Resolved shocks in clumpy media

We study the structure of shocks in clumpy media, using a multifluid formalism. As expected, shocks broaden as they weaken: for sufficiently weak shocks, no viscous subshock appears in the structure. This has significant implications for the survival of dense clouds in regions overrun by shocks in a wide range of astrophysical circumstances, from planetary nebulae to the nuclei of starburst galaxies.     

Anisotropic radiation transfer in dispersive media

Equations for radiation, scattered anisotropically from dispersive media are obtained for general boundary conditions. The Padé approximant technique is used to calculate the reflection coefficients for these media. Numerical results are given for diffuse reflected boundary condition.     

Radiation transfer in inhomogeneous dispersive media

Equations for the angular density of radiation, reflected and transmitted intensities associated with radiation scattered by inhomogeneous dispersive media are obtained. The Padé approximant technique is used to calculate these intensities in inhomogeneous and homogeneous media. The results for the [0/1] Padé approximant lead to numerical results that compared with the exact results.     

Angular radiation transfer in inhomogeneous dispersive media

The equation of radiative transfer for an inhomogenous dispersive finite medium subject to general boundary conditions is solved. The Padé approximation technique is used to calculate the angular distribution of radiation. Numerical results for the [0/1] Padé approximant lead to numerical results that compared with the exact results.     

Magnetosonic rogons in electron-ion plasma

Magnetosonic rogue waves (rogons) are investigated in an electron-ion plasma by deriving the nonlinear Schrödinger (NLS) equation for low frequency limit. The first- and second-order rogue wave solutions of the NLS equation are obtained analytically and examined numerically. It is found that for dense plasma and stronger magnetic field the nonlinearity decreases, which causes the rogon amplitude becomes shorter. However, the electron temperature pumping more energy to the background waves which are sucked to create rogue waves with taller amplitudes.     

Magnetosonic cylindrical soliton in electron-positron-ion plasma

Solutions in the form of cylindrical magnetosonic solitons of compression and rarefaction were obtained within the scope of the three-species electromagnetic gas-dynamic model of an electron-positron-ion plasma. These solutions can describe formation of cylindrical structures in accretion disks and jets in the vicinity of compact astrophysical objects.     

Magnetosonic waves in structured atmospheres with steady flows

The magnetosonic modes of magnetic plasma structures in the solar atmosphere are considered taking into account steady flows of plasma in the internal and external media and using a slab geometry. The investigation brings nearer the theory of magnetosonic waveguides, in such structures as coronal loops and photospheric flux tubes, to realistic conditions of the solar atmosphere. The general dispersion relation for the magnetosonic modes of a magnetic slab in magnetic surroundings is derived, allowing for field-aligned steady flows in either region. It is shown that flows change both qualitatively and quantitatively the characteristics of magnetosonic modes. The flow may lead to the appearance of a new type of trapped mode, namelybackward waves. These waves are the usual slab modes propagating in the direction opposite to the internal flow, but advected with the flow. The disappearance of some modes due to the flow is also demonstrated.The results are applied to coronal and photospheric magnetic structures. In coronal loops, the appearance of backward slow body waves or the disappearance of slow body waves, depending upon the direction of propagation, is possible if the flow speed exceeds the internal sound speed ( 300 km s^–1). In photospheric tubes, the disappearance of fast surface and slow body waves may be caused by an external downdraught of about 3 km s^–1.     

Magnetosonic waveguide model of solar wind flow tubes

We consider solar wind flow tubes as a magnetosonic wave-guide. Assuming a symmetric expansion in edges of slab-modelled wave-guide, we study the propagation characteristics of magnetosonic wave in the solar wind flow tubes. We present the preliminary results and discuss their implications.     

Padé approximant calculations for dispersive,isotropic scattering,homogeneous media

Exact relations for radiation heat flux at the boundaries of a slab with diffusely reflecting boundary conditions and internal source are obtained in terms of the reflection and transmission coefficients of a source free slab with isotropic boundary conditions. The integral equation defining the radiation heat flux contains explicitly the internal source. So, the particular solution for radiative transfer equation is not required. Available exact values for albedos give exact values of radiation heat flux. Padé approximant technique is used to obtain numerical values for homogenous media.     

