The formation of flare loops by magnetic reconnection and chromospheric ablation

Slow-mode shocks produced by reconnection in the corona can provide the thermal energy necessary to sustain flare loops for many hours. These slow shocks have a complex structure because strong thermal conduction along field lines dissociates the shocks into conduction fronts and isothermal subshocks. Heat conducted along field lines mapping from the subshocks to the chromosphere ablates chromospheric plasma and thereby creates the hot flare loops and associated flare ribbons. Here we combine a non-coplanar compressible reconnection theory with simple scaling arguments for ablation and radiative cooling, and predict average properties of hot and cool flare loops as a function of the coronal vector magnetic field. For a coronal field strength of 100 G the temperature of the hot flare loops decreases from 1.2 × 10⁷ K to 4.0 × 10⁶ K as the component of the coronal magnetic field perpendicular to the plane of the loops increases from 0% to 86% of the total field. When the perpendicular component exceeds 86% of the total field or when the altitude of the reconnection site exceeds 10⁶km, flare loops no longer occur. Shock enhanced radiative cooling triggers the formation of cool H flare loops with predicted densities of 10¹³ cm^–3, and a small gap of 10³ km is predicted to exist between the footpoints of the cool flare loops and the inner edges of the flare ribbons.     

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.     

Evolution of electron and proton temperatures in a flaring loop

We have investigated numerically how a temperature difference between electrons and protons is produced in a flaring loop by adopting a one-fluid, two-temperature model instead of a single-temperature model. We have treated a case in which flare energy is released in the form of heating of electrons located in the top part of the loop.In this case, a large temperature difference (T _e/T _p 10) appears in the corona in the energy-input phase of the flare. When the material evaporated from the chromosphere fills the corona, the temperature difference in the loop begins to shrink rapidly from below. Eventually, in the loop apex, the proton temperature exceeds the electron temperature mainly due to cooling of the electrons by conduction down the loop and heating of the protons by compression of the ascending material. In the late phase of the flare (t 15 min from the flare onset), the temperature difference becomes less than 2% of the mean temperature of electrons and protons at every point in the loop.     

Theoretical model of flares and prominences

A theoretical model of flare which explains observed quantities in H, EUV, soft X-ray and flare-associated solar wind is presented. It is assumed that large mass observed in the soft X-ray flare and the solar wind comes from the chromosphere by the process like evaporation while flare is in progress. From mass and pressure balance in the chromosphere and the corona, the high temperature in the soft X-ray flare is shown to be attained by the larger mass loss to the solar wind compared with the mass remained in the corona, in accord with observations. The total energy of 10³² erg, the electron density of 10^13.5 cm^–3 in H flare, the temperature of the X-ray flare of 10^7.3K and the time to attain maximum H brightness (600 s) are derived consistent with observations. It is shown that the top height of the H flare is located about 1000 km lower than that of the active chromosphere because of evaporation. So-called limb flares are assigned to either post-flare loops, surges or rising prominences.The observed small thickness of the H flare is interpreted by free streaming and/or heat conduction. Applications are suggested to explain the maximum temperature of a coronal condensation and the formation of quiescent prominences.     

A model of solar flares and faculae

Theories of solar flares based on the storage of energy (usually as magnetic energy) in the solar atmosphere are shown to be incompatible with observational data.The sunspot energy deficit and the photospheric faculae both involve energy fluxes comparable with the flare requirement ( 3 × 10²⁹ erg s^–1). Both also require a subsurface system of waves or oscillations, perhaps those discussed by Danielson and Savage and by Wilson. The flare model proposed is based on a temporary diversion of this energy carried by Alfvén waves through spots and magnetic elements or micro-pores; the calculated plasma perturbation velocity in the umbra is about 6 km s^–1 for a major flare.In the atmosphere the wave energy divides into two parts to produce the cool, stationary optical flare and the particle flare. The first part is dissipated around flux tubes which are mainly horizontal in the chromosphere and which tend to concentrate along the magnetic neutral line (B = 0). Each tube vibrates individually as a taut wire in a viscous fluid, to excite the fluid just outside the tube. The second part of the energy emerges along tubes mainly vertical in the chromosphere and is converted to shock waves in the corona and then to particle energy for the radio and X-ray flare and the blast wave.The model includes white-light faculae, quasi-permanent X-ray and fast-particle emissions, sympathetic flares and surges. An unambiguous test would be provided by observations of plasma motions of a few kilometres per second in spots and micro-pores.     

