Interaction of Weak Shock Waves with Current Sheets in an Active Region to Produce Nanoflares and Chains of Type I Radio Bursts

Interaction of weak shock waves with a current sheet is investigated by a two-dimensional numerical magnetohydrodynamic model. In accordance with solar coronal conditions, a ratio of thermal to magnetic pressures of 0.1 and a shock Alfvén Mach number slightly above 1 are considered. It is found that even weak shock waves trigger magnetic field reconnection in current sheets. Based on this result, it is suggested that drifting chains of type I radio bursts are radio manifestations of the interactions of weakly super-Alfvénic shock waves with pre-existing current sheets distributed in an active region. This model of type I noise storms is then discussed in connection with the concept of nanoflares (localized reconnections) and the heating of the solar corona.     

Current sheet models of solar flares

Current sheets have been suggested as the site for flare energy release because they can convert magnetic energy very rapidly into both heat and directed plasma energy. Also they contain electric fields with the potential of accelerating particles to high energies.The basic properties of current sheets are first reviewed. For instance, magnetic flux may be carried into a current sheet and annihilated. An exact solution for such a process in an infinitely long sheet has been found; it describes the annihilation of fields which are inclined at any angle, not just 180°. Moreover, field lines which are expelled from the ends of a current sheet can be described as having been reconnected. The only workable model for fast reconnection in the solar atmosphere, namely Petschek's mechanism, has recently been put on a firm foundation; it gives a reconnection rate which depends on the electrical conductivity but is typically a tenth or a hundredth of the Alfvén speed. A current sheet may be formed when the sources of an initially potential field start to move; a simple analytic technique for finding the position and shape of such a sheet in two dimensions now exists. Finally, a sheet with no transverse magnetic field component is subject to the tearing-mode instability, which rapidly produces a series of loops in the field.The main ways in which current sheets have been used for solar flare models is described. Syrovatskii's mechanism relies on the increase of the electric current density during the formation of a sheet, to a value in excess of the critical value j ^* for the onset of microinstabilities. But Anzer has recently demonstrated that the critical value is most unlikely to be reached during the initial formation process. Sturrock, on the other hand, has advocated the occurrence of the tearing-mode instability in an open streamer-like configuration (which may result from the eruption of a force-free field). But recent observations do not point to that as the relevant configuration. Rather, they suggest that flares are triggered by the emergence of new magnetic flux from below the solar photosphere. This has led Heyvaerts, Priest, and Rust (1976) to propose a new emerging flux model, according to which, as more and more flux emerges, so reconnection occurs, producing some preflare heating. When the current sheet reaches such a height (around the transition region) that its current density exceeds j ^*, then the impulsive phase of the flare is triggered. The main phase is caused by an enhanced level of magnetic energy conversion in a turbulent current sheet. The type of flare depends on the magnetic environment in which the emerging flux finds itself. A surge flare results if the flux appears near a strong unipolar region such as a simple sunspot, whereas a two ribbon flare may be produced by flux emergence near an active region filament, in which case the main phase energy is released from the field that surrounds the filament.     

太阳紫外高分辨观测

对近年来的紫外空间观测仪器（包括在研项目）作了扼要介绍，并对一些关键问题如烃基污染致使仪器灵敏度迅速下降，镜面紫外反射率低下及改进，探测器换代的必要性和困难等作了评述，文中还介绍了目前取得的紫外观测结果对宁静太阳及太阳活动区物理中的一些基本问题如色球和日冕加热，太阳风的加速，色球和过渡区中的物质流以及耀斑触发和能量传输方面所提供的有价值的诊断信息。     

Steady flows in the chromosphere and transition-zone above active regions as observed by OSO-8

Two years of data from the University of Colorado ultraviolet spectrometer aboard OSO-8 were searched for steady line-of-sight flows in the chromosphere and transition-zone above active regions. The most conspicuous pattern that emerges from this data set is that many sunspots show persistent blueshifts of transition-zone lines indicating velocities of about 20 km s^–1 with respect to the surrounding plage areas. The data show much smaller shifts in ultraviolet emission lines arising from the chromosphere: the shifts are frequently to the blue, but sometimes redshifts do occur. Plage areas often show a redshift of the transition-zone lines relative to the surrounding quiet areas, and a strong gradient of the vertical component of the velocity is evident in many plages. One area of persistent blueshift was observed in the transition-zone above an active region filament. The energy requirement of these steady flows over sunspots is discussed.     

