bremsstrahlung mechanism of mm-wave emission. The estimation of evaporated plasma energy has shown that for the flare of June 22, 1989 the energy content in electron beams is insufficient for chromospheric plasma evaporation. It is not excluded that the main energy release process occurs in the chromosphere.     

Small-scale high-temperature structures in flare regions

When analyzing YOHKOH/SXT, HXT (soft and hard X-ray) images of solar flares against the background of plasma with a temperature T?6 MK, we detected localized (with minimum observed sizes of ≈2000 km) high-temperature structures (HTSs) with T≈(20–50) MK with a complex spatial-temporal dynamics. Quasi-stationary, stable HTSs form a chain of hot cores that encircles the flare region and coincides with the magnetic loop. No structures are seen in the emission measure. We reached conclusions about the reduced heat conductivity (a factor of ～10³ lower than the classical isotropic one) and high thermal insulation of HTSs. The flare plasma becomes collisionless in the hottest HTSs (T>20 MK). We confirm the previously investigated idea of spatial heat localization in the solar atmosphere in the form of HTSs during flare heating with a volume nonlocalized source. Based on localized soliton solutions of a nonlinear heat conduction equation with a generalized flare-heating source of a potential form including radiative cooling, we discuss the nature of HTSs.     

Pulsations of non-thermal emissions from the solar flare of November 5, 1992 and the trap-plus-precipitation model

The fine structure of the time variations of microwave and hard X-ray emissions from the solar flare of November 5, 1992 was analyzed. On the basis of the wavelet analysis, pulsations of intensity with a period of about 6 s were revealed in both the data sets. The observed time delay between the coronal plasma emission measure maximum and the temperature maximum is consistent with the concept of chromospheric evaporation. The anticorrelation observed between the time profiles of the microwave and hard X-ray emissions and the nature of the time delays between the peaks are associated with the excitation of radial fast magneto-acoustic oscillations in the flare loop (a coronal trap). Consequences of the obtained results are discussed.