Temporal evolution of MHD shocks in the interstellar medium

We undertake calculations of the time-dependent structure of shock waves propagating in dark and diffuse interstellar clouds. The results of the time-dependent model are compared with those obtained by means of an independent steady-state code and found to agree well at sufficiently late times. Discontinuities in the flow of the neutral fluid are handled by introducing a pseudo-viscosity. Special procedures are adopted to correct for the associated widening of the discontinuity, in order not to distort the role of inelastic collision processes. We find that, in dark clouds, C shocks will tend to predominate, but are unlikely to have attained steady state in the cloud lifetime. On the other hand, in diffuse clouds, steady state may be reached but the discontinuity in the flow of the neutral fluid remains. We find no evidence for the existence of C* shocks, in which the neutral fluid undergoes a continuous transition from supersonic to subsonic flow (in the reference frame of the shock wave). Attention is drawn to the possible importance of these results for the interpretation of H₂ rovibrational line intensities.     

Ignition of MHD shocks associated with solar flares

We have selected single frequency recordings of 28 high-frequency type II bursts characterized by a starting frequency greater than 237 MHz to estimate as accurately as possible the launch-time of the flare-associated MHD shocks. We established the time associations between metric type II burst onsets and the time characteristics of the microwave and X-ray fluxes of the associated flares. The associated flares were impulsive events with rise times most often about 1 min in the hard X-ray range and 1–2 min in the microwave wavelength range. The majority of the type II bursts from our sample started about 1 min after the maximum of the microwave burst. Launch times of MHD shocks producing type II bursts were obtained using the 10 × Saito coronal model and shock velocities estimated from burst characteristics at different frequencies. Back-extrapolations of type II recordings indicate that MHD shocks are launched in the time interval prior to the maximum of the first peak in the associated microwave burst, most probably at the beginning of the rapid increase of the microwave burst.     

Time-dependent simulations of steady C-type shocks

Using a time-dependent multifluid, magnetohydrodynamic code, we calculated the structure of steady perpendicular and oblique C-type shocks in dusty plasmas. We included relevant processes to describe mass transfer between the different fluids, radiative cooling by emission lines and grain charging, and studied the effect of single- and multiple-sized grains on the shock structure. Our models are the first of oblique fast-mode molecular shocks in which such a rigorous treatment of the dust grain dynamics has been combined with a self-consistent calculation of the thermal and ionization structures including appropriate microphysics. At low densities, the grains do not play any significant rôle in the shock dynamics. At high densities, the ionization fraction is sufficiently low that dust grains are important charge and current carriers and, thus, determine the shock structure. We find that the magnetic field in the shock front has a significant rotation out of the initial upstream plane. This is most pronounced for single-sized grains and small angles of the shock normal with the magnetic field. Our results are similar to previous studies of steady C-type shocks showing that our method is efficient, rigorous and robust. Unlike the method employed in the previous most detailed treatment of dust in steady oblique fast-mode shocks, ours allow a reliable calculation even when chemical or other conditions deviate from local statistical equilibrium. We are also able to model transient phenomena.     

Numerical simulations for MHD coronal seismology

Magnetohydrodynamic（MHD） processes are important for the transfer of energy over large scales in plasmas and so are essential to understanding most forms of dynamical activity in the solar atmosphere. The introduction of transverse structuring into models for the corona modifies the behavior of MHD waves through processes such as dispersion and mode coupling. Exploiting our understanding of MHD waves with the diagnostic tool of coronal seismology relies upon the development of sufficiently detailed models to account for all the features in observations. The development of realistic models appropriate for highly structured and dynamical plasmas is often beyond the domain of simple mathematical analysis and so numerical methods are employed. This paper reviews recent numerical results for seismology of the solar corona using MHD.     

