Shock waves propagation in the turbulent interplanetary plasma

Effect of turbulence on interplanetary shock waves propagation is considered. It is shown that background turbulence results in the additional shock wave deceleration which may be comparable with the deceleration due to plasma sweeping. The turbulent deceleration is connected with the energy losses due to the strong turbulence amplification behind the moving shock front.     

Shock waves and vorticity generation in protogalactic medium

A theory of secondary vorticity is suggested on grounds of an isotropic Hot Big Bang. Vortical motions are generated in front of the shock waves, which appear as a result of supersonic hydrodynamic processes induced by gravitational instability at a later epoch of cosmological expansion. Inside large layers of gas compressed by shocks subsonic turbulence with both vortical and acoustic modes develops. Every such layer may be treated as a protocluster; and eddies, if strong enough, would give rise to protogalaxies. An effective mechanism of vorticity generation — scattering of density inhomogeneities on shock fronts — is examined in detail. Quantitative estimates show that the vortices that are due to this mechanism can be at least the order of magnitude to account for the angular mometa of spiral galaxies. The spectrum of initial irrotational perturbations remains open to discussion, but characteristic amplitudes required do not contradict any observational or theoretical restrictions.     

On turbulence in the quasi-perpendicular bow shock

In this paper we propose to review the fundamental aspects of turbulence theories and their relevance to particle distribution functions observed by the cluster satellites in the quasi-perpendicular shock. The paper focusses on the hierarchical model describing the different levels of plasma turbulence; from the linear theory, through the quasi-linear remedy, to strong turbulence theories in the context of the earth's bow shock. We will discuss very briefly the validity of these approximations, and their relevance as far as satellite observations are concerned. In particular, we will discuss the development of non-Gaussian features in the ion distribution functions through the evaluation of higher order moments such as the kurtosis or flatness and the skewness. We have found that the profile of the kurtosis versus skewness tends to collapse to a parabolic line. This in turn allows us to draw analogies with neutral fluid turbulence where such a collapse of the kurtosis-skewness profile has been observed.     

A nonlinear theory of stellar wind with allowance for the influence of relativistic particles

We solve the nonlinear problem of the dynamics of a steady-state, spherically symmetric stellar wind by taking into account particle acceleration to relativistic energies near the shock front. The particles are assumed to be accelerated through the Fermi mechanism, interacting with stellar-wind turbulence and crossing many times the shock front that separates the supersonic and subsonic stellar-wind regions. We take into account the influence of the accelerated particles on hydrodynamic plasma-flow parameters. Our method allows all hydrodynamic parameters of the shock front and plasma in the supersonic region to be determined in a self-consistent way and the accelerated-particle energy spectrum to be calculated. Our numerical and analytic calculations show that the plasma compression ratio at the shock front increases compared to the case where there are no relativistic particles and that the velocity profile in the supersonic region acquires a characteristic kink. The shape of the energy spectrum for the accelerated particles and their pressure near the front are essentially determined by the presumed dependence of the diffusion coefficient on particle energy, which, in turn, depends on the scale distribution of turbulent pulsations and other stellar-wind inhomogeneities.     

Effects of Initial Conditions on Compressible Mixing in Supernova-Relevant Laboratory Experiments

In core-collapse supernovae, strong blast waves drive interfaces susceptible to Rayleigh–Taylor (RT), Richtmyer–Meshkov (RM), and Kelvin–Helmholtz (KH) instabilities. In addition, perturbation growth can result from material expansion in large-scale velocity gradients behind the shock front. Laser-driven experiments are designed to produce a strongly shocked interface whose evolution is a scaled version of the unstable hydrogen–helium interface in core-collapse supernovae such as SN 1987A. The ultimate goal of this research is to develop an understanding of the effect of hydrodynamic instabilities and the resulting transition to turbulence on supernovae observables that remain as yet unexplained. This paper represents a summary of recent results from a computational study of unstable systems driven by high Mach number shock and blast waves. For planar multimode systems, compressibility effects preclude the emergence of a regime of self-similar instability growth independent of the initial conditions (ICs) by allowing for memory of the initial conditions to be retained in the mix-width at all times. With higher-dimensional blast waves, divergence restores the properties necessary for establishment of the self-similar state, but achieving it requires very high initial characteristic mode number and high Mach number for the incident blast wave. Initial conditions predicted by some recent stellar calculations are incompatible with self-similarity.     