Hα line profile observations of solar flares with high temporal resolution

H line profile observations of solar flares with high temporal resolution are an important tool for the analysis of the energy transport mechanism from the site of the flare energy release to the chromosphere. A specially designed instrument (imaging spectrograph) allows two-dimensional imaging of an active region simultaneously in 15 spectral channels along the H line profile with a temporal resolution of 5.4 s. Two flares have been observed in November 1982. The first one shows H signatures which one would typically expect in the case of explosive chromospheric evaporation produced by massive injection of non-thermal electrons. The observations of the other flare indicate that the heating of the upper chromosphere is dominated by thermal conduction, although during the impulsive hard X-ray burst there are also signatures of heating by non-thermal electrons.     

Remote flare brightenings and type III reverse slope bursts

We present two large flares which were exceptional in that each produced an extensive chain of H emission patches in remote quiet regions more than 10⁵ km away from the main flare site. They were also unusual in that a large group of the rare type III reverse slope bursts accompanied each flare.The observations suggest that this is no coincidence, but that the two phenomena are directly connected. The onset of about half of the remote H emission patches were found to be nearly simultaneous with RS bursts. One of the flares (August 26, 1979) was also observed in hard X-rays; the RS bursts occurred during hard X-ray spikes. For the other flare (June 16, 1973), soft X-ray filtergrams show coronal loops connecting from the main flare site to the remote H brightenings. There were no other flares in progress during either flare; this, along with the X-ray observations, indicates that the RS burst electrons were generated in these flares and not elsewhere on the Sun. The remote H brightenings were apparently not produced by a blast wave from the main flare; no Moreton waves were observed, and the spatially disordered development of the remote H chains is further evidence against a blast wave. From geometry, time and energy considerations we propose: (1) That the remote H brightenings were initiated by direct heating of the chromosphere by RS burst electrons traveling in closed magnetic loops connecting the flare site to the remote patches; and (2) that after onset, the brightenings were heated by thermal conduction by slower thermal electrons (kT1 keV) which immediately follow the RS burst electrons along the same loops.     

Photospheric vortex flows as a cause for two-ribbon flares: A topological model

By using a topological model for the potential magnetic field above the photosphere, the appearance and development of the separator as a result of vortex plasma flows in the locality of the photospheric neutral line is considered. The possible relation of such vortex flows with a flare activity is revealed. The arrangement and shape of the flare ribbons in the chromosphere, the formation of X-ray intersecting loops, the early appearance of bright knots on flare ribbon edges are naturally explained by the model provided a reconnecting current sheet arises along the separator in the coronal magnetic field of active regions as a result of the evolution of the magnetic field sources in the photosphere.     

A qualitative interpretation of 7 August 1972 impulsive phase flare Hα line profiles

Tanaka's (1977) unique H profiles of the kernels of the 7 August 1972 flare were quantitatively interpreted by Brown et al. (1978; henceforth BCR) in terms of a thick target electron beam model. They found that this interpretation required beam inhomogeneity and/or partial precipation and large (60–100 km s^–1) macroturbulence. The latter requirement is somewhat suspect, since the only independent evidence also comes from efforts to understand the profiles of optically thick chromospheric lines. Relationships between model atmosphere parameters and line profile parameters calculated by Dinh (1980) show that these requirements could be considerably reduced, if not totally eliminated, if the actual chromospheric flare heating mechanism were simultaneously capable of pushing the flare transition region to greater column density and causing less heating of the residual chromosphere than the BCR models. This then implies that the chromosphere is heated primarily by a mechanism through which the heating effects do not penetrate as far below the flare transition region as is the case for a power-law spectrum of non-thermal electrons whose parameters are chosen appropriate to the nonthermal thick target interpretation of hard X-rays. Thermal conduction and optically thick radiation are examples of such a mechanism.     

