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.     

Role of plasma flow in determining structure of the chromosphere-corona transition zone of the sun

Transfer of material between the chromosphere and corona of the Sun must occur whenever the geometry of any interconnecting magnetic structure changes, and there will also be a flow of plasma along field lines caused by any pressure difference between the two feet of each arch. Part of the energy conducted downwards towards the chromosphere is required to heat plasma rising into the corona, whereas material falling back towards the solar surface gives up energy to reinforce the conducted flow.This study shows that the term associated with flow is comparable to the radiation-loss term in the energy budget of the transition zone if the plasma speed at the base of the corona reaches about 3 km s^–1. This value is probably exceeded within most flux tubes during some period of their development, and speeds an order of magnitude higher can occur in favourable regions.This paper also examines limits to the temperature gradient of the transition zone set by the requirement of continuity of plasma flow.     

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.     

Nonthermal Electron Energy Deposition in the Chromosphere and the Accompanying Soft x-ray Flare Emission

We analyse four solar flares which have energetic hard X-ray emissions, but unusually low soft X-ray flux and GOES class (C1.0–C5.5). These are compared with two other flares that have soft and hard X-ray emission consistent with a generally observed correlation that shows increasing hard X-ray accompanied by increasing soft X-ray flux. We find that in the four small flares only a small percentage of the nonthermal electron beam energy is deposited in a location where the heating rate of the electron beam exceeds the radiative cooling rate of the ambient plasma. Most of the beam energy is subsequently radiated away into the cool chromosphere and so cannot power chromospheric evaporation thus reducing the soft X-ray emission. We also demonstrate that in the four small flares the nonthermal electron beam energy is insufficient to power the soft X-ray emitting plasma. We deduce that an additional energy source is required, and this could be provided by a DC-electric field (where quasi-static electric field channels in the coronal loops accelerate electrons, and those electrons with velocity below a critical velocity will heat the ambient plasma via Joule heating) in preference to a loop-top thermal source (where heat flux deposited in the corona is conducted along magnetic field lines to the chromosphere, heating the coronal plasma and giving rise to further chromospheric evaporation).     

Heat transfer in the corona and transition region

Thermal transfer in closed magnetic tubes in the corona and transition region is described on the basis of a static model in which all heat generated is radiated away, though conduction transfers much of the heat to the transition region prior to emission. The rate of conductive transfer depends on the cross-section of the magnetic tube as it passes through the chromosphere and transition region. This is derived from the pressure in the normal chromosphere. There is then only one main parameter to establish conditions in the corona and transition region, viz. the heating per unit area of the Sun's surface, which must equal the observed radiation from corona and transition region. The density adjusts itself so as to radiate away all heat generated within the tube; conditions in the tube below the transition region have little influence other than to decide where the base of the transition region lies and the width of the region particularly in its lower parts. For the observed rate of heating, the computed densities (or pressures), the ratio of coronal to transition region emissions, and the distribution of radiation in the EUV spectrum agree closely with those observed. The optimum maximum temperatures are found with heating concentrated in the highest regions of the flux tubes. It is only in the lowest 20–40 km of the transition region, where T<10⁵K, that any additional heating is needed to explain EUV line intensities. The equation of heat transfer also has solutions in which the temperature is oscillatory with disance. These do not apply to the normal corona, but may be relevant to prominences.     

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.     

The Mechanisms of Particle Kinetics and Dynamics Leading to Seismic Emission and Sunquakes

In this paper the mechanisms responsible for observational features associated with sunquakes induced by different classes of solar flares are compared. The role of high-energy particle beams via Coulomb and Ohmic heating of the ambient plasma and nonthermal excitation and ionization is explored for different beam parameters at various atmospheric depths. On the one hand, only hard electron beams with high-energy fluxes are found producing extensive nonthermal hydrogen ionization, four orders of magnitude higher than in the quiet atmosphere. This excess ionization leads to the white-light flares associated with the seismic emission appearing simultaneously with hard X-ray emission and, consequently, to a strong increase of Ni-line emission observed as the seismic emission measured with the holographic technique. On the other hand, the ambient plasma hydrodynamic response to heating by such beam electrons forms hydrodynamic shocks just below the transition region, in the upper chromosphere, and they travel with supersonic velocity for up to five minutes before reaching the photosphere. These hydrodynamic responses caused by the beam electrons are maximized in the lower chromosphere for moderate electron beams because of their smaller Ohmic losses in the upper atmosphere compared to those for higher-energy electron beams whose bulk energy is deposited in the transition region. These shocks caused by electron beams can explain the observations of seismic emission by time?–?distance (TD) diagrams and the holographic method in M- and C-class flares, whereas to account for the quakes in X-class flares, high-energy quasi-thermal protons or power-law proton beams either by themselves or blended with electron beams are the most likely agents. Nonthermal ionization and excitation of lower atmospheric levels during the beam injection followed by thermo-conductive heating after the beam is stopped can contribute to the seismic signatures observed with the holographic technique caused by strong nonthermal ionization and back-warming heating occurring in the shock while it loses its energy by optically-thick radiation in the photospheric lines and continua.     