Shock strengths in clumps impacted by winds of increasing power

We have performed spherically symmetric and axisymetric hydrodynamic simulations of wind–clump interactions in order to determine the conditions under which a wind, impacting upon a clump and increasing in power with time, drives a strong shock into the clump. If the wind ram pressure and the clump thermal pressure are comparable when the impact first occurs, then the wind ram pressure must increase on a time-scale markedly smaller than the sound-crossing time of the clump if it is to drive a shock that becomes strong at any point in the clump. We comment on the possible relevance of this result for the dynamics and chemistry of hot cores in regions of high-mass star formation.     

The cosmic rays of superhigh energies

The paper considers the generation mechanism of the relativistic particles of superhigh energies (10¹⁸ eV) in a plasma where the supersonic turbulence and the hydrodynamic shock waves occur. It is found that the conditions necessary for the formation of this turbulence are realized in supernovae shells during the period of the outburst. The estimations of the energy gain rate of the charged particles and comparison with their energy loss rate conditioned by synchrotron radiation and collisions with photons and nuclei show that in the actually determined conditions of shells in Crab and Cassiopeia nebulae, at the early stages of their expansion, acceleration surpasses deceleration. And finally, the estimations of the total number of superhigh energy particles generated during the flare are in agreement with the observed data.     

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.     

Basic Properties of Compressible MHD Turbulence: Implications for Molecular Clouds

Recent advances in understanding of the basic properties of compressible Magnetohydrodynamic (MHD) turbulence call for revisions of some of the generally accepted concepts. First, the MHD turbulence is not so messy as it is usually believed. In fact, the notion of strong nonlinear coupling of compressible and incompressible motions is not tenable. Alfven, slow and fast modes of MHD turbulence follow their own cascades and exhibit degrees of anisotropy consistent with theoretical expectations. Second, the fast decay of turbulence is not related to the compressibility of fluid. Rates of decay of compressible and incompressible motions are very similar. Third, the viscosity by neutrals does not suppress MHD turbulence in a partially ionized gas. Instead, MHD turbulence develops magnetic cascade at scales below the scale at which neutrals damp ordinary hydrodynamic motions. The implications of those changes of MHD turbulence paradigm for molecular clouds require further studies. Those studies can benefit from testing of theoretical predictions using new statistical techniques that utilize spectroscopic data. We briefly discuss advances in development of tools using which the statistics of turbulent velocity can be recovered from observations.     

Diffusive propagation of fast particles in the presence of a moving shock wave

Based on an analytical model, we determined the temporal dynamics of the spectral shape and spatial distribution of the particles that were impulsively (in time) injected with a specified spectrum in the vicinity of a moving plane shock front. We obtained a condition to determine the influence of the shock front on the particle propagation, where the spatial diffusion coefficient of the particles plays a major role. Diffusive shock acceleration is shown to strongly affect low-energy particles (the intensity maximum coincides spatially with the shock front; hard and soft spectral regions are formed in the spectrum) and weakly affect high-energy particles (the time at which the intensity reaches its maximum is well ahead of the shock arrival time; the spectral shape does not change). In events accompanied by a significant increase in the turbulence level, the influence of the shock front on high-energy particles can change from weak to strong. This change shows up in the spatial distribution and spectral shape of the particles. The dynamics of the particle intensity, calculated with the diffusion coefficients that were determined in accordance with the quasi-linear theory for measured turbulence levels, qualitatively corresponds to the observed solar energetic-particle intensity.     

Highly radiative shock experiments driven by GEKKO XII

In this paper, recent results obtained on highly radiative shocks generated in a xenon filled gas cell using the GEKKO XII laser facility are presented. Data show extremely high shock velocity (??150 km/s) never achieved before in gas. Preliminary analyses based on theoretical dimensionless numbers and numerical simulations suggest that these radiative shocks reach a new radiative regime where the radiative pressure plays a role in the dynamics and structure of the shock. A major effect observed is a strong anisotropic emission in the downstream gas. This unexpected feature is discussed and compared to available 2D radiation hydrodynamic simulations.     

