Relativistic hydrodynamics of a free expansion and a shock wave in one-dimension

Dynamical evolution of a relativistic explosion resulting from a large amount of energy release in a homogenous medium is studied using the Khalatnikov equation describing relativistic, hydrodynamic, planar flow. The early phase of the explosion is idealized to two stages: a free expansion and a shock wave stage. By the hodograph transformation inverting the dependent and independent variables, the hydrodynamic equations for the relativistic flow are reduced to second-order linear equations in a velocity-enthalpy space and they are solved by the method of Laplace transformation. The propagation laws and flow structures of the relativistic expansion are obtained at each stage. In the free expansion stage, the flow with a sufficiently high sound velocity forms a thin shell of the energy density in the comoving frame at the front and accelerates the front. In the shock wave stage, the Lorentz factor of the shock front decreases logarithmically with time. The transition time from a free expansion to a shock wave stage suggests that the super-light expansion observed in extragalactic radio sources has no spherical geometry but must be confined to a narrow cone.     

Relativistic effects in radar detection of ionization fronts produced by ultra-high energy cosmic rays

We revisit the radar echo technique as an approach to detect ultra-high energy cosmic rays (UHECR). The UHECR extensive air showers generate disk-like ionization fronts propagating with a relativistic velocity and creating fast decaying plasma. We study the reflection of a radio wave, such as the one from a radar transmitter or commercial radio and TV station, from the relativistic ionization front. The reflected wave will be frequency upshifted due to the relativistic Doppler effect and propagate almost normally to the front due to relativistic aberration. The amplitude of the reflected wave depends strongly on the front velocity and parameters (density, collision frequency) of the plasma behind the front. We develop a theory that allows one to find the reflected wave. Using this theory and typical parameters of extensive air showers, we discuss the feasibility of UHECR detection.     

Numerical solutions of ideal two-fluid equations very closed to the event horizon of Schwarzschild black hole

The 3+1 formalism of Thorne, Price and MacDonald has been used to derive the linear two-fluid equations describing transverse and longitudinal waves propagating in the two-fluid ideal collisionless plasmas surrounding a Schwarzschild black hole. The plasma is assumed to be falling in radial direction toward the event horizon. The relativistic two-fluid equations have been reformulate, in analogy with the special relativistic formulation as explained in an earlier paper, to take account of relativistic effects due to the event horizon. Here a WKB approximation is used to derive the local dispersion relation for these waves and solved numerically for the wave number k.     

Heliographic longitude distribution of the flares associated with type III bursts observed at kilometric wavelengths

We have grouped observed type III solar bursts according to the discrete frequencies of observation in the kilometric wavelength range. For each group we have obtained the bursts' frequency of occurrence as a function of the heliographic longitude of the associated optical flares. We found that flares occurring east of a certain cutoff longitude do not produce bursts observable near the earth below a given frequency. The cutoff on the west is determined by observational limitation for flares beyond the limb. The mean longitude and the extreme eastern end of the longitude distribution both shift to the west as the radio frequency decreases. We interpret these findings in terms of radio wave propagation effects and curved trajectories of the bursts' exciter particles.     

Torsional oscillations of magnetized relativistic stars

Strong magnetic fields in relativistic stars can be a cause of crust fracturing, resulting in the excitation of global torsional oscillations. Such oscillations could become observable in gravitational waves or in high-energy radiation, thus becoming a tool for probing the equation of state of relativistic stars. As the eigenfrequency of torsional oscillation modes is affected by the presence of a strong magnetic field, we study torsional modes in magnetized relativistic stars. We derive the linearized perturbation equations that govern torsional oscillations coupled to the oscillations of a magnetic field, when variations in the metric are neglected (Cowling approximation). The oscillations are described by a single two-dimensional wave equation, which can be solved as a boundary-value problem to obtain eigenfrequencies. We find that, in the non-magnetized case, typical oscillation periods of the fundamental     torsional modes can be nearly a factor of 2 larger for relativistic stars than previously computed in the Newtonian limit. For magnetized stars, we show that the influence of the magnetic field is highly dependent on the assumed magnetic field configuration, and simple estimates obtained previously in the literature cannot be used for identifying normal modes observationally.     