Maximum flux density of the gyrosynchrotron spectrum in a nonuniform source

The maximum flux density of a gyrosynchrotron radiation spectrum in a mag- netic dip|oe model with self absorption and gyroresonance is calculated. Our calculations show that the maximum flux density of the gyrosynchrotron spectrum increases with in- creasing low-energy cutoff, number density, input depth of energetic electrons, magnetic field strength and viewing angle, and with decreasing energy spectral index of energetic electrons, number density and temperature of thermal electrons. It is found that there are linear correlations between the logarithms of the maximum flux density and the above eight parameters with correlation coefficients higher than 0.91 and fit accuracies better than 10%. The maximum flux density could be a good indicator of the changes of these source parameters. In addition, we find that there are very good positive linear correla- tions between the logarithms of the maximum flux density and peak frequency when the above former five parameters vary respectively. Their linear correlation coefficients are higher than 0.90 and the fit accuracies are better than 0.5%.     

Heat flux as a source of ion-acoustic oscillations in the transition region of the solar atmosphere

Based on model calculations, we show that ion-acoustic oscillations can be excited by heat fluxes in a plasma. We discuss the probable effect of ion-acoustic oscillations on the formation of temperature gradients at critical heat fluxes. The local critical heat flux in the transition region of the solar atmosphere is close to the well-known experimental heat flux from the corona into the chromosphere.     

On the filling factor of emitting material in the upper atmosphere of ε Eri (K2 V)

The emission measure distribution in the upper transition region and corona of ε Eri is derived from observed emission-line fluxes. Theoretical emission measure distributions are calculated assuming that the radiation losses are balanced by the net conductive flux. We discuss how the area factor of the emitting regions as a function of temperature can be derived from a comparison between these emission measure distributions. It is found that the filling factor varies from ∼0.2 in the mid-transition region to ∼1.0 in the inner corona. The sensitivity of these results to the adopted ion fractions, the iron abundance and other parameters is discussed. The area factors found are qualitatively similar to the observed structure of the solar atmosphere, and can be used to constrain two-component models of the chromosphere. Given further observations, the method could be applied to investigate the trends in filling factors with indicators of stellar activity.     

On the nonthermal excitation and polarization of X-ray lines during solar flares

The energy distributions of nonthermal electrons are derived from hard X-ray spectra taken during the impulsive phase of two 2B flares in February 1969. They are used to calculate the fluxes of nonthermally excited X-ray lines of hydrogen-like and helium-like ions. These fluxes are compared to the total line fluxes observed at the same time with crystal spectrometers. The nonthermal excitation is found to give only small contributions to the total line intensities. This implies that the impact polarization which is to be expected for anisotropic velocity distributions of the energetic electrons, will be low. Nevertheless it should be feasible to detect line polarization during the impulsive phase of strong X-ray flares.NAS/NRC Research Associate.     

Alfvén waves in the solar atmosphere

The nonlinear propagation of Alfvén waves on open solar magnetic flux tubes is considered. The flux tubes are taken to be vertical and axisymmetric, and they are initially untwisted. The Alfvén waves are time-dependent axisymmetric twists. Their propagation into the chromosphere and corona is investigated by solving numerically a set of nonlinear time-dependent equations, which couple the Alfvén waves into motions parallel to the initial magnetic field (motion in the third coordinate direction is artificially suppressed). The principal conclusions are: (1) Alfvén waves can steepen into fast shocks in the chromosphere. These shocks can pass through the transition region into the corona, and heat the corona. (2) As the fast shocks pass through the transition region, they produce large-velocity pulses in the direction transverse to B _o. The pulses typically have amplitudes of 60 km s^–1 or so and durations of a few tens of seconds. Such features may have been observed, suggesting that the corona is in fact heated by fast shocks. (3) Alfvén waves exhibit a strong tendency to drive upward flows, with many of the properties of spicules. Spicules, and the observed corrugated nature of the transition region, may therefore be by-products of magnetic heating of the corona. (4) It is qualitatively suggested that Alfvén waves may heat the upper chromosphere indirectly by exerting time-dependent forces on the plasma, rather than by directly depositing heat into the plasma.     

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.     

The relation of energetic solar X-rays (hν>60 keV) and high frequency microwaves deduced from the periodic bursts of August 8, 1968 flare

Correlated sixteen-second periodic bursts were observed during the flash phase of a class 2b solar flare in energetic X-rays, microwaves, and EUV ionizing radiation. The observations of the periodic structures in the various X-ray energy channels indicate that the structures are predominantly a phenomenon of high energy electrons, E>80 keV. In view of the fact that the periodic X-ray structures were correlated extensively in microwave and EUV frequencies, a plausible conclusion is that these three types of radiation have a common energy source. The acceleration of the energetic electrons must occur deep in the chromosphere where there are sufficient solar constituents that can be ionized to produce the correlated periodic EUV radiation.     