Numerical Simulations of Impulsively Generated Magnetosonic Waves in a Coronal Loop

We consider impulsively excited magnetosonic waves in a highly magnetized coronal loop that is approximated by a straight plasma slab of enhanced mass density. Numerical results reveal that wavelet spectra of time signatures of these waves possess characteristic shapes that depend on the position of the initial pulse: in the case of a pulse launched inside the slab, these spectra are of a tadpole shape, while for a pulse excited in the ambient medium these spectra display more complex structures with branches of long and short-period waves. These short period oscillations correspond to waves that are trapped inside the slab, and the long-period oscillations are associated with waves that propagate through the ambient medium and reach the detection point. These findings are compatible with recent theoretical studies and observations by the solar eclipse coronal imaging system (SECIS).     

Alfvén-Jeans and Magnetosonic Modes in Multispecies Self-Gravitating Dusty Plasmas

Perpendicularly propagating electromagnetic waves in magnetized, multispecies, self-gravitating dusty plasmas are investigated in terms of their wave dispersion properties as well as with respect to their susceptibility to gravitational collapse. In particular, waves on the ordinary as well as extraordinary mode branches are considered. Within the one-dimensional propagation model employed, all modes except the ordinary mode produce density perturbations that can be unstable to gravitational collapse. The wavelengths that are unstable are comparable to the well-known Jeans length for a neutral gas/dust, but there are interesting modifications due to the presence of a magnetic field and charged particles. Furthermore, the effects of the gravitational coupling of a multicomponent plasma to a neutral dust are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Particle acceleration in shocks

The mechanism of particle acceleration by shocks is reviewed, and the resulting modifications of the shock structure contrasted with those which occur in molecular shocks with magnetic precursors. The danger associated with the use of steady models is emphasised and the applicability of the theory to cosmic ray acceleration in supernova remnants briefly discussed.     

Circumstellar shocks

The presence of shocks in a wide variety of circumstellar phenomena will be illustrated and discussed.     

Alfvén Wave Phase Mixing as a Source of Fast Magnetosonic Waves

The nonlinear excitation of fast magnetosonic waves by phase mixing Alfvén waves in a cold plasma with a smooth inhomogeneity of density across a uniform magnetic field is considered. If initially fast waves are absent from the system, then nonlinearity leads to their excitation by transversal gradients in the Alfvén wave. The efficiency of the nonlinear Alfvén–fast magnetosonic wave coupling is strongly increased by the inhomogeneity of the medium. The fast waves, permanently generated by Alfvén wave phase mixing, are refracted from the region with transversal gradients of the Alfvén speed. This nonlinear process suggests a mechanism of indirect plasma heating by phase mixing through the excitation of obliquely propagating fast waves.     

Particle acceleration in supernova-remnant shocks

It has been known for over 50 years that the radio emission from shell supernova remnants (SNRs) indicates the presence of electrons with energies in the GeV range emitting synchrotron radiation. The discovery of nonthermal X-ray emission from supernova remnants is now 30 years old, and its interpretation as the extension of the radio synchrotron spectrum requires electrons with energies of up to 100 TeV. SNRs are now detected at GeV and TeV photon energies as well. Strong suggestions of the presence of energetic ions exist, but conclusive evidence remains elusive. Several arguments suggest that magnetic fields in SNRs are amplified by orders of magnitude from their values in the ambient interstellar medium. Supernova remnants are thus an excellent laboratory in which to study processes taking place in very high Mach-number shocks. I review the observations of high-energy emission from SNRs, and the theoretical framework in which those observations are interpreted.     

Sputtering of grains in C-type shocks

Sputtering yields are reported for the release of Mg, Fe, Si and O under impact of He, C, O, Si and Fe on grain material composed of Mg- and Fe-bearing silicates. The yields were derived using the trim code, which simulates the results of the transport of ions in matter by means of classical Monte Carlo techniques. The energetics of the sputtering process are a key factor in the sputtering calculations, and so detailed determinations have been made of the energy with which atoms are bound to the lattice, using solid-state simulation programs. The probability of ejection of an atom is computed at a given energy, for a number of angles of incidence, and integrated to obtain the mean yield at that energy. These numerical results are then fitted with a simple function of energy for convenience in subsequent applications.
A grid of C-type shock models has been computed, using our new sputtering yields, for pre-shock densities in the range 10⁴ n _H n (H)+2 n (H₂)10⁶ cm⁻³ and shock speeds 20 v _s45 km s⁻¹. Sputtered fractions can be high, exceeding 50 per cent for shock speeds in excess of approximately 40 km s⁻¹. The column densities of Si and SiO were also computed, for comparison with observations.     

