Energy interconnection between the plasma cloud ejected from the active region and the shock wave

The relation between the ejected plasma cloud and the shock wave propagating ahead of it is examined for 27 pairs of such events. The flare sprays and the eruptive prominences observed in H line as well as the fast-moving sources of type-IV radio bursts have been considered as such ejected plasma clouds. Propagation of the shock wave in the solar corona has been examined from the observations of type-II radio bursts. Using the Parker model of the propagation of a shock wave, the shock wave velocity has been compared with the plasma cloud velocity. Energy interconnection between these two events has been studied. In the majority of the investigated cases there exists an energetic interconnection between the plasma cloud and the shock wave.     

Magnetic-cloud chamber effects behind flare-generated shock waves

A mechanism explaining the generation of the helium-enriched plasma-condensation colud (HAE-events) behind the front of shock waves associated with mass-ejecting flares is presented. The mechanism is based on the occurence of physical conditions, analogous to those in a Wilson cloud chamber in a magnetic field, behind the front of a flare-generated shock wave propagation out into interplanetary space. Consequently, if the solar atmosphere above the flare active region is saturated with ejected helium plasma, conditions are created for the forming of the helium-enriched plasma-condensation colud in the temperature-depressed region behind the shock wave front.     

WKB approach to the problem of MHD shock propagation through the heliospheric current sheet

The interplanetary shock wave front shape and intensity are calculated numerically by means of the WKB-approach, with nonlinear effects taken into account. The solar flare is modelled as an isotropic point explosion at the solar wind base. The heliospheric current sheet (HCS) is represented by a radially diverging stream with a higher plasma concentration and a lower wind speed. Fast magnetosonic shock wave propagation along the HCS is connected with the effect of regular accumulation of the wave energy in the vicinity of the HCS. In this place the wave intensity is increased, and the corresponding front fragments go ahead to form a shock-wave forerunner as a pimple. The primple, in turn, is located inside a quite a large, but less-contrast, dimple in the wave surface. This dimple approximately coincides with the HCS stream contours. If the flare is outside the HCS boundaries, the picture discussed above is conserved, but asymmetry effects arise. Thus the interplanetary shock is stronger when the Earth's observer and the flare are on the same side of the HCS and is weaker in the opposite case.     

On proton and electron acceleration by shock waves during large solar flares

The data on optical, X-ray and gamma emission from proton flares, as well as direct observations of flare-associated phenomena, show energetic proton acceleration in the corona rather than in the flare region. In the present paper, the acceleration of protons and accompanying relativistic electrons is accounted for by a shock wave arising during the development of a large flare. We deal with a regular acceleration mechanism due to multiple reflection of resonance protons and fast electrons from a collisionless shock wave front which serves as a moving mirror. The height of the most effective acceleration in the solar corona is determined. The accelerated particle energy and density are estimated. It is shown in particular that a transverse collisionless shock wave may produce the required flux of protons with energy of 10 MeV and of relativistic electrons of 1–10 MeV.The proposed scheme may also serve as an injection mechanism when the protons are accelerated up to relativistic energies by other methods.     

Brightness fluctuations of solar ultraviolet line intensities during a shock-wave passage

A simplified method is developed to derive the modifications induced at successive times by the passage of a shock wave in a standard unperturbed transition region atmosphere. Time dependent shocked models allow the evaluation of the effects of the vertically propagating shock wave upon the intensity of ultraviolet lines. Out of equilibrium effects are taken into account to evaluate time varying ion abundances. The behavior of the modified UV intensities is compared with the experimental results of Vernazza et al. (1975).     

Radio evidence of directive shock-wave propagation in the solar corona

Radioheliograph observations at 80 MHz are reported of a flare-associated event in which two type II bursts occur in four different sources. The projected centres of the sources lie along an arc subtending an angle of about 150° at the optical flare centre. If the arc represents the projection on the Sun's disk of a shock front passing through the 80 MHz plasma level, the source configuration suggests that the shock wave has originated from the optical flare region and propagated into the corona within a limited cone. On the opposite side of the flare centre, outside the shock cone, there was a stable bipolar source. Strong magnetic fields in this source may have acted as a magnetic wall to the shock wave and inhibited its propagation in this direction.     

