Propagation of sonic waves in an optically thick medium in the presence of magnetic field

This paper studies sonic waves in an optically thick medium under the influence of a magnetic field. The conductivity of the medium has been taken to be infinite. The effects of radiation, radiation energy density, radiative heat transfer and magnetic field have been taken into account. It has been obtained that the magnetic field has significant effect on sonic velocity. The fundamental differential equations governing the growth and decay of sonic waves are determined and solved.     

Peculiarities of entropy and magnetosonic waves in optically thin cosmic plasma

The stability problem for small magnetohydrodynamic (MHD) perturbations in an optically thin, perfectly conducting uniform plasma with a cosmic abundance of elements is solved in the linear approximation. The electron heat conduction along the magnetic field and the proton heat conduction across the field are taken into account. We have shown for the first time that the entropy waves can grow exponentially, while the magnetosonic waves are damped in a wide range of physical conditions closest to the conditions in stellar coronae with the proper allowance for radiative losses. Slow magnetosonic waves are damped particularly rapidly. For the solar corona, the calculated damping decrement of slow magnetosonic waves agrees well with the averaged one in 11 quasi-periodic events observed from the TRACE satellite in extreme ultraviolet radiation. Other possible astrophysical applications of the results obtained are briefly discussed.     

Attenuation of small-amplitude oscillations in a prominence–corona model with a transverse magnetic field

Observations show that small-amplitude prominence oscillations are usually damped after a few periods. This phenomenon has been theoretically investigated in terms of non-ideal magnetoacoustic waves, non-adiabatic effects being the best candidates to explain the damping in the case of slow modes. We study the attenuation of non-adiabatic magnetoacoustic waves in a slab prominence embedded in the coronal medium. We assume an equilibrium configuration with a transverse magnetic field to the slab axis and investigate wave damping by thermal conduction and radiative losses. The magnetohydrodynamic equations are considered in their linearised form and terms representing thermal conduction, radiation and heating are included in the energy equation. The differential equations that govern linear slow and fast modes are numerically solved to obtain the complex oscillatory frequency and the corresponding eigenfunctions. We find that coronal thermal conduction and radiative losses from the prominence plasma reveal as the most relevant damping mechanisms. Both mechanisms govern together the attenuation of hybrid modes, whereas prominence radiation is responsible for the damping of internal modes and coronal conduction essentially dominates the attenuation of external modes. In addition, the energy transfer between the prominence and the corona caused by thermal conduction has a noticeable effect on the wave stability, radiative losses from the prominence plasma being of paramount importance for the thermal stability of fast modes. We conclude that slow modes are efficiently damped, with damping times compatible with observations. On the contrary, fast modes are less attenuated by non-adiabatic effects and their damping times are several orders of magnitude larger than those observed. The presence of the corona causes a decrease of the damping times with respect to those of an isolated prominence slab, but its effect is still insufficient to obtain damping times of the order of the period in the case of fast modes.     

Weak MHD discontinuities in a radiation-induced flow field

The growth of weak MHD discontinuities have been studied in a radiation induced flow field at very high temperature. Growth and decay properties of weak MHD discontinuities have been discussed under the influences of time-dependent gasdynamic field, the radiation field and the magnetic field with finite electrical conductivity. The effects of thermal radiation and conduction of the global behaviour of weak MHD discontinuities have been studied under a quasi-equilibrium and quasi-isotropic hypothesis of the differential approximation to the radiative heat transfer equation. It is shown that the existence of the time-dependent radiation field gives rise to a radiation induced wave which has a negligibly small effect on the non-relativistic flow properties of the gasdynamic field. It is also shown that the radiation stresses resist the steepening tendency of a compressive weak wave and help in stabilizing it whereas the thermal conduction effects counteracts to destabilize it. It is found that under radiation effects the shock formation is either disallowed or delayed. The two cases of diverging waves and converging waves have been studied separately to answer a particular question as to when a shock discontinuity or a coustic will be formed or disallowed under curvature effects.     

The effect of non-uniform ionospheric conductivity on standing magnetospheric Alfven waves

We look at time-dependent normal mode solutions to the Alfven wave equation in a uniform magnetic field, between planar ionospheres. In particular, the effect of sharp gradients in ionospheric conductivity on the spatial and temporal structure of the waves is considered. We show that the electric field of the wave must always be perpendicular to any conductivity discontinuities present, and that this is achieved by the generation of circularly polarized Alfven waves at the discontinuity. The results are applied to an ionospheric strip of high conductivity; this being relevant to Pi2s.     

Gravitational instability in isotropic MHD plasma waves

The effect of compressive viscosity, thermal conductivity and radiative heat-loss functions on the gravitational instability of infinitely extended homogeneous MHD plasma has been investigated. By taking in account these parameters we developed the six-order dispersion relation for magnetohydrodynamic (MHD) waves propagating in a homogeneous and isotropic plasma. The general dispersion relation has been developed from set of linearized basic equations and solved analytically to analyse the conditions of instability and instability of self-gravitating plasma embedded in a constant magnetic field. Our result shows that the presence of viscosity and thermal conductivity in a strong magnetic field substantially modifies the fundamental Jeans criterion of gravitational instability.     