The formation of current sheets during the emergence of new magnetic flux from below the photosphere

Solar flares are frequently observed to occur where new magnetic flux is emerging and pressing up against strong active region magnetic fields. Since the solar plasma is highly conducting, current sheets develop at the boundary between the emergent and ambient flux, provided the two magnetic fields are inclined at a non-zero angle to one another.The present paper gives a simple two-dimensional model for the development of such sheets under the assumptions that no reconnection occurs and that the surrounding field remains a potential one. By using complex variable techniques, the position, orientation and shape of a current sheet may be determined, as well as the excess magnetic energy associated with it. Two examples are considered. The first, in which the ambient field is bipolar, may model new flux emergence near the edge of an active region, while the second example assumes a constant ambient field and may approximate the so-called fibril crossings which occur prior to some flares. In each case, the current sheets are curved, and the magnetic energy which is stored in excess of potential is sufficient to supply a solar flare when the sheets are long enough.     

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.     

A study of velocity fields in the transition region of ε Eri (K2 V)

Analyses of the widths and shifts of optically thin emission lines in the ultraviolet spectrum of the active dwarf ε Eri (K2 V) are presented. The spectra were obtained using the Space Telescope Imaging Spectrograph on the Hubble Space Telescope and the Far Ultraviolet Spectroscopic Explorer . The linewidths are used to find the non-thermal energy density and its variation with temperature from the chromosphere to the upper transition region. The energy fluxes that could be carried by Alfvén and acoustic waves are investigated, to test their possible roles in coronal heating. Acoustic waves do not appear to be a viable means of coronal heating. There is, in principle, ample flux in Alfvén waves, but detailed calculations of wave propagation are required before definite conclusions can be drawn concerning their viability. The high sensitivity and spectral resolution of the above instruments have allowed two-component Gaussian fits to be made to the profiles of the stronger transition region lines. The broad and narrow components that result share some similarities with those observed in the Sun, but in ε Eri the broad component is redshifted relative to the narrow component and contributes more to the total line flux. The possible origins of the two components and the energy fluxes implied are discussed. On balance our results support the conclusion of Wood, Linsky & Ayres, that the narrow component is related to Alfvén waves reaching to the corona, but the origin of the broad component is not clear.     

On the nature of the transition region between the solar corona and chromosphere

We have calculated an equilibrium temperature distribution over the column depth of plasma in the transition region between the solar corona and chromosphere by assuming the plasma in the transition region and the chromosphere to be heated by the heat flux from the corona and the energy fluxes from the convective zone, respectively. The corona-chromosphere transition region is shown to be actually a stable, very thin layer in which, however, the standard collision approximation is well applicable for describing the heat flux. The solution we found explains well the currently available results of satellite observations of extreme ultraviolet (EUV) radiation from the transition region.     

Magnetic fields and the temperature structure of the chromosphere-corona interface

The temperature structure of the transition region between the chromosphere and corona is discussed in the context of current ideas about magnetic fields in these layers. Magnetic channeling of the downward conductive heat flow from the corona into the regions of enhanced field at the supergranulation boundaries is proposed as a mechanism for explaining the measured intensities of solar ultraviolet emission lines which originate in layers with temperatures below 10⁵ °K. It is shown that nearly all of the observed ultraviolet line emission originates in interspicule regions, and that this emission plays an important part in the energy balance of the cooler layers of the transition region. It is suggested that certain motions observed in the upper chromosphere may represent the earliest visual evidence for conversion of inflowing conduction energy into kinetic motions.On leave from the Observatory Sonnenborgh at Utrecht, The Netherlands.     

Optimal Energy Growth in Current Sheets

In this article, we investigate the possibility of transient growth in the linear perturbation of current sheets. The resistive magnetohydrodynamics operator for a background field consisting of a current sheet is non-normal, meaning that associated eigenvalues and eigenmodes can be very sensitive to perturbation. In a linear stability analysis of a tearing current sheet, we show that modes that are damped as \(t\rightarrow \infty \) can produce transient energy growth, contributing faster growth rates and higher energy attainment (within a fixed finite time) than the unstable tearing mode found from normal-mode analysis. We determine the transient growth for tearing-stable and tearing-unstable regimes and discuss the consequences of our results for processes in the solar atmosphere, such as flares and coronal heating. Our results have significant potential impact on how fast current sheets can be disrupted. In particular, transient energy growth due to (asymptotically) damped modes may lead to accelerated current sheet thinning and, hence, a faster onset of the plasmoid instability, compared to the rate determined by the tearing mode alone.     