Conditions for Propagation of Torsional Waves in Solar Magnetic Flux Tubes

Propagation of torsional waves along isothermal and initially-untwisted magnetic-flux tubes embedded in the solar atmosphere is studied analytically. Conditions for wave propagation along thin and wide magnetic-flux tubes are determined, and it is shown that the propagation along thin tubes is cutoff free; however, for wide tubes the propagation is affected by a cutoff frequency. A method to determine the cutoff frequency is presented and applied to a specific model of solar magnetic flux tubes. An interesting result is that the cutoff frequency is a local quantity in the model and that its value at a given height determines the frequency that torsional tube waves must have to propagate at this height.     

On the r-mode spectrum of relativistic stars in the low-frequency approximation

The axial modes for non-barotropic relativistic rotating neutron stars with uniform angular velocity are studied, using the slow-rotation formalism together with the low-frequency approximation, first investigated by Kojima. The time-independent form of the equations leads to a singular eigenvalue problem, which admits a continuous spectrum. We show that for     , it is nevertheless also possible to find discrete mode solutions (the r modes). However, under certain conditions related to the equation of state and the compactness of the stellar model, the eigenfrequency lies inside the continuous band and the associated velocity perturbation is divergent; hence these solutions have to be discarded as being unphysical. We corroborate our results by explicitly integrating the time-dependent equations. For stellar models admitting a physical r-mode solution, it can indeed be excited by arbitrary initial data. For models admitting only an unphysical mode solution, the evolutions do not show any tendency to oscillate with the respective frequency. For higher values of l it seems that in certain cases there are no mode solutions at all.     

Isothermal plasma wave properties of the Schwarzschild de-Sitter black hole in a Veselago medium

In this paper, we study wave properties of isothermal plasma for the Schwarzschild de-Sitter black hole in a Veselago medium. We use ADM 3+1 formalism to formulate general relativistic magnetohydrodynamical (GRMHD) equations for the Schwarzschild de-Sitter spacetime in Rindler coordinates. Further, Fourier analysis of the linearly perturbed GRMHD equations for the rotating (non-magnetized and magnetized) background is taken whose determinant leads to a dispersion relation. We investigate wave properties by using graphical representation of the wave vector, the refractive index, change in refractive index, phase and group velocities. Also, the modes of wave dispersion are explored. The results indicate the existence of the Veselago medium.     

A full-wave study of downward propagating ELF waves in the ionosphere: Ion cutoff whistlers and the low frequency cutoff of ELF noise

The downward propagation of ELF waves (100–700 Hz) in the ionosphere is studied by means of a generalised multiple-reflection full-wave method. It is shown that for the production of an ion cutoff whistler the incident wave-normal must point inwards (equatorwards) with respect to the vertical, the ion cutoff whistler conversion coefficient R_RL being a maximum when the reflected wave normal lies close to the geomagnetic field direction at the crossover level.For a low frequency cutoff of ELF noise to exist, the incident wave-normals at the crossover level must lie outside a ‘cone of penetration’ of ~40° semi-vertical angle, whose axis coincides with the geomagnetic field line. For propagation in the magnetic meridian plane, total reflection of downgoing whistlers is obtained either for large outward (poleward) incident angles, with reflection heights generally above the crossover level and possibly even above the gyrofrequency level, or else for inward (equatorward) wave-normal directions, in which case the reflection process usually occurs below the crossover level, and involves an R to L mode conversion on the downgoing path.Analysis of a scatter plot of the lower cutoff frequencies of ELF noise as a function of altitude and latitude shows that widely varying abundances must be postulated at all latitudes in order to explain the observations.     

