75 research outputs found
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, 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
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