The role of non-thermal electrons in the optical continuum of stellar flares

The continuum emission of stellar flares in UV and visible bands can be enhanced by two or even three orders of magnitude relative to the quiescent level and is usually characterized by a blue colour. It is difficult for thermal atmospheric models to reproduce all these spectral features. If the flaring process involves the acceleration of energetic electrons which then precipitate downwards to heat the lower atmosphere, collisional excitation and ionization of ambient hydrogen atoms by these non-thermal electrons could be important in powering the continuum emission. To explore such a possibility, we compute the continuum spectra from an atmospheric model for a dMe star, AD Leo, at its quiescent state, when considering the non-thermal effects by precipitating electron beams. The results show that if the electron beam has an energy flux large enough (for example, ℱ₁∼10¹² erg cm⁻² s⁻¹), the U -band brightening and, in particular, the U − B colour are roughly comparable with observed values for a typical large flare. Moreover, for electron beams with a moderate energy flux ℱ₁≲10¹¹ erg cm⁻² s⁻¹, a decrease of the emission at the Paschen continuum appears. This can explain at least partly the continuum dimming observed in some stellar flares. Adopting an atmospheric model for the flaring state can further raise the continuum flux, but it yields a spectral colour incomparable with observations. This implies that the non-thermal effects may play the chief role in powering the continuum emission in some stellar flares.     

Parameters of the intense X-ray and gamma-ray radiation from the solar flare of May 20, 2002, as observed from the Coronas-F spacecraft

We consider temporal, spectral, and polarization parameters of the hard X-ray and gamma-ray radiation observed during the solar flare of May 20, 2002, in the course of experiments with the SONG and SPR-N instruments onboard the Coronas-F spacecraft. This flare is one of the most intense gamma-ray events among all of the bursts of solar hard electromagnetic radiation detected since the beginning of the Coronas-F operation (since July 31, 2001) and one of the few gamma-ray events observed during solar cycle 23. A simultaneous analysis of the Coronas-F and GOES data on solar thermal X-ray radiation suggests that, apart from heating due to currents of matter in the the flare region, impulsive heating due to the injection of energetic electrons took place during the near-limb flare S21E65 of May 20, 2002. These electrons produced intense hard X-ray and gamma-ray radiation. The spectrum of this radiation extends up to energies ≥7 MeV. Intense gamma-ray lines are virtually unobservable against the background of the nonthermal continuum. The polarization of the hard X-ray (20–100 keV) radiation was estimated to be ≤15–20%. No significant increase in the flux of energetic protons from the flare under consideration was found. At the same time, according to ACE data, the fluxes of energetic electrons in interplanetary space increased shortly (～25 min) after the flare.     

Relation between X-ray flux and radio flux from cosmic objects

The relationship between the X-ray flux and the radio flux from cosmic objects is investigated. We consider the emission from energetic electrons on the condition in which a plasma and a magnetic field exist. As energetic electrons under the circumstances emit both X-rays by the bremsstrahlung mechanism and radio waves by the gyrosynchrotron mechanism simultaneously, it is shown that the radio flux density is closely related to the X-ray flux density. Solving an integral equation describing the X-ray flux density at Earth, we obtain the energy spectrum of electrons in the emitting region. Inserting the result into equation of the radio flux density at Earth, we obtain the direct formula between the X-ray flux density and the radio flux density. The relation is independent of the distance between Earth and cosmic sources. Assuming a power-law X-ray spectrum, we evaluate the numerical relation between two flux densities.     

The polarization of continuum radiation in sunspots

Expressions are derived for the Stokes parameters of light scattered by a layer of free electrons and hydrogen atoms in a sunspot. A physically reasonable sunspot model was found so that the direction of the calculated linear polarization agrees reasonably with observations. The magnitude of the calculated values of the linear polarization agrees generally with values observed in the continuum at 5830 Å. Circular polarization in the continuum also accompanies electron scattering in spot regions; however for commonly accepted values of the longitudinal magnetic field, the predicted circular polarization is much smaller than observed.     

Coronal Temperature Profiles Obtained from Kinetic Models and from Coronal Brightness Measurements Obtained During Solar Eclipses

Coronal density, temperature, and heat-flux distributions for the equatorial and polar corona have been deduced from Saito’s model of averaged coronal white-light (WL) brightness and polarization observations. These distributions are compared with those determined from a kinetic collisionless/exospheric model of the solar corona. This comparison indicates similar distributions at large radial distances (>?7 R_⊙) in the collisionless region. However, rather important differences are found close to the Sun in the acceleration region of the solar wind. The exospheric heat flux is directed away from the Sun, while that inferred from all WL coronal observations is in the opposite direction, i.e. conducting heat from the inner corona toward the chromosphere. This could indicate that the source of coronal heating extends up into the inner corona, where it maximizes at r>1.5 R_⊙, well above 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.