Relativistic blast waves and synchrotron emission

Relativistic shocks can accelerate particles by the first-order Fermi mechanism; the particles then emit synchrotron emission in the post-shock gas. This process is of particular interest in the models used for the afterglow of gamma-ray bursts. In this paper we use recent results in the theory of particle acceleration at highly relativistic shocks to model the synchrotron emission in an evolving, inhomogeneous and highly relativistic flow. We have developed a numerical code that integrates the relativistic Euler equations for fluid dynamics with a general equation of state, together with a simple transport equation for the accelerated particles. We present tests of this code and, in addition, we use it to study the gamma-ray burst afterglow predicted by the fireball model, along with the hydrodynamics of a spherically-symmetric relativistic blast wave.
We find that, while broadly speaking the behaviour of the emission is similar to that already predicted with semi-analytic approaches, the detailed behaviour is somewhat different. The 'breaks' in the synchrotron spectrum behave differently with time, and the spectrum above the final break is harder than had previously been expected. These effects are due to the incorporation of the geometry of the (spherical) blast wave, along with relativistic beaming and adiabatic cooling of the energetic particles leading to a mix, in the observed spectrum, between recently injected 'uncooled' particles and the older 'cooled' population in different parts of the evolving, inhomogeneous flow.     

Equations of radiation gas dynamics in tetrad form for astrophysical applications

This paper deals with the representation of relativistic equations of gas dynamics with due regard to the general relativity theory effects in the form accepted and widely applied in the special relativity theory. With this purpose, a strict formal definition of a non-inertial co-moving reference frame without rotation is carried out on the basis of a tetrad formalism by use of the Fermi—Walker rules of transport of 4-frame. The equations of physical kinetics, relativistic collapse, Einstein's equations, equations of relatiivistic radiation gas dynamics for ideal and dissipative gases, Taub's equations for a shock wave, which allow for radiation and electron-positron pairs, are obtained in this reference frame. On the basis of the local Lorentz transformation and the Ricci rotation coefficients, these equations are written in the laboratory reference frame, in order to illustrate the fact that the general relativity effects can be simply taken into account in the equations having a form accepted in the special relativity theory.     

Generation of electromagnetic waves in the electron-positron plasma in the vicinity of a pulsar

The problem of the efficiency of the ion-synchrotron maser proposed by Hoshino and Arons is analyzed in a linear approximation. A hot, relativistic, electron-positron plasma penetrated by a relativistic ion beam is considered. At the front of the magnetosonic shock wave an electromagnetic wave is generated, which should be damped on positrons of the plasma. This should, in turn, result in synchrotron emission from energetic positrons in the high-frequency range, far above the natural frequencies of the plasma. It is shown that one must allow simultaneously for the conditions of resonance at a high harmonic of the ion-cyclotron frequency and at the fundamental of the electron-cyclotron frequency. Natural transverse waves are generated in the process, but within the framework of the linear theory there is no positron acceleration due to the kinetic energy of ions. Translated from Astrofizika, Vol. 43, No. 3, pp. 389-396, July–September, 2000.     

On Relativistic Equations of Motion of an Earth Satellite

For numerical integration of the geocentric equations of motion of Earth satellites in the general relativity framework one may choose now between rather simple equations involving in their relativistic dynamical part only the Earth-induced terms and very complicated equations taking into account the relativistic third-body action. However, it is possible quite easily to take into account the relativistic indirect third-body perturbations and to neglect much lesser direct third-body perturbations. Such approach is based on the use of the Newtonian third-body perturbations in geocentric variables with expressing them in the relativistic manner in terms of the barycentric arguments. Together with it, to extend the known results for the spheroid model of the Earth, the Earth-induced terms are treated in great detail by including the non-spin part of the Earth vector-potential and the Earth triaxial non-sphericity.This revised version was published online in October 2005 with corrections to the Cover Date.     

Effects of plasma rotation on alfvén solitons in pulsar magnetospheres

Nonlinear Alfvén wave in a hot rotating and strongly magnetized electron-positron plasma is considered. Using relativistic two fluid equations, the dispersion relation for Alfvén wave in the rotating plasma is obtained. Large amplitude Alfvén solitons are found to exist in the rotating pulsar plasma. Rotational effects on solitons are discussed.     