The formation of solar prominences by thermal instability in a current sheet

The energy balance equation for the upper chromosphere or lower corona contains a radiative loss term which is destabilizing, because a slight decrease in temperature from the equilibrium value causes more radiation and hence a cooling of the plasma; also a slight increase in temperature has the effect of heating the plasma. In spite of this tendency towards thermal instability, most of the solar atmosphere is remarkably stable, since thermal conduction is very efficient at equalizing any temperature irregularity which may arise. However, the effectiveness of thermal conduction in transporting heat is decreased considerably in a current sheet or a magnetic flux tube, since heat can be conducted quickly only along the magnetic field lines. This paper presents a simple model for the thermal equilibrium and stability of a current sheet. It is found that, when its length exceeds a certain maximum value, no equilibrium is possible and the plasma in the sheet cools. The results may be relevant for the formation of a quiescent prominence.     

Magnetospheric substorms and solar flares

Assuming that basic plasma processes associated with magnetospheric substorms and solar flares are similar and thus assuming also that a flare ribbon is produced by the impact of field-aligned current-carrying electrons on the chromosphere, a chain of processes leading to solar flares is considered, including the dynamo process in the photospheric level in the vicinity of bipolar sunspots, the formation of a sheet current in the lower coronal level, the interruption of the sheet current, the subsequent diversion of it to the chromosphere, the development of a potential drop along magnetic field lines, the acceleration of current-carrying electrons and their impact on the chromosphere, producing a pair of flare ribbons.     

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.     

Magnetic reconnection driven by recombination during collision of two current loops

It is shown by using a 3-D resistive MHD simulation code, taking into account the recombination effect, that magnetic reconnection during collision of two current loops can be enhanced by recombination. It is also shown that the temperature in the thin current sheet formed between two loops increases from few to about thirty times larger than a case of no recombination, depending on both the plasma beta and the strength of recombination. The simulation results obtained here may be applicable for a mechanism of chromospheric heating and as an explanation of X-ray bright points as well as solar flares observed in the chromosphere.Dedicated to Cornelis de Jager     

Radiative backwarming in white-light flares

We examine empirical atmospheric structures that are consistent with enhanced white-light continuum emission in solar flares. This continuum can be produced either by hydrogen bound-free emission in an enhanced region in the upper chromosphere, or by H^- emission in an enhanced region around the temperature minimum. In the former case, weak Paschen jumps in the spectrum will be present, with the spectrum being dominated by a strong Balmer continuum, while in the latter case the spectrum exhibits a weaker, flat enhancement over the entire visible spectrum.We find that when proper account is taken of radiative backwarming processes, the two enhanced atmospheric regions above are not independent, in that irradiation by Balmer continuum photons from the upper chromosphere creates sufficient heating around the temperature minimum to account for the temperature enhancements there. Thus the problem of main phase white-light flare production reduces to one of creating temperature enhancements of order 10⁴ K in the upper chromosphere; radiative backwarming then naturally accounts for the enhancements of order 100 K around the temperature minimum.Heating by electron and proton bombardment, and by XUV irradiation from above, are then considered as candidates for creating the necessary enhancements in the upper chromosphere. We find that electron bombardment can be ruled out, whereas bombardment by protons in the few-MeV energy range is a viable candidate, but one without strong observational support. The XUV irradiation hypothesis is examined by incorporating it self-consistently into the PANDORA radiative transfer algorithm used to construct the empirical model atmospheres; we find that the introduction of XUV radiation, with flux and spectrum appropriate to white-light flare events, does indeed produce sufficient radiative heating in the upper chromosphere to balance the radiative losses associated with the required temperature enhancements.In summary, we find that the radiative coupling of (i) the upper chromosphere and temperature minimum regions (through Balmer continuum photons) and (ii) the transition region and upper chromosphere (through XUV photons) can account for white-light emission in solar flares.Presidential Young Investigator.     