Formation of coronal MHD shock waves – II. The Pressure Pulse Mechanism

The ignition of coronal shock waves by flares is investigated. It is assumed that an explosive expansion of the source region caused by impulsive heating generates a fast-mode MHD blast wave which subsequently transforms into a shock wave. The solutions of 1-D MHD equations for the flaring region and for the external region are matched at their boundary. The obtained results show under what conditions flares can ignite shock waves that excite the metric type II bursts. The heat input rate per unit mass has to be sufficiently high and the preflare value of the plasma parameter in the flaring region has to be larger than ₀ ^crit. The critical values depend on the flare dimensions and impulsiveness. Larger and more impulsive flares are more effective in generating type II bursts. Shock waves of a higher Mach number require a higher preflare value of and a more powerful heating per unit mass. The results demonstrate why only a small fraction of flares is associated with type II bursts and why the association rate increases with the flare importance.     

Large-scale flow of interstellar gas in galactic spiral waves: Effects of thermal balance and self-gravitation

Using the recent observational data on atomic and molecular hydrogen in the Galaxy, we analyse the dynamics of the interstellar gas in a spiral density wave. Within the framework of Marochniket al.'s (1972) model of the galactic spiral structure, the gas flow is obtained, with self-gravitation and thermal processes taken into account.It is shown that: (1) the self-gravitation of gas does not practically affect the galactic shock if the dominant contribution into the gas density comes from atomic hydrogen; (2) the effects of self-gravitation could be essential for both the gas flow and the stellar spiral wave only if the density contribution of H₂ exceeded several times that ofHi, with molecular hydrogen as a continuous medium having the isothermal equation of state; (3) however, regardless of the estimates of H₂ abundance in the Galaxy, its reaction to the density wave is weak, since it forms a collisionless system not dragged by the intercloud gas.It has been found that, if we allow for thermal processes in the interstellar medium, new types of gas flow can develop alongside with a previously-known continuous flow and galactic shock. They are: (1) galactic shock with the phase transition leading to the formation of dense cold clouds; (2) a three-phase flow where hot cavities and dense cold clouds coexist with an initial, moderately dense and cold phase; (3) an accretion wave which is a specific type of nonlinear wave with an amplitude of 11/2 orders of magnitude larger than that of the isothermal galactic shock appearing under the same conditions, but without heating and cooling.     

Development of a real-time algorithm for detection of solar wind discontinuities

A study is presented of an algorithm, based on the statistical analysis of interplanetary magnetic field data, for the real-time detection of discontinuities in the solar wind. The analysis is based on the application of a sliding or searching algorithm together with a minimum variance treatment. A demonstration is given for a Pioneer data set from 29 August, 1966. This particular data set was chosen because it has been extensively studied (in terms of the fast forward MHD shock wave) by previous groups who utilized the three-dimensional Rankine-Hugoniot shock equations after identifying the shock on a subjective basis. Our procedure differs in that it is perfectly objective because of its searching technique. For this particular data set we identify the original shock with excellent agreement with the earlier studies of its normal vector, as well as an additional shock and tangential discontinuity, neither of which had been identified previously.     

Converging magnetogasdynamic cylindrical shock waves in a uniform atmosphere

A self-similar solution to the problem of the implosion of a cylindrical shock wave in the presence of a magnetic field has been investigated. A strong shock wave in a cylindrically-symmetric flow travels to the axis of symmetry through a gas of uniform initial density ₀ and zero-pressure. A comparative study has been made between the results obtained in ordinary gasdynamics and magnetogasdynamics with transverse and axial components of the magnetic field. The value of similarity exponent has been assigned from that found in the paper of Whitham (1958).     