Frequency shift of space-charge waves in a relativistic electron or positron beam

Nonlinear frequency shift of space-charge waves in a relativistic electron or positron beam is analyzed. The frequency shift is shown to be a function of the wave amplitude. It is suggested that the frequency shift of beam space-charge waves may be a saturation mechanism for astrophysical free-electron lasers.     

Reflection Properties of Gravito-MHD Waves in an Inhomogeneous Horizontal Magnetic Field

We derive the dispersion equation for gravito-magnetohydrodynamical (MHD) waves in an isothermal, gravitationally stratified plasma with a horizontal inhomogeneous magnetic field. Sound and Alfvén speeds are constant. Under these conditions, it is possible to derive analytically the equations for gravito-MHD waves. The high values of the viscous and magnetic Reynolds numbers in the solar atmosphere imply that the dissipative terms in the MHD equations are negligible, except in layers around the positions where the frequency of the MHD wave equals the local Alfvén or slow wave frequency. Outside these layers the MHD waves are accurately described by the equations of ideal MHD. We consider waves that propagate energy upward in the atmosphere. For the plane boundary, z=0, between two isothermal plasma regions with horizontal but different magnetic fields, we discuss the boundary conditions and derive the equations for the reflection and transmission coefficients. In the simpler case of a gravitationally stratified plasma without magnetic field, these coefficients describe the reflection and transmission properties of gravito-acoustic waves.     

Hot plasma waves in Veselago medium around Reissner-Nordström black hole

We investigate the general relativistic magnetohydronadynamic (GRMHD) equations for hot plasmas in a Veselago medium around the Reissner-Nordström (RN) black hole. Using the 3+1 formalisms of spacetime, we write the GRMHD equations and perturb them linearly. These are then Fourier analyzed for the magnetized and nonmagnetized plasmas in rotating and nonrotating backgrounds. We derive dispersion relations and analyze the wave properties by the graphs of wave vector, refractive index and change in refractive. The results confirm the presence of Veselago medium for rotating magnetized/nonmagnetized and nonrotating nonmagnetized plasmas.     

Modeling of high-frequency variability in X-ray binaries with black holes

The properties of the aperiodic variability in X-ray binaries with black holes are considered. The power spectra of the luminosity variability for a flat accretion disk that is an emission source with a powerlaw energy spectrum have been modeled. At low frequencies the derived power spectrum has the form of a power law with a slope ? ≈ ?1 and a cutoff at a frequency corresponding to the characteristic frequency of fluctuations at the inner disk edge; at higher frequencies the power spectrum has a complex form. The high-frequency variability is suppressed due to the arrival time delays of photons emerged in different parts of the disk. The presence of azimuthal accretion rate fluctuations in the disk and the disk surface brightness nonuniformity in the observer’s imaginary plane caused by the relativistic effects give rise to an additional variability component at frequencies ～ 200 Hz.     

A possible mechanism of jet formation in the nuclei of radio galaxies

A hypothesis is being put forward that the formation of jets in the nuclei of radio galaxies is due to a high-speed energy excretion (explosion) in the accretion disk around a massive black hole. The explosion can be induced, for example, by a fall of the star into the black hole. For the accretion disk featuring an exponential high-density distribution, an asymmetrical explosion can be obtained: the shock front moves in the direction of decreasing the density accelerately and achieves the relativistic velocity swiftly, carrying away the most fraction of the explosion energy. Radio emission of the jet involves synchrotron radiation of relativistic electrons which are accelerated by such shock wave in the magnetic field driven up by the shock front.     

射电喷流中相对论电子束激发的不稳定性

本文作者用相对论电子束在等离子体中运动时的色散关系讨论了纵向传播的波模的稳定性，发现静电Ｌａｎｇｍｕｉｒ波和Ａｌｆｖｅｎ波是不稳定的，并计算了其增长率，而高频电磁模和硝声模是稳定的。相对论电子束激发的Ｌａｎｇｍｕｉｒ波和Ａｌｆｖｅｎ波的不稳定性可用于解释射电喷流中相间的热斑、粒子再加速、辐射机制以及能量传输问题。