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.     

The physics of particle acceleration by collisionless shocks

Using analytic theory, test-particle simulations, and self-consistent hybrid simulations, we show that quasi-perpendicular shocks—those which propagate nearly perpendicular to the upstream magnetic field—accelerate particles directly out of the incident thermal population to energies much higher than the upstream ram energy of the plasma. It has already been established that quasi-parallel shocks—those which propagate nearly in the same direction as the upstream magnetic field—efficiently accelerate particles directly out of the incident thermal population; however, this has not yet been established for quasi-perpendicular shocks. Our results can be understood within the framework of the diffusive shock acceleration theory. We find that the accelerated-particle spectrum obtained from a more-general self-consistent hybrid plasma simulation are quantitatively consistent with a less-sophisticated test-particle simulation. The implications of this are discussed.     

Trajectories of ions specularly reflected from non-planar collisionless shocks

An important contribution to the thermalization of the solar wind ions at the Earth's bow shock for high Mach numbers comes from the reflection of a fraction of these ions from the shock. Previous studies have examined the trajectories of the reflected ions assuming the shock to be an infinite plane. In this paper a model is developed to describe the trajectories of particles after reflection for a variety of shock geometries. Of particular interest are the initial conditions which allow the particle to return to the shock with a greater normal velocity than at first encounter, or to return to the shock at all. The effects of the magnetic field direction and the curvature of the shock on particle trajectories are discussed for cylindrical and spherical shock geometries and compared to those for a planar shock.     

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 electron–cyclotron maser for astrophysical application

The electron–cyclotron maser is a process that generates coherent radiation from plasma. In the last two decades, it has gained increasing attention as a dominant mechanism of producing high-power radiation in natural high-temperature magnetized plasmas. Originally proposed as a somewhat exotic idea and subsequently applied to include non-relativistic plasmas, the electron–cyclotron maser was considered as an alternative to turbulent though coherent wave–wave interaction which results in radio emission. However, when it was recognized that weak relativistic corrections had to be taken into account in the radiation process, the importance of the electron–cyclotron maser rose to the recognition it deserves. Here we review the theory and application of the electron–cyclotron maser to the directly accessible plasmas in our immediate terrestrial and planetary environments. In situ access to the radiating plasmas has turned out to be crucial in identifying the conditions under which the electron–cyclotron maser mechanism is working. Under extreme astrophysical conditions, radiation from plasmas may provide a major energy loss; however, for generating the powerful radiation in which the electron–cyclotron maser mechanism is capable, the plasma must be in a state where release of susceptible amounts of energy in the form of radiation is favorable. Such conditions are realized when the plasma is unable to digest the available free energy that is imposed from outside and stored in its particle distribution. The lack of dissipative processes is a common property of collisionless plasmas. When, in addition, the plasma density becomes so low that the amount of free energy per particle is large, direct emission becomes favorable. This can be expressed as negative absorption of the plasma which, like in conventional masers, leads to coherent emission even though no quantum correlations are involved. The physical basis of this formal analogy between a quantum maser and the electron–cyclotron maser is that in the electron–cyclotron maser the free-space radiation modes can be amplified directly. Several models have been proposed for such a process. The most famous one is the so-called loss-cone maser. However, as argued in this review, the loss-cone maser is rather inefficient. Available in situ measurements indicate that the loss-cone maser plays only a minor role. Instead, the main source for any strong electron–cyclotron maser is found in the presence of a magnetic-field-aligned electric potential drop which has several effects: (1) it dilutes the local plasma to such an extent that the plasma enters the regime in which the electron–cyclotron maser becomes effective; (2) it generates energetic relativistic electron beams and field-aligned currents; (3) it deforms, together with the magnetic mirror force, the electron distribution function, thereby mimicking a high energy level sufficiently far above the Maxwellian ground state of an equilibrium plasma; (4) it favors emission in the free-space RX mode in a direction roughly perpendicular to the ambient magnetic field; (5) this emission is the most intense, since it implies the coherent resonant contribution of a maximum number of electrons in the distribution function to the radiation (i.e., to the generation of negative absorption); (6) it generates a large number of electron holes via the two-stream instability, and ion holes via the current-driven ion-acoustic instability which manifest themselves as subtle fine structures moving across the radiation spectrum and being typical for the electron–cyclotron maser emission process. These fine structures can thus be taken as the ultimate identifier of the electron–cyclotron maser. The auroral kilometric radiation of Earth is taken here as the paradigm for other manifestations of intense radio emissions such as the radiation from other planets in the solar system, from exoplanets, the Sun and other astrophysical objects.     