Shock surfing acceleration

Analytical and numerical analysis identify shock surfing acceleration as an ideal pre-energization mechanism for the slow pick-up ions at quasiperpendicular shocks. After gaining sufficient energy by shock surfing, pick-up ions undergo diffusive acceleration to reach their observed energies. Energetic ions upstream of the cometary bow shock, acceleration of solar energetic particles by magnetosonic waves in corona, ion enhancement in interplanetary shocks, generation of anomalous cosmic rays from interstellar pick-up ions at the termination shock are some of the cases where shock surfing acceleration apply. Inclusion of the lower-hybrid wave turbulence into the laminar model of shock surfing can explain the preferential acceleration of heavier particles as observed by Voyager at the termination shock. At relativistic energies, unlimited acceleration of ions is theoretically possible; because for sufficiently strong shocks main limitation of the mechanism, caused by the escape of accelerated particles downstream of the shock during acceleration no longer exists.     

Reverse shock wave in relativistic explosions

The dynamical evolution of a relativistic explosion in a homogeneous medium is studied by means of a time-dependent, hydrodynamic code. When the expanding velocity of the shock front reduces to the sound velocity in the relativistic fluid, the reverse shock wave propagating inward through the expanding material is generated. The radius of the turning point of the reverse shock wave is proportional to the explosion energy and hardly depends on the mass of the explosion products. In the case of the non-relativistic explosion, the reverse shock wave is generated just after the free expansion stage. The radius of the turning point of the reverse shock wave is proportional to the mass of the explosion products and little depends on the explosion energy. In both cases of the non-relativistic and relativistic explosion, the reverse shock wave is strong in a spherical explosion and weak in a cylindrical one. The plane symmetric explosion does not generate the reverse shock wave.     

Turbulence induced additional deceleration in relativistic shock wave propagation: implications for gamma-ray burst

The late afterglow of gamma-ray burst is believed to be due to progressive deceleration of the forward shock wave driven by the gamma-ray burst ejecta propagating in the interstellar medium. We study the dynamic effect of interstellar turbulence on shock wave propagation. It is shown that the shock wave decelerates more quickly than previously assumed without the turbulence. As an observational consequence, an earlier jet break will appear in the light curve of the forward shock wave. The scatter of the jet-corrected energy release for gamma-ray burst, inferred from the jet-break, may be partly due to the physical uncertainties in the turbulence/shock wave interaction. This uncertainties also exist in two shell collisions in the well-known internal shock model proposed for gamma-ray burst prompt emission. The large scatters of known luminosity relations of gamma-ray burst may be intrinsic and thus gamma-ray burst is not a good standard candle. We also discuss the other implications.     

Subcritical dynamos in shear flows

Identifying generic physical mechanisms responsible for the generation of magnetic fields and turbulence in differentially rotating flows is fundamental to understand the dynamics of astrophysical objects such as accretion disks and stars. In this paper, we discuss the concept of subcritical dynamo action and its hydrodynamic analogue exemplified by the process of nonlinear transition to turbulence in non‐rotating wall‐bounded shear flows. To illustrate this idea, we describe some recent results on nonlinear hydrodynamic transition to turbulence and nonlinear dynamo action in rotating shear flows pertaining to the problem of turbulent angular momentum transport in accretion disks. We argue that this concept is very generic and should be applicable to many astrophysical problems involving a shear flow and non‐axisymmetric instabilities of shearinduced axisymmetric toroidal velocity or magnetic fields, such as Kelvin‐Helmholtz, magnetorotational, Tayler or global magnetoshear instabilities. In the light of several recent numerical results, we finally suggest that, similarly to a standard linear instability, subcritical MHD dynamo processes in high‐Reynolds number shear flows could act as a large‐scale driving mechanism of turbulent flows that would in turn generate an independent small‐scale dynamo. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Turbulence in fast-mode shocks as a triggering mechanism in a solar flare

If a solar flare originates from the dissipation of magnetic energy, available in abundance in a larger region, this dissipation must take place very rapidly. A local topological change in the magnetic field structure may be sufficient to start the dissipation process. Such a change in topology might be obtained by fast reconnection in a smaller region, such as e.g. in the Sweet-Parker model, as a result of current-driven microinstabilities.Among the candidates satisfying the requirements to obtain large enough currents, such as magnetically neutral or current sheets and MHD shocks, the latter are shown to be most probable. In a fast MHD shock the (thermal) results of turbulence do in fact destroy the conditions for turbulence. However, in this work we show numerically that the nonlinear steepening mechanism of such a shock is able to restore the driving current for a large range of parameters and over a long time. This is still true if the most difficult threshold for turbulence, being that for Langmuir turbulence, is to be achieved. The critical parameter, not only for the occurrence of turbulence but also for the restoration of the driving current, is the shock thickness.     

