Multipole expansions in four-dimensional hyperspherical harmonics

The technique of vector differentiation is applied to the problem of the derivation of multipole expansions in four-dimensional space. Explicit expressions for the multipole expansion of the function r^n C_j (\hr) with \vvr=\vvr_1+\vvr_2 are given in terms of tensor products of two hyperspherical harmonics depending on the unit vectors \hr_1 and \hr_2. The multipole decomposition of the function (\vvr_1 \cdot \vvr_2)^n is also derived. The proposed method can be easily generalised to the case of the space with dimensionality larger than four. Several explicit expressions for the four-dimensional Clebsch-Gordan coefficients with particular values of parameters are presented in the closed form.Comment: 19 pages, no figure

Spatial Evidence for Transition Radiation in a Solar Radio Burst

Microturbulence, i.e. enhanced fluctuations of plasma density, electric and magnetic fields, is of great interest in astrophysical plasmas, but occurs on spatial scales far too small to resolve by remote sensing, e.g., at ~ 1-100 cm in the solar corona. This paper reports spatially resolved observations that offer strong support for the presence in solar flares of a suspected radio emission mechanism, resonant transition radiation, which is tightly coupled to the level of microturbulence and provides direct diagnostics of the existence and level of fluctuations on decimeter spatial scales. Although the level of the microturbulence derived from the radio data is not particularly high, /n^2 ~ 10^{-5}$, it is large enough to affect the charged particle diffusion and give rise to effective stochastic acceleration. This finding has exceptionally broad astrophysical implications since modern sophisticated numerical models predict generation of much stronger turbulence in relativistic objects, e.g., in gamma-ray burst sources.Comment: 13 pages, 4 figures, ApJL accepte

Modeling Bell's Non-resonant Cosmic Ray Instability

We have studied the non-resonant streaming instability of charged energetic particles moving through a background plasma, discovered by Bell (2004). We confirm his numerical results regarding a significant magnetic field amplification in the system. A detailed physical picture of the instability development and of the magnetic field evolution is given.Comment: 12 pages, 4 figures, accepted to Ap

Diffusive Shock Acceleration with Magnetic Amplification by Non-resonant Streaming Instability in SNRs

We investigate the diffusive shock acceleration in the presence of the non-resonant streaming instability introduced by Bell (2004). The numerical MHD simulations of the magnetic field amplification combined with the analytical treatment of cosmic ray acceleration permit us to calculate the maximum energy of particles accelerated by high-velocity supernova shocks. The estimates for Cas A, Kepler, SN1006, and Tycho historical supernova remnants are given. We also found that the amplified magnetic field is preferentially oriented perpendicular to the shock front downstream of the fast shock. This explains the origin of the radial magnetic fields observed in young supernova remnants.Comment: 18 pages, 9 figures, accepted to Ap

The Oscillating Universe: an Alternative to Inflation

The aim of this paper is to show, that the 'oscillating universe' is a viable alternative to inflation. We remind that this model provides a natural solution to the flatness or entropy and to the horizon problem of standard cosmology. We study the evolution of density perturbations and determine the power spectrum in a closed universe. The results lead to constraints of how a previous cycle might have looked like. We argue that most of the radiation entropy of the present universe may have originated from gravitational entropy produced in a previous cycle. We show that measurements of the power spectrum on very large scales could in principle decide whether our universe is closed, flat or open.Comment: revised version for publication in Classical and Quantum Gravity, 23 pages, uuencoded compressed tarred Latex file with 7 eps figures included, fig.8 upon reques

Influence of helicity on scaling regimes in the extended Kraichnan model

We have investigated the advection of a passive scalar quantity by incompressible helical turbulent flow in the frame of extended Kraichnan model. Turbulent fluctuations of velocity field are assumed to have the Gaussian statistics with zero mean and defined noise with finite time-correlation. Actual calculations have been done up to two-loop approximation in the frame of field-theoretic renormalization group approach. It turned out that space parity violation (helicity) of turbulent environment does not affect anomalous scaling which is peculiar attribute of corresponding model without helicity. However, stability of asymptotic regimes, where anomalous scaling takes place, strongly depends on the amount of helicity. Moreover, helicity gives rise to the turbulent diffusivity, which has been calculated in one-loop approximation.Comment: 16 pages, talk given by M. Hnatich at "Renormalization Group 2005", Helsinki, Finland 30 August - 3 September 2005. To apear in J. Phys. A: Math. Ge