An MHD gadget for cosmological simulations

Various radio observations have shown that the hot atmospheres of galaxy clusters are magnetized. However, our understanding of the origin of these magnetic fields, their implications on structure formation and their interplay with the dynamics of the cluster atmosphere, especially in the centres of galaxy clusters, is still very limited. In preparation for the upcoming new generation of radio telescopes (like Expanded Very Large Array, Low Wavelength Array, Low Frequency Array and Square Kilometer Array), a huge effort is being made to learn more about cosmological magnetic fields from the observational perspective. Here we present the implementation of magnetohydrodynamics (MHD) in the cosmological smoothed particle hydrodynamics (SPH) code gadget . We discuss the details of the implementation and various schemes to suppress numerical instabilities as well as regularization schemes, in the context of cosmological simulations. The performance of the SPH–MHD code is demonstrated in various one- and two-dimensional test problems, which we performed with a fully, three-dimensional set-up to test the code under realistic circumstances. Comparing solutions obtained using athena , we find excellent agreement with our SPH–MHD implementation. Finally, we apply our SPH–MHD implementation to galaxy cluster formation within a large, cosmological box. Performing a resolution study we demonstrate the robustness of the predicted shape of the magnetic field profiles in galaxy clusters, which is in good agreement with previous studies.     

Nucleosynthesis and Mixing in Cassiopeia A

We present results from the first light observations of the Cassiopeia A supernova remnant (SNR) by the Chandra X-Ray Observatory. Based on representative spectra from four selected regions, we investigate the processes of nucleosynthesis and mixing in Cas A. We make the first unequivocal identification of iron-rich ejecta produced by explosive silicon burning in a young Galactic SNR. Elsewhere in the remnant, we see silicon-rich ejecta from explosive oxygen burning. The Fe-rich ejecta lie outside the Si-rich material, indicating that bulk motions were extensive and energetic enough in Cas A to cause a spatial inversion of a significant portion of the supernova core. It is likely that this inversion was caused by "Fe"-rich ejecta emerging in plumes from the rising bubbles in the neutrino-driven convection layer during the supernova explosion. In addition, the radioactive decay energy from 56Ni may have contributed to the subsequent evolution of the material. We have also discovered faint, well-defined filaments with featureless X-ray spectra that are possibly sites of cosmic-ray acceleration in Cas A.     

MHD simulations of solar and interplanetary phenomena

Workers in the field of magnetohydrodynamics (MHD) have been interested in the hypothesis that observed solar activities can be utilized in a deterministic way to predict the bulk flow consequences of these activities in the three-dimensional heliosphere. Exploration of this hypothesis, using the conventional/classic initial boundary value approach, will be reviewed against the background of basic, ideal (except for shocks) one-fluid approximations. This work has been divided into two parts: near-Sun simulations in two dimensions of coronal mass ejections (CMEs) as well as interplanetary simulations in 2D and 3D of propagating shocks. In the latter case, the flows behind the shocks should be thought of as interplanetary ICMEs, i.e., the interplanetary, evolutionary consequences of the near-Sun simulations.Initialization of these simulations has been based on observations (optical, soft X-ray, radio) from both ground-and space-based instruments. Simulation outputs have been compared within situ plasma and field observations and interplanetary scintillations (IPS). Improvements in the initialization procedures — spatial/temporal variations of solar plasma and field parameters at the coronal base — are expected from YOHKOH, SOHO, CORONAS-I, and TRACE experiments. Ground truth observations from WIND, SOHO, ACE, and INTERBALL experiments should then be compared with three-dimensional MHD outputs in tests of the fluid hypothesis noted above.     

MHD simulations of jets from accretion disks

We present the MHD simulation including accretion flows in disks, acceleration of outflows from disks, and collimation of the outflows self-consistently. Although it was considered that this kind of simulations only shows the transient phenomena of jets, we found that the outflow and accretion flow reached a quasi-steady state by performing a long-term calculation in a large calculation region. Though the final stage is not exactly the steady state, the acceleration and collimation mechanisms of the outflow were the same as those of the steady theory. The scale of the calculation is approaching to the scale that was observed by the VLBI technique, which provides the current highest resolution for YSO jets.     

