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.     

The explosive phase of solar flares

The explosive phase of a flare can be defined by a simple photometric measurement of H film records of the flare development. Using the quantitative definition, improved correlations are found between the start of the explosive phase and the start of 10.7 cm radio bursts and Sudden Frequency Deviations compared to earlier correlations of the same data using visual estimates of the start of the explosive phase. Explosive development may be confined to only part of a flare.     

A new microwave/X-ray diagnostic for the thermal phase of solar flares

We have observed 10 solar bursts during the thermal phase using the Haystack radio telescope at 22 GHz. We show that these high frequency flux observations, when compared with soft X-ray band fluxes, give useful information about the temperature profile in the flare loops. The microwave and X-ray band fluxes provide determinations of the maximum loop temperature, the total emission measure, and the index of the differential emission measure (q(T)/T = cT^–1). The special case of an isothermal loop ( = ) has been considered previously by Thomas et al. (1985), and we confirm their diagnostic calculations for the GOES X-ray bands, but find that the flare loops we observed departed significantly from the isothermal regime. Our results ( = 1–3.5) imply that, during the late phases of flares, condensation cooling ( 3.5) competes with radiative cooling ( 1.5). Further, our results appear to be in good agreement with previous deductions from XUV rocket spectra ( 2–3).     

Impulsive and hot thermal solar flares

Some X-class flares (hot thermal flares, HTF) observed with the Hinotori satellite show unique behavior: slow time variability, a compact hard X-ray source containing dense (n > 10¹¹ cm^–3) and hot (T > 3 × 10⁷ K) plasma, and unusually weak microwave emission in spite of the intense magnetic field (B > 330 G) required theoretically to sustain the hot plasma. These observations show that HTF's have essentially thermal characteristics throughout the flare evolution, while in impulsive flares, there is a transition in the energy release mode from particle acceleration (impulsive phase) to plasma heating (gradual phase). This behavior can be explained in a unified manner by employing parallel DC electric field acting over large distances.     

Impulsive and hot thermal solar flares

Solar Physics - Some X-class flares (hot thermal flares, HTF) observed with the Hinotori satellite show unique behavior: slow time variability, a compact hard X-ray source containing dense (n...     

The decay phase of solar flare events

A study of the properties of the cosmic radiation of energy - 10 MeV generated by solar flares is reported. Data from four Pioneer spacecraft in interplanetary orbits, and separated by 180° in heliocentric longitude are employed. Attention is restricted to the properties evident at times in excess of 1 day after the occurrence of the parent flare. The anisotropic character of the radiation; the gradients in heliocentric longitude; the decay time constants; and the energy spectra of the radiation are all studied in detail.It is found that the equilibrium anisotropy assumes a direction - 45° E of the satellite-Sun line at very late times. It is suggested that the anisotropy at such times is parallel to E × B. This observation confirms that convection is the determining process in the escape of the solar cosmic rays from the solar system. It indicates that a positive radial gradient of solar cosmic radiation density has builtup at orbit of Earth some 4 days after a flare. This results in an effective convective velocity of approximately 1/2 the solar wind velocity. Direct measurements indicate the presence of strong gradients in heliocentric longitude even at very late times ( 4 days). These gradients are essentially invariant with respect to time, e-folding angles of n - 30° have been observed at - 10 MeV. The presence of these gradients has a major effect on the temporal variation of the cosmic ray flux during the decay phase of the flare effect. Thus, the observed decay time constant is either increased or decreased relative to the convective value depending on the position of the observer relative to the centroid of the cosmic ray population injected by the flare. The effect of the gradient becomes more pronounced at lower energies, and may even exceed the convective removal rate. The observed decay time constant, the characteristics of the anisotropy, and the gradient in longitude are shown to be inter-related as demanded by theory. It is shown that the exponent of the cosmic ray spectrum is dependent on the location of the observer relative to the centroid of the cosmic ray population injected by the parent flare. At a given point in the frame of reference of the cosmic ray population, the spectral exponent is invariant with time.Now at CSIRO, G.P.O. Box 124, Port Melbourne, Victoria 3207, Australia.On leave from Physical Research Laboratory, Ahmedabad, India.     

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.     

Expansion of chromospheric matter in the gradual phase of solar flares

Interferometric radio observations together with soft X-ray observations are presented here to show that during the growth phase of soft X-ray flares, a large mass increase occurs simultaneously with the creation of an X-ray hot region in the corona. The lack of an increase of radio flux from pre-flare active regions absolutely excludes the possibility of the coronal accumulation of low-temperature matter just prior to flare onset. Therefore we suggest a hypothesis that a large amount of hot matter, which contains almost the entire energy in the flare, is supplied from the chromosphere into the corona during each flare. Since even small flares produce coronal hot regions radiating thermal soft X-rays and microwaves, the formation of the hot region may be a basic process in most flares. Energy, created by some instability in the corona, travels by thermal conduction to the chromosphere where the dense matter is heated and subsequently expands into the corona, producing the observed hot region. Impulsive heating of the chromosphere by nonthermal electrons which simultaneously emit hard X-rays is not sufficient to be the energy source in our model. Slower heating, which supplies the flare more energy than that supplied in the impulsive phase, is required. If the temperature of the energy source in the corona exceeds 2 × 10⁷ K, the conductive energy flux becomes sufficient to exceed the radiation loss from the chromosphere-corona transition region. This excess energy may cause the chromospheric gas expansion.     