Turbulence and its parameterization in accretion discs

Accretion disc turbulence is investigated in the framework of the shearing box approximation. The turbulence is either driven by the magneto‐rotational instability or, in the non‐magnetic case, by an explicit and artificial forcing term in the momentum equation. Unlike the magnetic case, where most of the dissipation occurs in the disc corona, in the forced hydrodynamic case most of the dissipation occurs near the midplane. In the hydrodynamic case evidence is presented for the stochastic excitation of epicycles. When the vertical and radial epicyclic frequencies are different (modeling the properties around rotating black holes), the beat frequency between these two frequencies appear to show up as a peak in the temporal power spectrum in some cases. Finally, the full turbulent resistivity tensor is determined and it is found that, if the turbulence is driven by a forcing term, the signs of its off‐diagonal components are such that this effect would not be capable of dynamo action by the shear–current effect. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Turbulence in clusters of galaxies and X-ray line profiles

Large-scale bulk motions and hydrodynamic turbulence in the intergalactic gas that fills clusters of galaxies significantly broaden X-ray emission lines. For lines of heavy ions (primarily helium-like and hydrogen-like iron ions), the hydrodynamic broadening is appreciably larger than the thermal broadening. Since clusters of galaxies have a negligible optical depth for resonant scattering in the forbidden and intercombination lines of these ions, these lines are not additionally broadened. At the same time, they are very intense, which allows deviations of the spectrum from the Gaussian spectrum in the line wings to be investigated. The line shape proves to be an important indicator of bulk hydrodynamic processes. Doppler probing of turbulence becomes possible, because the cryogenic detectors of the X-ray observatories now ready for launch and being planned will have a high energy resolution (from 5 eV for ASTRO-E2 to 1–2 eV for Constellation-X and XEUS). We use the spectral representation of a Kolmogorov cascade in the inertial range to calculate the characteristic shapes of radiation lines. Significant deviations in the line profiles from the Gaussian profile (shape asymmetry, additional peaks, sharp breaks in the exponential tails) are expected for large-scale turbulence. The kinematic SZ effect and the X-ray line profiles carry different information about the hydrodynamic velocity distribution in clusters of galaxies and complement each other, allowing the redshift, the peculiar velocity of the cluster, and the bulk velocity dispersion to be separated.     

Parallel high β shocks and relaxation phenomena

The structure of collisionless shocks propagating parallel to the magnetic field is discussed in the case of a large ratio of plasma pressure to magnetic pressure. The theory makes use of the basic ideas of Kennel and Sagdeev and it is shown that their shock model is to be interpreted in terms of relaxation shocks. The calculations are based on a purely macroscopic set of equations including finite Larmor radius effects. The resulting shock structure is determined both in a quasilinear WKB-type approximation and through a direct numerical integration of the basic non-linear equations. The results from both methods agree fairly well, although the level of the turbulence is high. It is argued that strong parallel shocks have a double structure, where the main transition is followed by a broad relaxation wave. It is suggested that the magnetosheath should be considered as the relaxation zone of the Earth's bow shock.     

The influence of the Mach number on the stability of radiative shocks

We study the stability properties of hydrodynamic shocks with finite Mach numbers. The linear analysis supplements previous analyses which took the strong shock limit. We derive the linearized equations for a general specific heat ratio as well as temperature and density power-law cooling functions, corresponding to a range of conditions relevant to interstellar atomic and molecular cooling processes. Boundary conditions corresponding to a return to the upstream temperature  ( R = 1)  and to a cold wall  ( R = 0)  are investigated. We find that for Mach number   M > 5  , the strong shock overstability limits are not significantly modified. For   M < 3  , however, shocks are considerably more stable for most cases. In general, as the shock weakens, the critical values of the temperature power-law index (below which shocks are overstable) are reduced for the overtones more than for the fundamental, which signifies a change in basic behaviour. In the   R = 0  scenario, however, we find that the overstability regime and growth rate of the fundamental mode are increased when cooling is under local thermodynamic equilibrium. We provide a possible explanation for the results in terms of a stabilizing influence provided downstream but a destabilizing effect associated with the shock front. We conclude that the regime of overstability for interstellar atomic shocks is well represented by the strong shock limit unless the upstream gas is hot. Although molecular shocks can be overstable to overtones, the magnetic field provides a significant stabilizing influence.