Instability of the structure of strong oblique MHD cosmic-ray shocks

A criterion of the instability of a flow of a thermal plasma and cosmic rays in front of an oblique MHD shock wave with respect to short-wavelength magnetosonic disturbances is derived. The dependence of a cosmic-ray diffusion tensor on a plasma density and a large-scale magnetic field is taken into account. The most unstable disturbances propagate at an angle to the magnetic field if diffusion is strongly anisotropic. In some cases the most strong instability connects with the off-diagonal terms of the diffusion tensor.     

MHD simulations of rayleigh-taylor instability in young supernova remnants

Radio observations shows that young supernova remnants such as Tycho and Cas A generally exhibit a circular clumpy shell. This shell shows a radial magnetic field whose equipartition strength is 2 to 3 orders of magnitude higher than the interstellar field. A simple compression of the ambient field by the shock can explain neither of these observations. We show that the Rayleigh-Taylor instability which occurs at the ejecta/ISM interface can explain these observations. We have done MHD simulations of the instability in the shell of Type-I supernova remnants for the first time by utilizing moving grid technique. Our simulation shows that Rayleigh-Taylor and Kelvin-Helmholtz instabilities amplify ambient magnetic fields locally and produce the clumpy radio shell. Strong magnetic field lines draped around the Rayleigh-Taylor fingers produce the radial B-vector polarization, whereas thermal bremsstrahlung from the dense fingers themselves produce the clumpy X-ray emission.     

Numerical simulations of driven MHD waves in coronal loops

The solar corona, modeled by a low-, resistive plasma slab, sustains MHD wave propagations due to footpoint motions in the photosphere. Simple test cases are undertaken to verify the code. Uniform, smooth and steep density, magnetic profile and driver are considered. The numerical simulations presented here focus on the evolution and properties of the Alfvén, fast and slow waves in coronal loops. The plasma responds to the footpoint motion by kink or sausage waves depending on the amount of shear in the magnetic field. The larger twist in the magnetic field of the loop introduces more fast-wave trapping and destroys initially developed sausage-like wave modes. The transition from sausage to kink waves does not depend much on the steep or smooth profile. The slow waves develop more complex fine structures, thus accounting for several local extrema in the perturbed velocity profiles in the loop. Appearance of the remnants of the ideal singularities characteristic of ideal plasma is the prominent feature of this study. The Alfvén wave which produces remnants of the ideal x ^–1 singularity, reminiscent of Alfvén resonance at the loop edges, becomes less pronounced for larger twist. Larger shear in the magnetic field makes the development of pseudo-singularity less prominent in case of a steep profile than that in case of a smooth profile. The twist also causes heating at the edges, associated with the resonance and the phase mixing of the Alfvén and slow waves, to slowly shift to layers inside the slab corresponding to peaks in the magnetic field strength. In addition, increasing the twist leads to a higher heating rate of the loop. Remnants of the ideal log ¦x¦ singularity are observed for fast waves for larger twist. For slow waves they are absent when the plasma experiences large twist in a short time. The steep profiles do not favour the creation of pseudo-singularities as easily as in the smooth case.     

Long-wavelength MHD instability in the prefront of collisionless shocks with accelerated particles

Collisionless shocks in turbulent space plasmas accelerate particles by the Fermi mechanism to ultrarelativistic energies. The interaction of accelerated particles with the plasma inflow produces extended supersonic MHD flows of multicomponent plasma. We investigate the instabilities of a flow of three-component turbulent plasma with relativistic particles against long-wavelength perturbations with scales larger than the accelerated particle transport mean free path and the initial turbulence scales. The presence of turbulence allows us to formulate the system of single-fluid equations, the equation of motion for the medium as a whole, and the induction equation for the magnetic field with turbulent magnetic and kinematic viscosities. The current of accelerated particles enters into the induction equation with an effective magnetic diffusion coefficient. We have calculated the local growth rates of the perturbations related to the nonresonant long-wavelength instability of the current of accelerated particles for MHD perturbations in the WKB approximation. The amplification of long-wavelength magnetic field perturbations in the flow upstream of the shock front can affect significantly the maximum energies of the particles accelerated by a collisionless shock and can lead to the observed peculiarities of the synchrotron X-ray radiation in supernova remnants.     

