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.     

Energetics of a double flare on November 8, 1980

Here we complete an energy balance analysis of a double impulsive hard X-ray flare. From spatial observations, we deduce both flares probably occur in the same loop within the resolution of the data. For the first flare, the energy in the fast electrons (assuming a thick-target model) is comparable to the convective up-flow energy, suggesting that these are related successive modes of energy storage and transfer. The total energy lost through radiation and conduction, 2.0 × 10²⁸ erg, is comparable to the energy in fast electrons 2.5 × 10²⁸ erg. For the second flare, the energy in the fast electrons is more than one order of magnitude greater than the energy of the convective up-flow. Total energy losses are within a factor of two lower than the calculated fast electron energy. We interpret the observations as showing that the first flare occurred in a small loop with fast electrons heating the chromosphere and resulting in chromospheric evaporation increasing the density in the loop. For the second flare most of the heating occurred at the electron acceleration site. The two symmetrical components of the Ca xix resonance line and a high velocity down-flow of 115 km s ^–1 observed at the end of the second hard X-ray burst are consistent with the flare eruption (reconnection) region being high in the flare loop. The estimated altitude of the acceleration site is 5500 km above the photosphere.     

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.     

A model of hot loops associated with solar flares

A dynamical model is proposed for the formation of soft X-ray emitting hot loops in solar flares. It is examined by numerical simulations how a solar model atmosphere in a magnetic loop changes its state and forms a hot loop when the flare energy is released in the form of heat liberation either at the top part or around the transition region in the loop.When the heat liberation takes place at the top part of the loop which arches in the corona, the plasma temperature around the loop apex rises rapidly and, as the result, the downward thermal conductive flux is increased along the magnetic tube of force. Soon after the thermal conduction front rushes into the upper chromosphere, a local peak of pressure is produced near the conduction front and the chromospheric material begins to expand into the corona to form a high-temperature (10⁷ K-3 × 10⁷ K at the loop apex) and high-density (10¹⁰ cm^–3-10¹¹ cm^–3 at the loop apex) loop. The velocity of the expanding material can reach a few hundred kilometres per second in the coronal part. The thermal conduction front also plays a role of piston pushing the chromospheric material downward and gives birth to a shock wave which propagates through the minimum temperature region into the photosphere. If, on the other hand, the heat source is placed around the transition region in the loop, the expansion of the material into the corona occurs from the beginning of the flare and the formation process of the hot loop differs somewhat from the case with the heat source at the top part of the loop.Thermal components of radiations emitted from flare regions, ranging from soft X-rays to radio wavelengths, are interpreted in a unified way by using physical quantities obtained as functions of time and position in our flare loop model as will be discussed in detail in a following paper.     

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.     

Dissipation of Standing Slow Magnetoacoustic Waves in Hot Coronal Loops

The damping of standing slow waves in hot (T>6 MK) coronal loops of semicircular shape is revisited in both the linear and nonlinear regimes. Dissipation by thermal conduction, compressive viscosity, radiative cooling, and heating are examined for nonstratified and stratified loops. We find that for typical conditions of hot SUMER loops, thermal conduction increases the period of damped oscillations over the sound-crossing time, whereas the decay times are mostly shaped by compressive viscosity. Damping from optically thin radiation is negligible. We also find that thermal conduction alone results in slower damping of the density and velocity waves compared to the observations. Only when compressive viscosity is added do these waves damp out at the same rate as the observed rapidly decaying modes of hot SUMER loop oscillations, in contrast to most current work, which has pointed to thermal conduction as the dominant mechanism. We compare the linear predictions with numerical hydrodynamic calculations. Under the effects of gravity, nonlinear viscous dissipation leads to a reduction of the decay time compared to the homogeneous case. In contrast, the linear results predict that the damping rates are barely affected by gravity.     