Nonlinear waves in a low-density plasma with a strong magnetic field

The nonlinear evolution of waves in a low-density plasma in a strong magnetic field is investigated on the basis of the Chew-Goldberger-Low approximation. The nonlinear effects are found to be essentially different for the magneto-acoustic and Alfvén modes. For the magnetic-acoustic mode, waveform distortion occurs at order ² (where is a measure of the linear wave amplitude) and shock formation occurs over a time-scale of order ^–1. For the Alfvén wave, modulation occurs at order ³ and shock formation over a time-scale of order ^–2. The nature of the waveform distortion is qualitatively different for the two modes.     

Interaction of interplanetary MHD shock waves with the magnetopause

The interaction between a shock-wave and the magnetopause is formulated on the basis of one-dimensional magnetohydrodynamics. The magnetopause is assumed to be a tangential discontinuity, and the magnetic field is limited to the case of perpendicularity. Both the forward and reverse shocks' impact on the magnetopause are considered and analyzed separately. The forward shock-magnetopause interaction results in a transmitted shock, a tangential discontinuity, and a simple rarefaction wave. The reverse shock-magnetopause interaction creates a transmitted shock, a tangential discontinuity, and a reflected wave. The propagation of an SSC signal which is related to an interplanetary shock-induced geomagnetic storm's onset-time on Earth is discussed in general terms. It was found in earlier work (Shen and Dryer, 1972) that the propagation velocity of an inter-planetary shock is decreased by about 1015% following its impact with the earth's bow shock; the present study shows that its velocity is then suddenly increased by a factor of two to three after impact with the magnetopause. The fast propagating shock-wave inside the magnetosphere degenerates into a hydromagnetic wave as it advances into an increasing intensity of the distorted dipole geomagnetic field.     

Effect of overtaking disturbances on the propagation of spherical shock wave through self-gravitating gas

Effect of overtaking disturbances on the propagation of a spherical shock wave in self gravitating gas has been studied by the technique developed by the first author [Mod. Meas. Cont. B,46(4), 1 (1992)]. The analytical expressions for modified shock velocity and shock strength have been obtained for an initial density distribution0 =r ^–w, where is the density at the axis of symmetry andw is a constant; simultaneously, for the two cases viz.; (i) when the shock is strong and ii) when it is weak. The results accomplished here have been compared with those for freely propagation of shock.It is observed that the conclusions arrived at here agree with experimental observations. Finally, the modified expressions for the pressure, the density and the particle velocity immediately behind the shock have also been derived from, for both cases.     

Heating of the solar transition zone and corona

Theoretical temperature, velocity and density profiles for the area above an optical depth = 10^–8 in the Sun were computed. An approximation for the coefficient of thermal conductivity was used; dissipation of shock wave energy as well as that of sound wave energy was taken into account and the height of shock formation was determined by a condition on the pressure. Comparison shows that our theoretical curves correspond very well with the observations.     

The motion of the cylindrical-symmetrical relativistic shock wave in the presence of an axial magnetic field

Some observed astrophysical phenomena, such as the blast of a supernova, suggest the necessity to study the motion of shock waves in a relativistic fluid flow in the presence of a magnetic field. This paper deals with the motion of a special relativistic shock wave which propagates from the center line outwardly after an explosion with the assumption that the magnetic field which has an axial component only. Similarity solutions which depend on the parameter =r/t are constructed. Two special cases are then studied in detail. In the first case, there is an ultrarelativistic fluid in front of the shock and in the second case, there is a cold fluid in front of the shock.     

