V. S. Beskin

Theory of the radio emission of pulsars

A consistent theory of excitation, stabilization, and propagation of electromagnetic oscillations in a relativistic one-dimensional electron-positron plasma flowing along curved magnetic field lines is presented. It is shown that in such a medium which is typical of the magnetosphere of a neutron star there exist unstable natural modes of oscillations. Nonlinear saturation of the instability leads to an effective energy conversion into transverse oscillations capable of leaving the magnetosphere of a pulsar. The polarization spectrum and the directivity pattern of generated radiation are determined. A comparison with observations has shown that the theory makes it possible to explain practically all the basic characteristics of observed pulsar radio emission.

Spin-down of pulsars by the current: Comparison of theory with observations

Observational data are analysed on the basis of pulsar magnetosphere theory and the Ruderman-Sutherland plasma generation mechanism. The results of theory and experiment are shown to be in good agreement. The existence of a special group of long-lived, weakly-radiating fast (the periodP≃0.1–0.4 s) and superfast (P≲0.01) pulsars is predicted.

Two-dimensional structure of thin transonic discs: Theory and observational manifestations

We study the two-dimensional structure of thin transonic accretion discs in the vicinity of black holes. We use the hydrodynamical version of the Grad-Shafranov equation and focus on the region inside the marginally stable orbit (MSO), r < rms. We show that all components of the dynamical force in the disc become significant near the sonic surface and especially important in the supersonic region. Under certain conditions, the disc structure is shown to be far from radial, and we review the affected disc properties, in particular the role of the critical condition at the sonic surface: it determines neither the accretion rate nor the angular momentum in the accretion disc. Finally, we present a simple model explaining quasi-periodical oscillations that have been observed in the infrared and X-ray radiation of the Galactic Centre.

Giant dark matter-neutron star halo and the nature of gamma bursts

Abstract It is shown that dark matter forms a halo around the galaxy. The size of the halo and the moment of its formation are respectively estimated to be R0=300−400 kpc and Z0=5−7. The same halo is formed by relic neutron stars (RNS) occuring in the protogalaxy as a result of supernova bursts which cause a change in the original chemical composition. The second component of the neutron stars, which were born in the galactic disk and were pulsars at the early stage of their evolution, occurs much later. The statistic distribution of γ-bursts determined by both neutron-star components is shown to be in good agreement with observations. A method of direct verification of the model is proposed.

Theory of radio emission from pulsars (review)

The authors construct mathematical formulations for the radio emission of pulsars with rotating neutron stars from the standpoint of simulation of magnetospheric plasmas and the production and interaction of photons and electron-positron pairs. Equations are derived for the dielectric permittivity and also the electrodynamic behavior of a relativistic electron-positron plasma in a curvilinear magnetic field. Wave propagation, dispersion relations, and hydrodynamic instabilities are included in the models.

Force-Free Approximation — the Black Hole Magnetosphere

This chapter mainly deals with the magnetosphere structure of supermassive black holes for which the magnetic fields are of greater importance than for galactic solar mass black holes. Therefore, it is advisable to discuss the problems of the magnetic field generation in accretion disks in this chapter. We also briefly discuss the effect of the magnetic field on the disk accretion and matter outflow processes. Since the black hole itself cannot have a self-magnetic field (so-called ‘‘no hair’’ theorem), the large-scale magnetic field in the vicinity of the black hole can be generated only in the accretion disk. The missing link that helps one understand the energy release mechanism, which effectively transfers the energy from the rotating black hole and/or the inner parts of the disk to the active regions, is, in most cases, exactly associated with this regular magnetic field and the collimation mechanism responsible for the jet formation. In other words, to explain the galactic nuclei activity we use the pulsar idea of a unipolar inductor, the work of which is just provided by the regular poloidal magnetic field, the central object rotation (giving rise to the induction electric field E), and the longitudinal electric current (giving rise to the toroidal magnetic field B φ). Within this model, the energy flux, as in the case of the radio pulsar magnetosphere, is fully connected with the electromagnetic energy flux, and the jet formation is, ultimately, due to the known property of the parallel current attraction. Thus, the main constituent elements of the central engine are a supermassive black hole, the accretion disk, and the regular magnetic field. On the basis of this model, the physical nature of the Blandford–Znajek mechanism is discussed in detail. Finally, the exact analytical solutions obtained by the force-free approximation are discussed.