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.     

Magnetic fields,bremsstrahlung and synchrotron emission in the flare of 24 October 1969

An impulsive flare October 24, 1969 produced two bursts with virtually identical time profiles of 8800 MHz emission and X-rays above 48 keV. The two spikes of hard X-rays correspond in time to the times of sharp brightening and expansion in the H flare. The first burst was not observed at frequencies below 3000 MHz. This cut off is ascribed to plasma cutoff above the low-lying flare.A model of the flare based on H observations at Big Bear shows that the density of electrons with energy above 10 keV is 5 × 10⁷ if the field density is 10¹¹. The observed radio flux would be produced by this electron distribution with the observed field of 200 G. The H emission accompanying the hard electron acceleration is presumed due to excitation of the field atoms by the hard electrons.     

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.     

Relationship between electric currents,photospheric motions,chromospheric activity,and magnetic field topology

Through coordinated observations made during the Max'91 campaign in June 1989 in Potsdam (magnetograms), Debrecen (white light and H), and Meudon (MSDP), we follow the evolution of the sunspot group in active region NOAA 5555 for 6 days. The topology of the coronal magnetic field is investigated by using a method based on the concept of separatrices - applied previously (Mandriniet al., 1991) to a magnetic region slightly distorted by field-aligned currents. The present active region differs by having significant magnetic shear. We find that the H flare kernels and the main photospheric electric current cells are located close to the intersection of the separatrices with the chromosphere, in a linear force-free field configuration adapted to the observed shear. Sunspot motions, strong currents, isolated polarities, or intersecting separatrices are not in themselves sufficient to produce a flare. A combination of them all is required. This supports the idea that flares are due to magnetic reconnection, when flux tubes with field-aligned currents move towards the separatrix locations.     

A multiwavelength study of a double impulsive flare

Extensive data from the Solar Maximum Mission (SMM) and ground-based observatories are presented for two flares; the first occurred at 12:48 UT on 31 August, 1980 and the second just 3 min later. They were both compact events located in the same part of the active region. The first flare appeared as a typical X-ray flare: the Caxix X-ray lines were broadened ( 190±40 km s^-1) and blue shifted ( 60±20 km s^-1) during the impulsive phase, and there was a delay of about 30 s between the hard and soft X-ray maxima. The relative brightness of the two flares was different depending on the spectral region being used to observe them, the first being the brighter at microwave and hard X-ray wavelengths but fainter in soft X-rays. The second flare showed no significant mass motions, and the impulsive and gradual phases were almost simultaneous. The physical characteristics of the two flares are derived and compared. The main difference between them was in the pre-flare state of the coronal plasma at the flare site: before the first flare it was relatively cool (3 × 10⁶ K) and tenuous (4 × 10⁹ cm^-3), but owing to the residual effects of the first flare the coronal plasma was hotter (5 × 10⁶ K) and more dense (3 × 10¹¹ cm^-3) at the onset of the second flare. We are led to believe from these data that the plasma filling the flaring loops absorbed most of the energy released during the impulsive phase of the second flare, so that only a fraction of the energy could reach the chromosphere to produce mass motions and turbulence.A simple study of the brightest flares observed by the SMM shows that at least 43% of them are multiple. Thus, the situation studied here may be quite common, and the difference in initial plasma conditions could explain at least some of the large variations in observed flare parameters. We draw a number of conclusions from this study. First, the evolution of the second flare is substantially affected by the presence of the first flare. Secondly, the primary energy release in the second event is in the corona. Thirdly, the flares occur in a decaying magnetic region, probably as a result of the interaction of existing sheared loops; there is no evidence of emerging magnetic flux. Also, magnetic structures of greatly varying size participate in the flare processes. Lastly, there is some indication that the loops are not symmetrical or stable throughout the flares, i.e. the magnetic field does not act as a uniform passive bottle for the plasma, as is often assumed in flare models.NOAA/Space Environment Laboratory, currently at NASA/MSFC, Ala., U.S.A.Now at Sacramento Peak Observatory, Tucson, Ariz., U.S.A.     

