Relativistic acceleration of protons in reconnecting current sheets of solar flares

Acceleration of protons in a reconnecting current sheet (RCS), which forms as a consequence of filament eruption in the corona, is considered as a possible mechanism of generation of the relativistic particles during the late phase of solar flares. In order to explain the acceleration of protons and heavier ions up to several GeV in a time of < 0.1 s, the transverse electric field outside the RCS must be taken into account. Physically, this field is always present as a consequence of electric charge separation owing to the difference in the electron and proton masses. The new effect demonstrated in this paper is that the transverse electric field efficiently locks nonthermal ions in the RCS, thus allowing their acceleration by the direct electric field in the RCS. The mechanism considered may be useful in construction of a model for generation of relativistic ions in large gamma-ray/proton flares.     

Thermal instability of the reconnecting current layer in solar flares

To interpret the present-day satellite observations of the sequential brightening of coronal loops in solar flares, we have solved the problem of the stability of small longitudinal perturbations of a homogeneous reconnecting current layer (CL). Within the magnetohydrodynamic approximation we show that an efficient suppression of plasma heat conduction by amagnetic field perturbation inside the CL serves as an instability condition. The instability in the linear phase grows in the characteristic radiative plasma cooling time. A periodic structure of cold and hot filaments located across the direction of the electric current can be formed as a result of the instability in the CL. The proposed mechanism of the thermal instability of a reconnecting CL can be useful for explaining the sequential brightening (“ignition”) of flare loops in solar flares.     

Internal structure of reconnecting current sheets and the emerging flux model for solar flares

We present a steady-state model for reconnecting current sheets, which relates the central values of temperature, density and pressure within the sheet to the prescribed external values of these parameters as well as the magnetic field strength and inflow velocity (or reconnection rate). The simplifying feature of our model is the assumption of quasi-one-dimensionality so that only variations across the sheet at the centre of symmetry are considered in detail. The dimensions of the sheet, the spatial profiles and their variation with the prescribed dimensionless parameters are obtained from the model. We also obtain the conditions on the dimensionless parameters for the existence of a steady state. A beta-limitation is discovered, such that steady reconnection is impossible when the plasma beta is too small. Also, the sheet dimensions may be an order of magnitude larger than previously thought. Finally, these general results are applied to the emerging flux model for solar flares. A state of thermal nonequilibrium ensues when the current sheet between the emerging and ambient flux reaches a critical height. The effect of the beta-limitation is to make this critical height decrease with increasing magnetic field strength.Now at A.W.R.E., Aldermaston, Berks., England.     

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.     

On discontinuous plasma flows in the vicinity of reconnecting current sheets in solar flares

The question about the interpretation of numerical experiments on magnetic reconnection in solar flares is considered. A correspondence between the standard classification of magnetohydrodynamic discontinuities and the parameters characterizing the mass flux through a discontinuity and the magnetic field configuration has been established within a classical formulation of the problem on discontinuous magnetohydrodynamic flows. A pictorial graphical representation of the relationship between the angles of the magnetic field vector relative to the normal to the discontinuity plane on both its sides has also been found. The relations between the parameters of a two-dimensional discontinuous flow have the simplest form in a frame of reference where the magnetic field lines (B) are parallel to the matter velocity (u)—the deHoffmann-Teller frame. The question about the transformation of the magnetic field configuration when passing to a “laboratory” frame of reference where (v · B) ≠ 0, i.e., an electric field is present, is considered in this connection. The result is applied to the analytical solution of the problem on the magnetic field structure in the vicinity of a reconnecting current sheet obtained previously by Bezrodnykh et al. The regions of nonevolutionary shocks are shown to appear near the endpoints of a current sheet with reverse currents.     

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.     

Thermal cyclotron radio emission of neutral current sheets in the solar corona

Cyclotron radiation (its frequency spectrum and polarization) of thermal electrons in a neutral current sheet is considered. It is shown that cyclotron radiation is able to escape only from a thin edge of the sheet where the magnetic field is practically homogeneous. Due to this, the frequency spectrum has the form of comparatively narrow lines with integer ratio of frequencies. This fact enables one to recognize neutral current sheets in the solar corona by their radio emission.     