Oscillations of magnetohydrodynamic shock waves on the surfaces of T Tauri stars

This work treats the matter deceleration in a magnetohydrodynamic radiative shock wave at the surface of a star. The problem is relevant to classical T Tauri stars where infalling matter is channelled along the star's magnetic field and stopped in the dense layers of photosphere. A significant new aspect of this work is that the magnetic field has an arbitrary angle with respect to the normal to the star's surface. We consider the limit where the magnetic field at the surface of the star is not very strong in the sense that the inflow is super-Alfvénic. In this limit, the initial deceleration and heating of plasma (at the entrance to the cooling zone) occurs in a fast magnetohydrodynamic shock wave. To calculate the intensity of radiative losses we use 'real' and 'power-law' radiative functions. We determine the stability/instability of the radiative shock wave as a function of parameters of the incoming flow: velocity, strength of the magnetic field, and its inclination to the surface of the star. In a number of simulation runs with the 'real' radiative function, we find a simple criterion for stability of the radiative shock wave. For a wide range of parameters, the periods of oscillation of the shock wave are of the order of  0.02–0.2 s  .     

Self-gravitational instability of rotating viscous Hall plasma with arbitrary radiative heat-loss functions and electron inertia

The effects of arbitrary radiative heat-loss functions and Hall current on the self-gravitational instability of a homogeneous, viscous, rotating plasma has been investigated incorporating the effects of finite electrical resistivity, finite electron inertia and thermal conductivity. A general dispersion relation is obtained using the normal mode analysis with the help of relevant linearized perturbation equations of the problem, and a modified Jeans criterion of instability is obtained. The conditions of modified Jeans instabilities and stabilities are discussed in the different cases of our interest. We find that the presence of arbitrary radiative heat-loss functions and thermal conductivity modifies the fundamental Jeans criterion of gravitational instability into a radiative instability criterion. The Hall parameter affects only the longitudinal mode of propagation and it has no effect on the transverse mode of propagation. For longitudinal propagation, it is found that the condition of radiative instability is independent of the magnetic field, Hall parameter, finite electron inertia, finite electrical resistivity, viscosity and rotation; but for the transverse mode of propagation it depends on the finite electrical resistivity, the strength of the magnetic field, and it is independent of rotation, electron inertia and viscosity. From the curves we find that the presence of thermal conductivity, finite electrical resistivity and density-dependent heat-loss function has a destabilizing influence, while viscosity and magnetic field have a stabilizing effect on the growth rate of an instability. The effect of arbitrary heat-loss functions is also studied on the growth rate of a radiative instability.     

Helical waves in type-1 comet tails

Oscillations of type-1 comet tails with plasma compressibility taken into account are studied. A comet tail is treated as a plasma cylinder separated by a tangential discontinuity surface from the solar wind. The dispersion equation obtained in the linear approximation is solved numerically with typical plasma parameters. A sufficient condition for instability of the cylindrical tangential discontinuity in the compressible fluid is obtained. The phase velocity of helical waves is shown to be approximately coincident with Alfvén speed in the tail in the reference system moving with the bulk velocity of the plasma outflow in the tail. The instability growth rate is calculated.This theory is shown to be in good agreement with observations in the tails of Comets Kohoutek, Morehouse and Arend-Roland. Hence we conclude that helical waves observed in type-1 comet tails are produced due to the Kelvin-Helmholtz instability, and the model under consideration is justified. If so, one may estimate comet tail magnetic field from the pressure balance at the tangential discontinuity; it turns out to be of the order of the interplanetary magnetic field.     

Magnetic field reconnection in a compressible plasma

An extension of Sonnerup's model for the magnetic field-line reconnection for a compressible plasma is given. The plasma is considered to be only slightly compressible so that the leading wave in Sonnerup's model can still be taken to be a thin discontinuity. The flow is assumed to occur under adiabatic conditions, and de Hoffmann-Teller jump conditions are used to connect the state variables across the shocks. The compressibility effects are found to increase the reconnection rate. The signaling problem is finally considered to study the evolution of MHD waves in a compressible, dissipative plasma so as to investigate the conditions under which the assumption of MHD waves in a compressible plasma to be thin discontinuities is valid.     

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.     

Radiative Cooling in MHD Models of the Quiet Sun Convection Zone and Corona

We present a series of numerical simulations of the quiet-Sun plasma threaded by magnetic fields that extend from the upper convection zone into the low corona. We discuss an efficient, simplified approximation to the physics of optically thick radiative transport through the surface layers, and investigate the effects of convective turbulence on the magnetic structure of the Sun’s atmosphere in an initially unipolar (open field) region. We find that the net Poynting flux below the surface is on average directed toward the interior, while in the photosphere and chromosphere the net flow of electromagnetic energy is outward into the solar corona. Overturning convective motions between these layers driven by rapid radiative cooling appears to be the source of energy for the oppositely directed fluxes of electromagnetic energy.     