The optical continuum of solar and stellar flares

A further development of the Kostyuk-Pikelner's model is presented. The response of the chromosphere heated by non-thermal electrons of the power-law energy spectrum has been studied on the basis of the numerical solution of the one-dimensional time-dependent equations of gravitational gas dynamics. The ionization and energy loss for the emissions in the Lyman and Balmer lines have been determined separately for the optically thin and thick L-line layers. Due to the initial heating, a higher-pressure region is formed. From this region, disturbances propagate upwards (a shock wave with a velocity of more than 1000 km s^-1) and downwards. A temperature jump propagates downwards, and a shock is formed in front of the thermal wave. During a period of several seconds after the beginning of this process, the temperature jump intensifies the downward shock wave and the large radiative loss gives rise to the high density jump ( ₂/ ₁ 100). The numerical solution has been analyzed in detail for the case heating of the ionized and neutral plasma, and a value of this heating is close to the upper limit of the admissible values. In this case, the condensation located between the temperature jump and the shock wave front, may emit in the observed optical continuum.In their essential features, the gas dynamic processes during the flares in red dwarf atmospheres are the same as those in the solar atmosphere. However, the high atmospheric densities, smaller height scale in red dwarf atmospheres, and greater energy of this processes in stellar flares, give rise, in practice, to the regular generation of optical continuum. The photometric parameters of a source with n 0¹⁵ cm^-3, T 9000 K, and _z 10 km are in a good agreement with observations.     

Analysis of the complex solar particle event on April 29–30, 1973

Based on the data of the high-apogee satellite Prognoz-3, the April 29–30, 1973 solar particle event is analysed. The event's complex energetic particle, interplanetary magnetic field and solar wind plasma properties are discussed. The unusual behaviour of solar particles up to energies 100 MeV can well be explained in terms of the interaction with an interplanetary shock wave system passing the Earth. Assuming that the structure of the interplanetary shock wave system is similar to that considered first by Parker (1961) and Gold (1959) and reviewed later by Hundhausen (1972) and Dryer (1974, 1975), the main characteristics of the energetic particle fluxes, solar wind and interplanetary magnetic field can be understood.     

Non-Homogeneous Charge-Consistent Model for Acceleration of Iron in the Solar Corona

Acceleration of iron ions by a spherical shock wave moving through non-homogeneous solar corona is considered. The energy dependence of the mean charge of iron, _Fe(E), is determined by the characteristic acceleration time, T _a, trapping time, T _tr, and time for charge changes, T _q. The latter varies along with plasma number density during the propagation of the shock wave in the corona. Our calculations have demonstrated that adiabatic energy changes, Coulomb losses and shock broadening do not sufficiently influence the dependence _Fe(E). According to our estimations, the photoionizing processes can scarcely affect the ionic states of accelerated iron, except probably for the most powerful X10 class events.     

Non-radial oscillations and energy transport in rotating solar (stellar) wind

The propagation of non-radial, small amplitude perturbations superposed on a zero-order, stationary, non-magnetic, polytropic, rotating stellar wind is studied in the limit of the local theory, i.e. for k r 1, k being the module of the wave vector and r the characteristic scale of the zero-order flow. The resulting dispersion equation is of the 3rd order in (complex) frequency and the possible modes correspond to two acoustic type waves, and to a gravity-shear wave with strongly anisotropic propagation properties, due to coupling between the internal gravity waves and shear motion. The gravity-shear mode allows velocity differences in the medium to exist with no corresponding density fluctuations and hence with no shock wave formation. It is suggested that this mode corresponds to some of the fast-slow velocity streams observed in the interplanetary medium and may provide means for wave energy being transported outwards with the zero-order flow, with little dissipation in the inner region of the solar wind.     

Why are spicules absent over plages and long under coronal holes?

One-dimensional hydrodynamic simulations are performed in order to examine the influence of initial atmospheric structures on the dynamics of spicules. This is an extended version of our previous spicule theory: spicules are produced by the shock wave (MHD slow mode shock) which originates from a bright point appearance (sudden pressure increase) at the network in the photosphere or in the low chromosphere. Simulation results well reproduce the observational facts that spicules are absent over plages and long under coronal holes. The physical reason is that the growth of a shock wave during its propagation through the chromosphere is small in plage regions and large in coronal hole regions, since the growth of a shock is determined by the density ratio ( _{h 0}/ _c ) between the bright point and the corona. An empirical formula H _max ( _{h 0}/ _c )^0.46 is obtained, where H _max is the maximum height of spicules above the transition region. The cross-section of the vertical magnetic flux tube is assumed to be constant in the numerical simulations.