The effect of Alfvén waves on MHD fast shocks

The Rankine-Hugoniot equations for hydromagnetic shocks are extended to include the energy and momentum flux due to Alfvén waves incident on the shock. The shock relations are solved numerically for a wide variety of parameters typical of interplanetary conditions. The presence of the waves can cause appreciable changes in the structure of fast shocks of low Mach number.     

Numerical simulations of fast MHD waves in a coronal plasma

The temporal evolution of ducted waves under coronal conditions is studied in the framework of linearized low MHD by means of numerical simulations. Coronal loops are represented by smoothed slabs of enhanced gas density embedded within a uniform magnetic field. The simulations show that for a smoothed density profile there is an energy leakage from the slab, associated with the propagation of sausage and kink waves. Wave energy leakage in the kink wave is generally small, whereas the wave energy in sausage waves leaks more strongly for long wavelengths and smoother slabs.     

Numerical simulations of fast MHD waves in a coronal plasma

A method is presented for the numerical study of the temporal evolution of nonlinear periodic waves in solar coronal loops which are approximated by smoothed slabs of enhanced gas density embedded within a uniform magnetic field. This method uses a fast Fourier transform technique to calculate spatial derivatives and a modified Euler algorithm for the time scheme for solving cold magnetohydrodynamic equations that govern nonlinear perturbations. The numerical results show that nonlinearity can play a significant role, leading to wave breaking of the kink wave and slab demolition for the sausage one. The kink periodic wave adjusts better to the smoothed slab than the sausage wave.     

Structure and stationarity of quasi-perpendicular shocks: Numerical simulations

This paper presents an overview of numerical simulation studies of fast collisionless shocks and compares these simulation results with observations of the Earth's bow shock and theoretical works. Especially, we review the structure and stationarity of the supercritical quasi-perpendicular shocks. In situ observations indicate that these shocks are generally quasi-stationary whereas full particle simulations as well as hybrid simulations often present a strong nonstationary behavior, a shock self-reformation. The simulation results, along with theoretical and observational works, suggest that the classical models of the quasi-stationary structure generated by reflected protons or by dispersive whistlers are not generally applicable for the supercritical quasi-perpendicular shocks and other phenomena are to be included into the model to ensure the observed quasi-stationarity: The role of a small scale turbulence and shock ripples is investigated. The downstream turbulence and the electron dynamics in the quasi-perpendicular shocks are also discussed.     

MHD simulations of sunspot rotation and the coronal consequences

A simplified magnetic configuration is used to model some aspects of observations of a rotating sunspot and its overlying coronal loops. In the observations a large sunspot rotates over a few days and two smaller pores spiral into it. The coronal loops become sigmoidal in shape and flares are seen in Yohkoh/SXT and GOES. We have modeled the sunspot, one of the pores and the loops connecting these to a diffuse region of plasma of the opposite polarity. Two sets of MHD simulations are considered: (i) rotation of the sunspot and pore alone and (ii) rotation of the sunspot with inflow of the pore. Rotation alone can trigger the ideal kink instability in the loops but only for a rotation that is much greater than the observed value. There is no build-up of current which is needed for magnetic reconnection to occur. However, when inflow is included a strong build-up of current is seen as the pore merges with the sunspot. Comparing these results from the simulations with the observations, we find that the observed merging of the pores coincides with the timing of the flare. Therefore, we suggest that the merging of the pores with the large sunspot may be responsible for the flaring.     

Cosmic-ray energetics in the supernova remnant Cassiopeia A

Based on the observed radio spectrum for the supernova remnant Cassiopeia A, we have established that it represents synchrotron radiation of relativistic electrons with a nonpower-law energy spectrum in the form of Kaplan-Tsytovich’s standard distribution. The total density of relativistic electrons is 10^?3 cm^?3, only 20% of which form the radio spectrum. The particle number ratio of the proton-nuclear and electron cosmicray components inside the shell differs significantly from the mean Galactic ratio (100) and probably does not exceed unity.