Effect of Hall Current and Finite Larmor Radius Corrections on Thermal Instability of Radiative Plasma for Star Formation in Interstellar Medium (ISM)

The effects of finite ion Larmor radius (FLR) corrections, Hall current and radiative heat-loss function on the thermal instability of an infinite homogeneous, viscous plasma incorporating the effects of finite electrical resistivity, thermal conductivity and permeability for star formation in interstellar medium have been investigated. A general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. The wave propagation is discussed for longitudinal and transverse directions to the external magnetic field and the conditions of modified thermal instabilities and stabilities are discussed in different cases. We find that the thermal instability criterion gets modified into radiative instability criterion. The finite electrical resistivity removes the effect of magnetic field and the viscosity of the medium removes the effect of FLR from the condition of radiative instability. The Hall parameter affects only the longitudinal mode of propagation and it has no effect on the transverse mode of propagation. Numerical calculation shows stabilizing effect of viscosity, heat-loss function and FLR corrections, and destabilizing effect of finite resistivity and permeability on the thermal instability. The outcome of the problem discussed the formation of star in the interstellar medium.     

Evolution and decay of acceleration waves in perfectly conducting inviscid radiative magnetogasdynamics

The paper examines the evolutionary behaviour of acceleration waves in a perfectly conducting inviscid radiating gas permeated by a transverse magnetic field. Solution of the problem in the characteristic plane has been determined. It is shown that a linear solution in the characteristic plane exhibits nonlinear behaviour in the physical plane. Transport equation governing the behaviour of acceleration waves has been derived. The effect of radiative heat transfer under the influence of magnetic field on the formation of shock wave with generalized geometry is analyzed. The critical amplitude of the initial disturbance has been obtained such that the initial amplitude of any compressive wave greater than the critical one always terminates into shock wave. Critical time, when the compressive wave will grow into a shock wave, has been determined. Also, it is assessed as to how the radiative heat transfer in the presence of magnetic field affects the shock formation.     

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.     

Binary stellar winds

Stellar winds from a binary star pair will interact with each other along a contact discontinuity. We discuss qualitatively the geometry of the flow and field resulting from this interaction in the simplest case where the stars and winds are identical. We consider the shape of the critical surface (defined as the surface where the flow speed is equal to the sound speed) as a function of stellar separation and the role of shock waves in the flow field. The effect of stellar spin and magnetic sectors on the field configuration is given. The relative roles of mass loss and magnetic torque in the evolution of orbital parameters are discussed.     

Laboratory Observation of Secondary Shock Formation Ahead of a Strongly Radiative Blast Wave

We have previously reported the experimental discovery of a second shock forming ahead of a radiative shock propagating in Xe. The initial shock is spherical, radiative, with a high Mach number, and it sends a supersonic radiative heat wave far ahead of itself. The heat wave rapidly slows to a transonic regime and when its Mach number drops to two with respect to the downstream plasma, the heat wave drives a second shock ahead of itself to satisfy mass and momentum conservation in the heat wave reference frame. We now show experimental data from a range of mixtures of Xe and N₂, gradually changing the properties of the initial shock and the environment into which the shock moves and radiates (the radiative conductivity and the heat capacity). We have successfully observed second shock formation over the entire range from 100% Xe mass fraction to 100% N₂. The formation radius of the second shock as a function of Xe mass fraction is consistent with an analytical estimate.     

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.     

The Role of Magnetic Fields in Transient Seismic Emission Driven by Atmospheric Heating in Flares

Transient seismic emission in flares remains largely mysterious. Its discoverers proposed that seismic transients are driven by impulsive heating of the flaring chromosphere. Simulations of such heating show strong shocks, but these are damped by heavy radiative losses as they proceed downward. Because compression of the gas the shock enters both heats it and increases its density, the radiative losses increase radically with the strength of the shock, leaving doubt that sufficient energy can penetrate into the solar interior to explain helioseismic signatures. We note that simulations to date have no account for strong, inclined magnetic fields characteristic of transient-seismic-source environments. A strong horizontal magnetic field, for example, greatly increases the compressional modulus of the chromospheric medium, greatly reducing compression of the gas, hence radiative losses. Inclined magnetic fields, then, must be fundamental to the role of impulsive heating in transient seismic emission.     

Thermal and dynamical stability of prominences

A comprehensive examination of the stability of prominences is presented, and the gross behavior of prominences is considered in terms of the stability of an optically thin plasma supported by a magnetic field against gravity, including thermal effects on the energy balance. It is shown that (1) hydromagnetic as well as hydrodynamic waves of short wavelengths could induce instability which leads to the formation of prominences, and (2) in quiescent prominences, the dominant factor which controls the instability is the shear between the permeated and the supporting magnetic fields. The dependence of these instabilities on the radiative loss and other hydromagnetic effects are discussed. The National Center for Atmospheric Research is sponsored by the National Science Foundation.