Relaxation of ions during the impulsive phase of solar flares

We present a model describing changes in ion charges during solar flares based on the observed fact that low temperature magnetic loops emerge before flare bursts and the plasma is rapidly heated during the impulsive phase. Results of numerical calculations of the charge state distribution and mean ionic charges of the elements C, N and O agree perfectly with the observations.     

High energetic solar proton flares on the declining phase of solar cycle 22

The year 1991 is a part of the declining phase of the solar cycle 22, during which high energetic flares have been produced by active regions NOAA/USAF 6659 in June. The associated solar proton events have affected the Earth environment and their proton fluxes have been measured by GOES space craft. The evaluation of solar activity during the first half of June 1991, have been carried out by applying a method for high energetic solar flares prediction on the flares of June 1991. The method depends on cumulative summation curves according to observed H-alpha flares, X-ray bursts, in the active region 6659 during one rotation when the energetic solar flares of June 1991 have occurred. It has been found that the steep trend of increased activity sets on several tens of hours prior to the occurrence of the energetic flare, which can be used, together with other methods, for forecasts of major flares. All the used data at the present work are received from NOAA, Boulder, Colorado, USA.     

Particle acceleration and the decay of soft X-ray non-thermal line broadening in solar flares

The relationship between the production of -ray emitting particles and non-thermal soft X-ray line broadening is investigated. A model of particle acceleration via the stochastic interaction with MHD turbulence is assumed and the time development of the wave energy density derived under the condition of energy conservation between waves and particles. The inferred numbers and energy distribution of accelerated protons for four -ray flares are used to define the wave energy density and its temporal development. The presence of Alfvén wave turbulence is considered as the source of the non-thermal motions in the ambient plasma. These motions are observed as excess widths in the soft X-ray line emission from these events. The decay of the waves via the particle acceleration process is compared with the observed decays of this non-thermal line broadening. Our results show that both the -ray emission and excess soft X-ray line widths in these flares can be explained by the single physical phenomenon of Alfvén wave turbulence.     

Further analysis of temperature and emission measure during the decay phase of solar flares derived from soft X-ray light curves

The light curves of soft X-ray lines, observed by the Flat Crystal Spectrometer on Solar Maximum Mission during eight solar flares are modeled to determine the plasma temperature and emission measure as functions of time using the method first presented by Bornmann (1985, Paper I), but modified to include a ² search routine. With this modification the technique becomes more general, more accurate, and applicable throughout the gradual phase of the flare. The model reproduces the light curves of the soft X-ray lines throughout these flares. Model fits were repeated for each flare using five different sets of published line emissivity calculations. The emissivities of Mewe and Gronenschild (1981) consistenly gave the best fits to the observed light curves for each flare.     

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.     

Impulsive phase heating by uni-directional current systems in solar flares

The thermal interpretation of solar flare impulsive phase hard X-ray emission requires rapid heating of a substantial coronal volume to very high temperatures. In this study we investigate the possibility of producing such heating by current dissipation, driven by a tearing instability associated with a single uni-directional current system. Earlier research is synthesized by coupling the energy equation, including loss terms previously neglected, with an equation describing the evolution of the growing electric field. The resistivity due to the excitation of ion-cyclotron and ion-acoustic waves is computed by assuming marginal stability.It is found, for the fast tearing mode, that for initial growth rates _f 0.3 s^-1 (corresponding to a current channel width l 3 × 10⁵ cm), the electron heating is offset by convective losses, resulting in a very slow temperature rise. Furthermore, hard X-ray emitting temperatures (2 × 10⁸ K) are never realized. For the larger growth rates corresponding to smaller current channel widths, heating from 10⁷ to 10⁸ K can be achieved in a few seconds. However, in this regime the maximum volume that can be heated is only of order 10²⁰ cm³, some three to five orders of magnitude less than the volume of heated material that is inferred from hard X-ray emission measures. These results suggest that in the case of the fast tearing mode a more complicated geometry involving multiple small-scale, oppositely-directed, current channels may be necessary to achieve the required heating.     