Transfer of Polarized Radiation in Strongly Magnetized Plasmas and Thermal Emission from Magnetars: Effect of Vacuum Polarization

We present a theoretical study of radiative transfer in strongly magnetized electron-ion plasmas, focusing on the effect of vacuum polarization due to quantum electrodynamics. This study is directly relevant to thermal radiation from the surfaces of highly magnetized neutron stars, which have been detected in recent years. Strong-field vacuum polarization modifies the photon propagation modes in the plasma, and induces a ``vacuum resonance'' at which a polarized X-ray photon propagating outward in the neutron star atmosphere can convert from a low-opacity mode to a high-opacity mode and vice versa. The effectiveness of this mode conversion depends on the photon energy and the atmosphere density gradient. For a wide range of field strengths, $7\times 10^{13}< B < 10^{16}$ G, the vacuum resonance lies between the photospheres of the two photon modes, and the emergent radiation spectrum from the neutron star is significantly modified by the vacuum resonance. (For lower field strengths, only the polarization spectrum is affected.) Under certain conditions, which depend on the field strength, photon energy and propagation direction, the vacuum resonance is accompanied by the phenomenon of mode collapse (at which the two photon modes become degenerate) and the breakdown of Faraday depolarization. Thus, the widely used description of radiative transfer based on photon modes is not adequate to treat the vacuum polarization effect rigorously. We study the evolution of polarized X-rays across the vacuum resonance and derive the transfer equation for the photon intensity matrix (Stokes parameters), taking into account the effect of birefringence of the plasma-vacuum medium, free-free absorption, and scatterings by electrons and ions.Comment: 19 pages with 9 figures; minor additions (mainly the at end of sec.5.2); ApJ in press (v588, n2, May 10, 2003 issue

The polarization effects of radiation from magnetized envelopes and extended accretion structures

The results of numerical calculations of linear polarization from magnetized spherical optically thick and optically thin envelopes are presented. We give the methods how to distinguish magnetized optically thin envelopes from optically thick ones using observed spectral distributions of the polarization degree and the positional angle. The results of numerical calculations are used for analysis of polarimetric observations of OB and WR stars, X-ray binaries with black hole candidates (Cyg X-1, SS 433) and supernovae. The developed method allows to estimate magnetic field strength for the objects mentioned above.Comment: 18 pages, 6 figure

Magnetic fields of active galactic nuclei and quasars with polarized broad H-alpha lines

We present estimates of magnetic field in a number of AGNs from the Spectropolarimetric atlas of Smith, Young & Robinson (2002) from the observed degrees of linear polarization and the positional angles of spectral lines (H-alpha) (broad line regions of AGNs) and nearby continuum. The observed polarization is lower than the Milne value in a non-magnetized atmosphere. We hypothesize that the polarized radiation escapes from optically thick magnetized accretion discs and is weakened by the Faraday rotation effect. This effect is able to explain both the value of the polarization and the position angle. We estimate the required magnetic field in the broad line region by using simple asymptotic analytical formulas for Milne's problem in magnetized atmosphere, which take into account the last scattering of radiation before escaping from the accretion disc. The polarization of a broad spectral line escaping from disc is described by the same mechanism. The characteristic features of polarization of a broad line is the minimum of the degree of polarization in the center of the line and continuous rotation of the position angle from one wing to another. These effects can be explained by existence of clouds in the left (velocity is directed to an observer) and the right (velocity is directed from an observer) parts of the orbit in a rotating keplerian magnetized accretion disc. The base of explanation is existence of azimuthal magnetic field in the orbit. The existence of normal component of magnetic field makes the picture of polarization asymmetric. The existence of clouds in left and right parts of the orbit with different emissions also give the contribution in asymmetry effect. Assuming a power-law dependence of the magnetic field inside the disc, we obtain the estimate of the magnetic field strength at first stable orbit near the central SMBH for a number of AGNs.Comment: 15 pages, 4 figure