Soft X-ray oscillations from AT Mic: Flare plasma diagnostics

We consider the flare oscillations from the active red dwarf AT Mic detected with the XMM-Newton space observatory in the soft X-ray energy range (0.2–12 keV). Following Mitra-Kraev et al. (2005a), we associate the observed oscillations with a period of ≈750 s with the excitation of a standing slow magnetoacoustic (SMA) wave in a coronal loop. The damping of flare loop SMA oscillations is shown to be governed by electron thermal conduction. We have estimated the plasma density (≈3 × 10¹⁰ cm^?3) and the minimum magnetic field strength (≈100 G) in the region of flare energy release. The adopted model is consistent with the results of a spectral analysis of the soft X-ray emission. The piston mechanism is assumed to be responsible for the excitation of loop SMA oscillations.     

Multiwavelength Flare Observations: Temporal Evolution of the 20 August 1992 Flare

The 20 August 1992 flare around 14:28 UT was observed in H, H and Ca ii H with the imaging spectrographs at Locarno-Monti, Switzerland, with the radiotelescopes in Bern, and in soft and hard X-rays by the Yohkoh satellite. In this paper we discuss the analysis of the temporal and spatial evolution of this flare, well observed at chromospheric and coronal layers. We find that the chromospheric electron density shows well-correlated rises with the hard X-rays emphasizing the direct response of the chromosphere to the energy deposition. Although both footpoints of the loops show simultaneous rises of the electron density, non-thermal electron injection is only observed in one of the footpoints, while an additional heating mechanism, like thermal conduction, must be assumed for the other footpoint. However, it is puzzling that all the chromospheric observations in both footpoints are delayed by 3 s compared to the hard X-ray light curve. Although this would be compatible with the thermal heating of one footpoint, it is in contradiction to the non-thermal heating of the other one. Finally, we observed evidence that during the first part of the flare a thermal conduction front propagates at a speed of 2000 km s^-1 into a second loop, in which the energy release occurs in the second part of the flare.     

Plasma waves caused by transient heat conduction in a coronal loop and anomalous resistivity

Numerical simulation is made of the transient heat conduction during local heating in a model coronal magnetic loop with an axial electric current. It is assumed that a segment near the top of the normal coronal loop is heated to above 10⁷ K by a sufficiently small heat input as compared with the total flare energy. A hump appears in the velocity distribution of electrons moving down the temperature gradient with speeds slightly below the thermal one. Consequently, electron plasma waves are excited. The high intensity of the waves persists in the upper region of the loop for more than a second until the termination of the simulation. The energy density of the plasma waves normalized with respect to thermal density is 10^–3.5 at maximum. A theoretical estimate gives an anomalous resistivity 5 orders of magnitude greater than an initial value. Based on the above result, we propose a model for impulsive loop flares.     

The structure of radiative slow-mode shocks

We investigate the structure of slow-mode MHD shocks in a plasma where both radiation and thermal conduction are important. In such a plasma a slow shock dissociates into an extended foreshock, an isothermal subshock, and a downstream radiative cooling region. Our analysis, which is both numerical and analytical, focuses on the nearly switch-off shocks which are generated by magnetic reconnection in a strong magnetic field. These shocks convert magnetic energy into kinetic energy and heat, and we find that for typical flare conditions about f of the conversion occurs in the subshock while the remaining 1/3 occurs in the foreshock. We also find that no stable, steady-state solutions exist for radiative slow shocks unless the temperature in the radiative region downstream of the subshock falls below 10⁵ K. These results suggest that about 2/3 of the magnetic energy released in flare loops is released at the top of the loop, while the remaining 1/3 is released in the legs of the loop.     

Small-scale high-temperature structures in flare regions

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

Damping of slow magnetoacoustic waves in an inhomogeneous coronal plasma

We study the propagation and dissipation of slow magnetoacoustic waves in an inhomogeneous viscous coronal loop plasma permeated by uniform magnetic field. Only viscosity and thermal conductivity are taken into account as dissipative processes in the coronal loop. The damping length of slow-mode waves exhibit varying behaviour depending upon the physical parameters of the loop in an active region AR8270 observed by TRACE. The wave energy flux associated with slow magnetoacoustic waves turns out to be of the order of 10⁶ erg cm^?2 s^?1 which is high enough to replace the energy lost through optically thin coronal emission and the thermal conduction below to the transition region. It is also found that only those slow-mode waves which have periods more than 240s provide the required heating rate to balance the energy losses in the solar corona. Our calculated wave periods for slow-mode waves nearly match with the oscillation periods of loop observed by TRACE.     