Inhibition of degeneracy by intense magnetic fields: Derivation and astrophysical application

Strong magnetic fields inhibit degeneracy in Fermi gases, that is, they postpone degeneracy to higher densities or lower temperatures. We derive this principle, virtually unknown in the physical and astrophysical literature, for the case of an ideal Dirac electron gas. Its possible importance in astrophysics is due to the fact that the equations of state of Fermi gases at given density and temperature can be qualitatively changed by this degeneracy-inhibition by strong fields. All astrophysical work with strong fields up to the present has used the field-free equations of state and the usual MHD approximation: permeability 1. Their interest was focussed on the effects of a strong Lorentz force term. We consider an application to hypothetical degenerate stellar objects with arbitrarily strong fields to see what effects the changed equations of state would lead to. One result is that the luminosity-temperature relation of the star is changed: the luminosity is reduced for given mass and interior temperature.     

Vortical mechanism for generation of astrophysical jets

A vortical mechanism for generation of astrophysical jets is proposed based on exact solutions of the hydrodynamic equations with a generalized Rankine vortex. It is shown that the development of a Rankine vortex in the polar layer of a rotating gravitating body creates longitudinal fluxes of matter that converge toward the vortex trunk, providing an exponential growth in the angular rotation velocity of the trunk and a pressure drop on its axis. The increased rotational velocity of the vortex trunk and the on-axis pressure drop cease when the discontinuity in the azimuthal velocity at the surface of the trunk reaches the sound speed. During this time, ever deeper layers of the gravitating body are brought into the vortical motion, while the longitudinal velocity of the flow along the vortex trunk builds up, producing jet outflows of mass from its surface. The resulting vortices are essentially dissipationless. Dedicated to the 100-th birthday of Academician V. A. Ambartsumyan __________ Translated from Astrofizika, Vol. 51, No. 2, pp. 201–218 (May 2008).     

Polyatomic molecules,molecular ions,and radicals of astrophysical interest,II

This paper has been devoted to a basic molecular studies of polyatomics. A critical analysis of the 70 available references in literature has been made to select 37 polyatomic molecules, molecular ions, and radicals containing six, seven, eight, nine, ten, eleven, twelve, and thirteen atoms of astrophysical significance. The results have been arranged in a text-cum-tabular form. The compilation contains various information for each molecule, such as the spectral region, transition levels, astrophysical objects where the respective molecules have been detected (say, comet, meteorite, Sun, planet, star, interstellar matter, interstellar cloud, molecular cloud, interstellar space, Galaxy, etc.). Two-hundred fourteen new polyatomic molecules (containing 6, 7, 8, 9, and 10 atoms) of astrophysical significance have also been listed.Astrophysics and Space Science Review Paper II.     

Polyatomic molecules,molecular ions,and radicals of astrophysical interest,i

This paper has been devoted to basic molecular studies of polyatomics. A critical analysis of the 356 available references in literature has been made to select 98 polyatomic molecules, molecular ions, and radicals containing three, four, and five atoms of astrophysical significance. The results have been arranged in a text-cum-tabular form. The compilation contains various information for each molecule, such as the spectral region, transition levels, astrophysical objects, where the respective molecules have been detected (say, comet, meteorite, Sun, planet, star, interstellar matter, interstellar cloud, molecular cloud, interstellar space, Galaxy, etc.).A few important areas of active research in laboratory astrophysics have also been identified in this article: laboratory astrophysics, molecular cloud chemistry, isotopic abundance, planetary and cometary atmospheres through satellites. Seventy-five new polyatomic molecules (containing three, four, and five atoms) of astrophysical significance have also been listed.Astrophysics and Space Science Review Paper I     

Autoionization rate coefficients for some ions of astrophysical interest

Autoionization rate coefficients for some quadruply and quintuply ionized atoms have been computed in the temperature range 10⁵–10⁸ K. Typical temperature dependence has been found and simple expressions are given for their quick estimation.     