From Gigahertz to Millihertz: A Multiwavelength Study of the Acoustically Active 14 August 2004 M7.4 Solar Flare

We carried out an electromagnetic acoustic analysis of the solar flare of 14 August 2004 in active region AR10656 from the radio to the hard X-ray spectrum. The flare was a GOES soft X-ray class M7.4 and produced a detectable sun quake, confirming earlier inferences that relatively low energy flares may be able to generate sun quakes. We introduce the hypothesis that the seismicity of the active region is closely related to the heights of coronal magnetic loops that conduct high-energy particles from the flare. In the case of relatively short magnetic loops, chromospheric evaporation populates the loop interior with ionised gas relatively rapidly, expediting the scattering of remaining trapped high-energy electrons into the magnetic loss cone and their rapid precipitation into the chromosphere. This increases both the intensity and suddenness of the chromospheric heating, satisfying the basic conditions for an acoustic emission that penetrates into the solar interior.     

On an efficient shock wave generation mechanism in the quiet solar transition region

Two competing fundamental hypotheses are usually postulated in the solar coronal heating problem: heating by nanoflares and heating by waves. In the latter it is assumed that acoustic and magnetohydrodynamic disturbances whose amplitude grows as they propagate in a medium with a decreasing density come from the convection zone. The shock waves forming in the process heat up the corona. In this paper we draw attention to yet another very efficient shock wave generation process that can be realized under certain conditions typical for quiet regions on the Sun. In the approximation of stationary dissipative hydrodynamics we show that a shock wave can be generated in the quiet solar chromosphere–corona transition region by the fall of plasma from the corona into the chromosphere. This shock wave is directed upward, and its dissipation in the corona returns part of the kinetic energy of the falling plasma to the thermal energy of the corona. We discuss the prospects for developing a quantitative nonstationary model of the phenomenon.     

Energetics of an Active Region Observed from Helium-Like Sulphur Lines

We report temperature diagnostics derived from helium-like ions of sulphur for an active region NOAA 7978 obtained with Bragg Crystal Spectrometer (BCS) on board the Yohkoh satellite. For the same region we estimate conductive flux downward to the chromosphere by the Coronal Diagnostic Spectrometer (CDS) on board the Solar and Heliospheric Observatory (SOHO) satellite. This region appeared as a region of soft X-ray enhancement in May 1996, underwent a period of enhanced activity coinciding with flux emergence between 6 July and 12 July, and then continued to exist in a nearly flareless state for several solar rotations until November 1996. Energy balance of the non-flaring active region is basically consistent with a model of an arcade of coronal loops having an average loop-top temperature of 4×10⁶ K. Energy from flare activity during a period of flux emergence is comparable to the energy requirements of the non-flaring active region. However, the non-flaring energy is roughly constant for the subsequent solar rotations following the birth of the active region even after the flare activity essentially subsided. Energy partition between flare activity and steady active-region heating thus varies significantly over the lifetime of the active region, and active-region emission cannot always be identified with flaring.     

Physical conditions in the chromosphere of a two-ribbon solar flare accompanied by a surge: 1

We studied changes in thermodynamic parameters of the chromosphere at the initial stage of the two-ribbon solar flare accompanied by a surge that occurred on September 4, 1990. The inhomogeneous semiempirical models of the flare chromosphere and surge are constructed for four observation moments. The spectra were obtained with the ATsU-26 horizontal solar telescope of the Main Astronomical Observatory of the National Academy of Sciences of Ukraine (Terskol Peak). Photometric transections of the spectra passed through two bright kernels of one of the flare ribbons and through the surge. The comparison of the observed profiles of the line H_α in the solar active and quiet-Sun regions reveals the substantial emission in the line wings (up to 1–1.2 nm) with a residual intensity of 0.6–0.77 at the center of the line profiles. Calculations within the two-component models of the chromosphere have shown that this may be the evidence of the existence of the details (unresolved by the telescope and occupying 5–12% of the total area) with a deep heating of the chromosphere layers. A strong asymmetry of the line profiles and the shift with respect to the line profile for the quiet-Sun region are explained by peculiarities of the line-of-sight velocity distribution over the height. It is found that the motion is directed to the observer in the upper chromosphere (10–30 km/s) and from the observer in the lower chromosphere (5–20 km/s) for the larger part of the active region under study. According to the models calculated for the surge, the line-of-sight velocities reach a value of 70 km/s.     

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.