Flare loops heated by thermal conduction

A flare observed with the Hard X-Ray Imaging Spectrometer (HXIS) was studied during its rise to maximum temperature and X-ray emission rate. Two proximate flare loops, of lengths 2.8 × 10⁹ cm and 1.1 × 10¹⁰ cm, rose to temperatures of 21.5 × 10⁶ K and 30 × 10⁶ K, respectively, in 30 s. Assuming equal heat flux F into each loop from a thermal source at the point where they met, we derive a simple relationship between temperature T and loop length , which gives a loop temperture ratio of 0.68, in close agreement with the observed ratio of 0.72. The observations imply that heating in each loop was maintained by a thermal flux of 5 × 10⁹ ergs cm^-2 s^-1. It is suggested that conductive heating adequately describes the rise and maximum phase emissions in the loops and that long flare loops reach higher temperatures than short loops during the impulsive phase because of an equipartition of energy between them at their point of interaction.     

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 model of impulsive loop flares caused by anomalous heat conduction

Numerical simulation is made of the impulsive loop flare caused by transient heat conduction along the loop with an applied axial electric current.It is assumed that a segment near the top of the coronal loop is heated to above 10⁷ K by a heat input that is small compared with the total flare energy, which is given by the magnetic energy of the initial current. Due to the heat conduction, a hump appears in the velocity distribution of electrons, which may excite electron plasma waves with a sufficiently high intensity to cause an anomalous resistivity, as shown theoretically in a previous paper. In that paper, an effect of the plasma waves on the dynamics of electrons was taken into account consistently, but an anomalous heating due to an ohmic dissipation of the initial current under the anomalous resistivity was not taken into account.The aim of the present study is to study the subsequent dynamics of the heated gas caused by the anomalous heating, but in order to avoid an unpractically long computation time, the energy density of the plasma waves is estimated by the energy density of electrons in the velocity hump, without taking into account the effect of the plasma waves consistently in the dynamics of the electrons.The initial current starts to decay gradually by an ohmic dissipation under the anomalous resistivity occurring near the top of the loop to heat this region more. The enhanced heat conduction causes the velocity humps in a wider location. Consequently, the anomalous heating continues and spreads in a self-generating way even after the end of the initial minor heating. Thus the temperature near the loop top becomes above 10⁸ K and the high-temperature region spreads in both directions along the loop with such a high speed as (2–3) × 10⁴ km s^–1, which is nearly equal to the speed of flux-limited heat conduction. On the other hand, induced electric field estimated from the anomalous resistivity is 3.3 × 10⁷ V at the termination of the present simulation, under the modest initial current of 1.5 A m^–2.X-ray emissions expected from the present model loop, show three sources, two footpoints with unequal brightness and a coronal source expanding along the loop in both directions.     

The Queens' flare: Its structure and development; precursors,pre-flare brightenings,and aftermaths