Soft X-ray line profiles in the impulsive phase of electron-heated solar flares

We have measured the motion of facular points and granules in the same region near a decaying sunspot. It is found that both features move away across the moat surrounding the sunspot. The mean speed of facular points is larger than that of granules: 0.65 km s^–1 and 0.4 km s^–1, respectively. These results are consistent with previous measurements of the speed of bright network features and moving magnetic fields, as well as of non-magnetic photospherical material. They support models in which a decaying sunspot is at the center of a supergranule, whose horizontal motions sweep out granules and magnetic flux tubes associated to the facular points. It is also found that granules are dragged by supergranular motions away of the moat.Contributions from the Kwasan and Hida Observatories, University of Kyoto.A part of this work was done while one of the authors (R.M.) was staying at the Kwasan and Hida Observatories, University of Kyoto, Japan, as a JSPS research fellow.     

Relation between VLF phase deviations and solar X-ray fluxes during solar flares

Sudden phase anomalies (SPA's) observed in the phase of GBR 16 kHz VLF signals during the years 1977 to 1983 have been analysed in the light of their associated solar X-ray fluxes in the 0.5–4 Å and 1–8 Å bands. An attempt has been made to investigate the solar zenith angle () dependence of the integrated solar X-ray flux for producing SPA's. It is deduced from the observations for < 81° that the phase deviation increases linearly as a whole with increasing solar X-ray fluxes in these two bands. The threshold X-ray flux needed to produce a detectable SPA effect has been estimated to be 1.6 × 10^–4 ergcm^–2 s^–1 and 1.8 × 10^–3 ergcm^–2 s^–1 in the 0.5–4 Å and 1–8 Å bands, respectively. For both bands the average cross section for all atmospheric constituents at a height of 70 km is almost equal to the absorption cross section for the 3 Å X-ray emission.     

The role of eruption in solar flares

This article focuses on two problems involved in the development of models of solar flares. The first concerns the mechanism responsible for eruptions, such as erupting filaments or coronal mass ejections, that are sometimes involved in the flare process. The concept of loss of equilibrium is considered and it is argued that the concept typically arises in thought-experiments that do not represent acceptable physical behavior of the solar atmosphere. It is proposed instead that such eruptions are probably caused by an instability of a plasma configuration. The instability may be purely MHD, or it may combine both MHD and resistive processes. The second problem concerns the mechanism of energy release of the impulsive (or gradual) phase. It is proposed that this phase of flares may be due to current interruption, as was originally proposed by Alfvén and Carlqvist. However, in order for this process to be viable, it seems necessary to change one's ideas about the heating and structure of the corona in ways that are outlined briefly.     

The importance of solar white-light flares

The basic results of white-light flare (WLF) photometric and spectrographic observations are reviewed. WLFs represent the most extreme density conditions in solar optical flares and are similar to stellar flares in many respects. It is shown that WLFs originate in the low chromosphere and upper photosphere, and that their huge radiative losses remain difficult to explain within the context of known mechanisms of energy transport.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation. Partial support for the National Solar Observatory is provided by the USAF under a Memorandum of Understanding with the NSF.     

The initial development of solar flares

The extent to which the early phases of solar-flare development can be accounted for by a simple high-temperature chromospheric explosion model is investigated without involving a particular energy source. A model is developed in which it is shown that a point explosion in the lower chromosphere can be treated as a virtually instantaneous release of energy throughout a volume of radius R 100 km, which subsequently expands as a classical hydrodynamic blast wave in which R~ t ( < 2/3). This model is in substantial agreement with areal growth-rate observations of disk flares. An explanation for the fact that limb-flare observations can imply > 2/3 is suggested by considering the effects of the large atmospheric density gradient in the lower chromosphere on an upward travelling shock wave.     

The magnetic nature of solar flares

The main challenge for the theory of solar eruptions has been to understand two basic aspects of large flares. These are the cause of the flare itself and the nature of the morphological features which form during its evolution. Such features include separating ribbons of H emission joined by a rising arcade of soft x-ray loops, with hard x-ray emission at their summits and at their feet. Two major advances in our understanding of the theory of solar flares have recently occurred. The first is the realisation that a magnetohydrodynamic (MHD) catastrophe is probably responsible for the basic eruption and the second is that the eruption is likely to drive a reconnection process in the field lines stretched out by the eruption. The reconnection is responsible for the ribbons and the set of rising soft x-ray loops, and such a process is well supported by numerical experiments and detailed observations from the Japanese satellite Yohkoh. Magnetic energy conversion by reconnection in two dimensions is relatively well understood, but in three dimensions we are only starting to understand the complexity of the magnetic topology and the MHD dynamics which are involved. How the dynamics lead to particle acceleration is even less well understood. Particle acceleration in flares may in principle occur in a variety of ways, such as stochastic acceleration by MHD turbulence, acceleration by direct electric fields at the reconnection site, or diffusive shock acceleration at the different kinds of MHD shock waves that are produced during the flare. However, which of these processes is most important for producing the energetic particles that strike the solar surface remains a mystery. Received 2 January 2001 / Published online 17 July 2001