Soft X-ray emission from a hot turbulent current sheet and the precursor phase of solar flares

The properties and development of a high-temperature current sheet characterized by increasing merging velocity are studied and related to the early phases of solar flares. It is shown that the system can be described by the Petschek-type geometry for a wide range of merging velocities. In the diffusion region and the standing MHD shocks a certain low-frequency plasma microturbulence is generated from the very beginning of the reconnection process. We present qualitative solutions for the case of ion-acoustic turbulence in marginally stable state, which provide a comparison with observations. The increasing merging velocity leads to the appearance of the soft X-ray precursor. The precursor temperature maximum should appear during the current sheet formation, before the Petschek regime is established. In the Petschek regime the temperature of the hot plasma decreases due to the decrease of the magnetic field strength at the diffusion region boundary, while the soft X-ray radiation still increases, reaching precursor maximum for merging velocities about 1% of the external Alfvén velocity. The precursor phase ends when the value of the merging velocity surpasses the upper limit for the Petschek regime and the system enters into the pile-up regime, causing a new increase of plasma temperature and soft X-ray radiation.It is shown that Alfvén velocities in the range 800–1200 km s ^–1 are sufficient to explain typical soft X-ray precursors. Cases of low merging velocities and low Alfvén velocities are discussed and can be applied to describe the properties of spotless flares.     

Thermal trigger for solar flares and coronal loops formation

A longitudinal stability is considered for the quasi-steady current sheet which is uniform along the current. In the MHD approximation, the stability problem is solved for the plane neutral sheet and small disturbances propagating along the current. The current sheet is shown to break-up into the system of cooler and more dense filaments due to radiative cooling. The filaments are parallel to magnetic field lines. This process corresponds to the condensation mode of a thermal instability and can play a trigger role for a solar flare. Moreover, at the nonlinear stage of development, it can lead to the formation of very dense cold filaments surrounded by high-temperature low-density plasma inside the current sheet. Flowing into the filaments, hot plasma is cooled by radiation and compressed. Then the cold dense plasma flows out from the current sheet along the filaments. We think that the process under consideration is responsible for the often observed picture of an arcade of cold loops in the solar corona.The text of this paper was written by B. V. Somov after the death of Prof. S. I. Syrovatskii.     

Preflare current sheets in the solar atmosphere

Neutral current sheets are expected to form in the solar atmosphere when photospheric motions or the emergence of new magnetic flux causes oppositely directed magnetic fields to be pressed together. Magnetic energy may thus be stored slowly in excess of the minimum energy associated with a purely potential field and released suddenly during a solar flare. For simplicity, we investigate the neutral sheet which forms between two parallel line dipoles when either the distance between them decreases or their dipole moments increase. It is found that, when the dipoles have approached by an amount equal to a tenth of their original separation distance, the stored energy is comparable with that released in a major flare. In addition, a similarity solution for one-dimensional magnetohydro-dynamic flow within such a neutral sheet is presented; it demonstrates that rapid conversion of magnetic energy into heat is possible provided conditions at the edge of the neutral sheet are changing sufficiently quickly.     

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.     

Thermal nonequilibrium: A trigger for solar flares?

In this paper, we suggest that a solar flare may be triggered by a lack of thermal equilibrium rather than by a magnetic instability. The possibility of such a thermal nonequilibrium (or catastrophe) is demonstrated by solving approximately the energy equation for a loop under a balance between thermal conduction, optically thin radiation and a heating source. It is found that, if one starts with a cool equilibrium at a few times 10⁴ K and gradually increases the heating or decreases the loop pressure (or decreases the loop length), then, ultimately, critical metastable conditions are reached beyond which no cool equilibrium exists. The plasma heats up explosively to a new quasi-equilibrium at typically 10⁷ K. During such a thermal flaring, any magnetic disruption or particle acceleration are secondary in nature. For a simple-loop (or compact) flare, the cool core of an active-region loop heats up and the magnetic tube of plasma maintains its position. For a two-ribbon flare, the material of an active-region (or plage) filament heats up and expands along the filament; it slowly rises until, at a critical height, the magnetic configuration becomes magnetohydrodynamically unstable and erupts violently outwards. In this case thermal nonequilibrium acts as a trigger for the magnetic eruption and subsequent magnetic energy release as the field closes back down.     

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.     

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.     

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.     

Stellar and solar flares

Some ideas are developed concerning solar flares which have been presented earlier by the author (Schatzman, 1966a). Emphasis is laid on the problem of energy transport; from the energy supply to the region of the optical flare, on the storage of low energy cosmic ray particles in a magnetic bottle before the beginning of the optical flare, and the mechanism which triggers both the optical flare, and the production of high-energy cosmic rays. The relation between solar and stellar flares is considered.Lecture given at Goddard Space Flight Center, November 4, 1966.     

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.