We continue previous research on the limb flare of 30 April, 1980, 20:20 UT, observed in X-rays by several instruments aboard the Solar Maximum Mission (SMM). It is shown quantitatively that the flare originated in an emerging magnetically confined kernel (diameter ～ 20″) which existed for about ten to fifteen minutes, and from which energetic electrons streamed, in at least two injections, into a previously existing complicated magnetic loop system thus forming a less bright but extended and long-lived tongue. The tongue had a length of ～ 35 000 km and lasted ～ 90 min in X-rays (～ 10 keV); at lower energies (～ 0.7 keV) it was larger (～ 80 000 km) and lasted longer. The total number of energetic electrons (≈ 10³⁷) initially present in the kernel is of the same order as the number present in the tongue after the kernel's decline. This gives evidence that the energetic electrons in the tongue originated mainly in the kernel. The electron number densities in the kernel and tongue at maximum brightness were ～ 4.5 × 10¹¹ and ～ 1 × 10¹¹ cm^#X2212;3, respectively. During the first eight minutes of its existence the tongue was hotter than the kernel, but it cooled off gradually. Its decline in intensity and temperature was exponential; energy was lost by radiation and by conduction through the footpoints of the loop system. These footpoints have a cross-section of only ～ 3 × 10⁶ km². This small value, as well as photographs in a Civ UV emission line, suggests a highly filamentary structure of the system; this is further supported by the finding that the tongue had a ‘filling factor’ of ～ 10^#X2212;2. Several faint X-ray brightenings (? 0.005 of the flare's maximum intensity) were observed at various locations along the solar limb for several hours before and after the flare. At ～ 30 min before the flare's onset a faint (? 0.02) flare precursor occurred, coinciding in place and shape with the flare. First the kernel precursor was brightest but the tongue precursor increased continuously in brightness and was the brightest part of the precursor some 10–15 min after the first visibility of the kernel precursor, until the start of the main flare. This suggests (weak) continuous electron acceleration in the tongue during a period of at least 30 min. The main flare was caused by strong emergence of magnetic field followed by two consecutive field line reconnections and accelerations in a small loop system, causing footpoint heating. Subsequently plasma streamed (convectively) into a pre-existing system of larger loops, forming the tongue.     

Heat flux saturation in hydrodynamic soft X-ray solar flare plasmas

The role of heat flux limitation in soft X-ray emitting solar flare plasmas is considered. Simple analytic arguments suggest that flux limitation is likely to be important during the explosive heating phase, even for relatively modest coronal energy fluxes (say 10⁹ erg cm^-2 s^-1). This conclusion is reinforced by a detailed flare loop simulation of the heating phase. Since flux saturation effectively bottles up the coronal heat flux, mass motions now assume a dominant role in transferring energy from the coronal flare source to the lower transition region. The mass-energy exchange between the corona and chromosphere produces dramatic changes in the thermal structure of the plasma which are reflected in the differential emission measure profile of the flaring loop.     

Evolution of a flaring loop after injection of energetic electrons

For the November 5, 1980 flare it is investigated how the plasma in a large flaring loop responds to the injection of energetic electrons. Observations are compared with the results of a one-dimensional numerical simulation. For the simulation it is assumed that at the time the injection is started, the plasma is in an equilibrium state with a constant pressure along the loop and conductive heating compensated by radiative losses. Especially important for the evolution of the impulsively heated plasma is the penetration depth of the fast electrons compared to the depth of the transition layer. Both parameters are known from the observations. The injected energy is 2.6 × 10¹¹ ergs cm ^?2 in 30 s (as derived from the hard X-ray observations) and computations show that the high temperature plasma of the loop responds to it with upward motions of about 50 km s^?1, i.e. with velocities much smaller than the ion sound speed (≈ 500km s^?1). The heating of the plasma due to the absorption of beam energy can be understood using a constant density approximation. After the heating phase the plasma returns in about 5 min to its initial state by conductive cooling. The downward conducted energy is radiated away in the transition zone. The numerical simulation shows that impulsive heating by non-thermal electrons only does not explain the observed large increase in the density of the loop during the flare. It is therefore required that continuous energy and/or mass input occur after the impulsive phase.     

Hydrodynamic response of the solar chromosphere to an elementary flare burst

The problem of hydrodynamic response of the solar chromosphere on impulsive heating by energetic electrons is discussed. All basic physical processes are considered in a one-dimensional approximation, due to presence of a strong magnetic field. The calculations are performed for the heating of the chromosphere by electrons having a power-law energetic spectrum. In the upper chromosphere the electron temperature rises rapidly to values of order 10⁷ K. The ion temperature is more than the order of magnitude less than the temperature of electrons. The heated high-temperature chromospheric plasma expands into corona with a velocity up to 1500 km s^–1. In more dense layers, the fast re-emission of supplied energy takes place. This process gives rise to short-lived EUV flash. Just below the flare transition layer the thermal instability produces cold plasma condensation which moves downward at a velocity exceeding the sonic one in the quiet chromosphere.     

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.