Magnetic reconnection acceleration of astrophysical jets for different jet geometries

The acceleration mechanisms of relativistic jets are of great importance for understanding various astrophysical phenomena such as gamma-ray bursts,active galactic nuclei and microquasars.One of the most popular scenarios is that the jets are initially Poynting-flux dominated and succumb to magnetohydrodynamic instability leading to magnetic reconnections.We suggest that the reconnection timescale and efficiency could strongly depend on the geometry of the jet,which determines the length scale on which the orientations of the field lines change.In contrast to a usuallyassumed conical jet,the acceleration of a collimated jet can be found to be more rapid and efficient(i.e.a much more highly saturated Lorentz factor can be reached)while the jets with lateral expansion show the opposite behavior.The shape of the jet could be formed due to the lateral squeezing on the jet by the stellar envelope of a collapsing massive star or the interaction of the jet with stellar winds.     

Undamped oscillations of collisionless stellar systems: Spheres,spheroids and discs

The collisionless Boltzmann equation governing self-gravitating systems such as galaxies has recently been shown to admit exact oscillating solutions with planar and spherical symmetry. The relation of the spherically symmetric solutions to the Virial theorem, as well as generalizations to non-uniform spheres, uniform spheroids and discs form the subject of this paper. These models generalize known families of static solutions. The case of the spheroid is worked out in some detail. Quasiperiodic as well as chaotic time variation of the two axes is demonstrated by studying the surface of section for the associated Hamiltonian system with two degrees of freedom. The relation to earlier work and possible implications for the general problem of collisionless relaxation in self gravitating systems are also discussed     

A quantitative model of coherent,stimulated emission in astrophysical jets

On the basis of issues raised by observations of BL Lac objects and the qualitative jet model proposed by Bakeret al. in 1988, we have been led to consider the quantitative role of coherent, stimulated emission in jets and construct a new jet model of blazars in which a relativistic electron beam with an axial symmetric, power-law distribution is injected from the central engine into the jet plasma. We study quantitatively the synchrotron emission of the relativistic electron beams. Using the weak turbulent theory of plasma, we discuss the interaction between relativistic electron beams and jet plasma, and the roles of stimulated emission. The main results are:

1. The synchrotron emission increases sensitively with the increase of the angle between the direction of the beam and the magnetic field. When the direction of the beam is vertical to the magnetic field, the synchrotron emission reaches its maximum, i.e. the emitted waves are beamed in the direction of the jet axis. We suggest that radio selected BL Lac objects belong to this extreme classification.
2. The synchrotron emission of the relativistic beam increases rapidly with the increase of the Lorentz factor of the relativistic electron,γ, whenγ ≤ 22.5, then decreases rapidly with increase ofγ.
3. The stimulated emission also increases with increasing Lorentz factorγ of the relativistic electrons whenγ ≤ 35 and then decreases with the increasingγ. The maximum stimulated emission and the maximum synchrotron emission occur at different frequencies. Stimulated emission is probably very important and reasonable flare mechanism in blazars.
4. The rapid polarization position angle (PA) swings may arise from the interaction between the relativistic electron beam and the turbulent plasma.

     

Transition probability parameters for the band systems G, H and I-B of astrophysical molecule PO

The transition probability parameters, Franck – Condon factors and r-centroids, have been evaluated by the more reliable numerical integration procedure for the bands of G, H and I-B systems of astrophysical molecule PO, using a suitable potential. This revised version was published online in July 2006 with corrections to the Cover Date.     

GRB 080319B: evidence for relativistic turbulence, not internal shocks

We show that the excellent optical and gamma-ray data available for GRB 080319B rule out the internal shock model for the prompt emission. The data instead point to a model in which the observed radiation was produced close to the deceleration radius  (∼10¹⁷ cm)  by a turbulent source with random Lorentz factors of ∼10 in the comoving frame. The optical radiation was produced by synchrotron emission from relativistic electrons, and the gamma-rays by inverse-Compton scattering of the synchrotron photons. The gamma-ray emission originated both in eddies and in an inter-eddy medium, whereas the optical radiation was mostly from the latter. Therefore, the gamma-ray emission was highly variable whereas the optical was much less variable. The model explains all the observed features in the prompt optical and gamma-ray data of GRB 080319B. We are unable to determine with confidence whether the energy of the explosion was carried outwards primarily by particles (kinetic energy) or magnetic fields. Consequently, we cannot tell whether the turbulent medium was located in the reverse shock (we can rule out the forward shock) or in a Poynting-dominated jet.