Hydrodynamic response of the solar chromosphere to an elementary flare burst

Impulsive heating of the upper chromosphere by a very powerful thermal flux is studied as the cause of hard X-rays during a solar flare. The electron temperature at the boundary between the corona and chromosphere is assumed to change in accordance with the hard X-ray intensity in an elementary flare burst (EFB). A maximum value of about 10⁸ K is reached after 5 s, after which the boundary temperature decreases. These high-temperature changes lead to fast propagation of heat into the chromosphere. Numerical solution of the hydrodynamic equations, which take into account all essential dissipative processes, shows that classical heat conduction is not valid due to heat flux saturation in the case of impulsive heating from a high-temperature source. The saturation effect and hydrodynamic flow along a magnetic field lead to electron temperature and density distributions such that the thermal X-ray spectrum of a high-temperature plasma can be well enough approximated by an exponential law or by two power-law spectra. According to this dissipative thermal model for the source of hard X-rays, the emission measure of the high-temperature plasma increases monotonously during the whole EFB even after the temperature maximum. Some results for the low-temperature region are discussed in connection with short-lived chromospheric bright points.     

Magnetic Model of HD 2453

A model is constructed for the magnetic field of the star HD 2453, which has a very long rotation period (P=521^d). It is found that the structure of the field corresponds to the model of a dipole shifted by r=0.09R from the center. The angle of inclination of the axis of the dipole to the axis of rotation, =5°; that is, the star is viewed almost from its equator of rotation and magnetic equator. This explains the low amplitude of the phase dependence of the magnetic field, Be(P), and the low amplitude of the photometric variability. The field at the magnetic poles is equal to Bp=+4400 and -7660 G. The magnetic field parameters turn out to be close to those obtained by Landstreet and Mathys assuming a dipole-quadrupole-octupole model. A Mercator map of the magnetic field distribution of HD 2453 is produced.     

MULTISPECTRAL OBSERVATIONS OF AN ERUPTIVE FLARE

We analyze the pre-flare and impulsive phase of an eruptive (two-ribbon) flare at several wavelengths. The total energy (mechanical plus radiative) released by the flare is 8 x 10³⁰ erg, about a factor 6 higher than the free magnetic energy (1.3 10³⁰ erg) estimated from the non-potentiality of the magnetic field configuration in the flare area. During the impulsive phase, we find a very good time coincidence between the hard X-ray light curve and the light curves for 2 small areas ( 4 in size) in the red wing of the H line and in the He-D₃ line center. This temporal coincidence is compatible with the interpretation that hard X-ray emission is produced by bremsstrahlung of accelerated electron beams striking these dense areas. For the other regions of the H ribbons we find more gradual light curves, suggesting a different energy transport mechanism such as conduction.     

Analysis of X-ray observations of the 15 June 1973 flare in active region NOAA 131

Observations and analyses of the 1B/M3 flare of 15 June, 1973 in active region NOAA 131 (McMath 12379) are presented. The X-ray observations, consisting of broadband photographs and proportional counter data from the Skylab/ATM NASA-MSFC/Aerospace S-056 experiment, are used to infer temperatures, emission measures, and densities for the flaring plasma. The peak temperature from the spatially resolved photographs is 25 × 10⁶ K, while the temperature from the full-disk proportional counter data is 15 × 10⁶ K. The density is 3 × 10¹⁰cm^–3. The X-ray flare emission appears to come primarily from two low-lying curvilinear features lying perpendicular to and centered on the line where the photospheric longitudinal magnetic field is zero. Similarities in the preflare and postflare X-ray emission patterns indicate that no large-scale relaxation of the coronal magnetic configuration was observed. Also discussed are H and magnetic field observations of the flare and the active region. Finally, results of numerical calculations, including thermal conduction, radiative loss and chromospheric evaporation, are in qualitative agreement with the decay phase observations.Presently at NASA/Marshall Space Flight Center.