Hydrodynamical Limit — Classical Problems of Accretion and Ejection

There are several reasons why it is useful to start from the pure hydrodynamical case. First of all, the hydrodynamical version of the Grad–Shafranov equation is not as popular as the full MHD one. On the other hand, it has all the features of the full MHD version in the simplest form. In particular, within the hydrodynamical approach one can introduce the 3+1-splitting language—the most convenient one for the description of the ideal flows in the vicinity of a rotating black hole. Starting from the well-known set of equations describing the nonrelativistic ideal flow, we will go step by step to more complicated cases up to the most general one corresponding to the axisymmetric stationary flows in the Kerr metric. Finally, several examples will be considered which demonstrate how the approach under study can be used to obtain the quantitative information of the real transonic flows in the vicinity of rotating black holes. The necessity of taking into account the effects of General Relativity is not so obvious for most compact sources. For instance, one cannot exclude that the black hole plays only a passive role in the jet formation process, and the effects of General Relativity in this case may be unimportant for flow description in the region of jet formation. At the same time, gravitational effects make, apparently, an appreciable contribution to the determination of physical conditions in compact objects. First, this is indicated by the hard spectra and the e + e - annihilation line observed in galactic X-ray sources, which are believed to be solar mass black holes. Such characteristics are never observed in the X-ray sources which are firmly established to show accretion not onto a black hole but onto a neutron star. Another indication comes from superluminal motion in quasars which may be due to the relativistic plasma flow ejected along with a weakly relativistic jet. All these testify in favor of the existence of an additional mechanism for particle creation and acceleration for which the effects of General Relativity may be of principal importance. So, it is undoubtedly interesting to consider the flow structure in the most general conditions, i.e., in the presence of a rotating black hole.

Force-Free Approximation — The Magnetosphere of Radio Pulsars

The general view of the radio pulsar activity seems to have been established over many years. On the other hand, some fundamental problems are still to be solved. It is, first of all, the problem of the physical nature of the coherent radio emission of pulsars. In particular, as in the 1970 s, there is no common view of the problem of the coherent radio emission mechanism of a maser or an antenna type.Moreover, there is no common view of the pulsar magnetosphere structure. The point is that the initial hypothesis for the magnetodipole energy loss mechanism is, undoubtedly, unrealistic. Therefore, the problem of the slowing-down mechanism can be solved only if the magnetosphere structure of neutron stars is established. However, a consistent theory of radio pulsar magnetospheres has not yet been developed. Thus, the structure of longitudinal currents circulating in the magnetosphere has not been specified and, hence, the problems of neutron star braking, particle acceleration, and energy transport beyond the light cylinder have not been solvedeither. The theory of the inner structure of neutron stars is also far from completion. Naturally, it is impossible to dwell on all these problems here and, therefore, we discuss in detail only the problems directly associated with themain theme of this book, viz., the theory of radio pulsar magnetospheres. The first two sections consider the basic physical processes in neutron star magnetospheres and the secondary plasma generation mechanism. Then we formulate a pulsar equation, i.e., the force-free Grad–Shafranov equation in flat space providing the correct determination of the energy losses of radio pulsars. Further, the exact analytical solutions obtained for radio pulsar magnetospheres are also discussed in detail. It is demonstrated that, within the force-free approximation, a self-consistent theory cannot be formulated. Finally, the current pulsar magnetosphere models are analyzed.

Full MHD Version — General Properties

The full MHD version of the Grad–Shafranov equation combines a well-conducting hydrodynamical medium and an electromagnetic field. Within this version, we can rather simply describe both the transformation of the energy of the electromagnetic field into particles and the whole magnetic field structure. As a result, one of the main problems in theory—the construction of the current system and the determination of the energy losses—can be posed in a mathematically rigorous way. This chapter deals with the general properties of the full MHD version of the GS equation. As in the presence of the magnetic field, as the number of normal modes increases, the structure of the GS equation becomes much more complicated than that in the hydrodynamical case; the properties of the critical surfaces are to be described in detail. This makes it possible to formulate some important theorems on the general properties in the magnetosphere of compact objects. In particular, it is shown that, within the full MHD approach, the electric current circulating in the magnetosphere is no longer a free parameter but is to be determined from the critical conditions on the singular surfaces. Asymptotic behavior of the flows at infinity and in the vicinity of the black hole horizon is considered in detail as well.

Full MHD Version — Particle Acceleration and Collimation

In this chapter, we discuss the analytical solutions obtained for cylindrical jets, quasimonopole outflows, and the black hole magnetosphere. It is demonstrated that the self-consistent analysis makes it possible to determine the main characteristics of the outgoing wind, including the determination of the total energy loss and the poloidal magnetic field structure. The conditions of the effective energy transformation from the electromagnetic flux to the particle flux are given as well. For cylindrical jets both the relativistic and nonrelativistic versions are discussed. It is shown that taking into account the finite ambient pressure, one can determine the magnetic flux within the central core. For nonrelativistic flows, which are magnetically dominated near the origin, the solution can be constructed only in the presence of an oblique shock near the jet base, where additional heating is to take place. The analytical solutions obtained for quasimonopole and parabolic magnetic fields illustrated the general property that the efficient particle acceleration can take place only for the strongly collimated outflows. Two toy solutions for the black hole magnetosphere support the physical nature of the Blandford–Znajek process. Finally, the results obtained by the self–similar approach and in the numerical simulation are briefly discussed. It is demonstrated that there is now a lot of numerical data that confirms the analytical results obtained by the Grad–Shafranov equation method.