Continuum-driven shocks in active galactic nuclei

In this paper, we extend the study of instabilities in flows driven by the radiation pressure of an ionizing continuum to flows that are not plane parallel. It is well known that the plane-parallel instability leads eventually to the formation of continuum-driven shocks backed by a sonic transition. If these structures are thin, we find that they are unstable to a corrugation mode, and evolve to form sharp-peaked triangular profiles. Once this has occurred, the thin-shock approximation is no longer valid.
We study the further development of the shocks by numerical hydrodynamic simulations. The flow tends to break up into numerous discrete bow-shaped components. The speed of these components through the upstream material is almost constant. As a result, the maximal velocity of radiatively driven shocks through the upstream gas may be determined by instabilities rather than by other physical effects. Interactions between gas in the wings of neighbouring bowshocks can, however, form subsequent generations of bowshocks that are faster and more acute than their predecessors.
One likely location where continuum-driven shocks may occur is in the broad-line regions of active nuclei. We discuss the application of our results to such flows.     

Molecular shocks in star forming regions

The role of excited molecular hydrogen as a powerful observational tool is examined in the context of shock phenomena in molecular clouds, particularly in star forming regions. Conclusions that may be drawn from line intensities and line profiles, and the properties of J and C shocks in a bow shock structure are discussed.     

Fundamentals of collisionless shocks for astrophysical application, 2. Relativistic shocks

In this concise review of the recent developments in relativistic shock theory in the Universe we restrict ourselves to shocks that do not exhibit quantum effects. On the other hand, emphasis is given to the formation of shocks under both non-magnetised and magnetised conditions. We only briefly discuss particle acceleration in relativistic shocks where much of the results are still preliminary. Analytical theory is rather limited in predicting the real shock structure. Kinetic instability theory is briefed including its predictions and limitations. A recent self-similar relativistic shock theory is described which predicts the average long-term shock behaviour to be magnetised and to cause reasonable power-law distributions for energetic particles. The main focus in this review is on numerical experiments on highly relativistic shocks in (i) pair and (ii) electron-nucleon plasmas and their limitations. These simulations do not validate all predictions of analytic and self-similar theory and so far they do not solve the injection problem and the self-modification by self-generated cosmic rays. The main results of the numerical experiments discussed in this review are: (i) a confirmation of shock evolution in non-magnetised relativistic plasma in 3D due to either the lepton-Weibel instability (in pair plasmas) or to the ion-Weibel instability; (ii) the sensitive dependence of shock formation on upstream magnetisation which causes suppression of Weibel modes for large upstream magnetisation ratios σ>10⁻³; (iii) the sensitive dependence of particle dynamics on the upstream magnetic inclination angle θ _Bn , where particles of θ _Bn >34° cannot escape upstream, leading to the distinction between ‘subluminal’ and ‘superluminal’ shocks; (iv) particles in ultra-relativistic shocks can hardly overturn the shock and escape to upstream; they may oscillate around the shock ramp for a long time, so to speak ‘surfing it’ and thereby becoming accelerated by a kind of SDA; (v) these particles form a power-law tail on the downstream distribution; their limitations are pointed out; (vi) recently developed methods permit the calculation of the radiation spectra emitted by the downstream high-energy particles; (vii) the Weibel-generated downstream magnetic fields form large-amplitude vortices which could be advected by the downstream flow to large distances from the shock and possibly contribute to an extended strong field region; (viii) if cosmic rays are included, Bell-like modes can generate upstream magnetic turbulence at short and, by diffusive re-coupling, also long wavelengths in nearly parallel magnetic field shocks; (ix) advection of such large-amplitude waves should cause periodic reformation of the quasi-parallel shock and eject large-amplitude magnetic field vortices downstream where they contribute to turbulence and to maintaining an extended region of large magnetic fields.