Search

We study the polarization properties of the jitter and synchrotron radiation produced by electrons in highly turbulent anisotropic magnetic fields. The net polarization is provided by the geometry of the magnetic field the directions of which are parallel to a certain plane. Such conditions may appear in the relativistic shocks during the amplification of the magnetic field through the so-called Weibel instability. While the polarization properties of the jitter radiation allows extraction of direct information on the turbulence spectrum as well as the geometry of magnetic field, the polarization of the synchrotron radiation reflects the distribution of the magnetic field over its strength. For the isotropic distribution of monoenergetic electrons, we found that the degree of polarization of the synchrotron radiation is larger than the polarization of the jitter radiation. For the power-law energy distribution of electrons the relation between the degree of polarization of synchrotron and jitter radiation depends on the spectral index of the distribution.

A stationary distribution function that describes the entire processes of propagation of relativistic particles, including the transition between the ballistic and diffusion regimes, is obtained. The spacial component of the constructed function satisfies to the first two moments of the Boltzmann equation. The angular part of the distribution provides accurate values for the angular moments derived from the Boltzmann equation, and gives a correct expression in the limit of small-angle approximation. Using the derived function, we studied the gamma-ray images produced through the $pp$ interaction of relativistic particles with gas clouds in the proximity of the accelerator. In general, the morphology and the energy spectra of gamma-rays significantly deviate from the "standard" results corresponding to the propagation of relativistic particles strictly in the diffusion regime.

It is generally believed that the radiation of relativistic particles in a curved magnetic field proceeds in either the synchrotron or the curvature radiation modes. In this paper we show that in strong curved magnetic fields a significant fraction of the energy of relativistic electrons can be radiated away in the intermediate, the so-called synchro-curvature regime. Because of the persistent change of the trajectory curvature, the radiation varies with the frequency of particle gyration. While this effect can be ignored in the synchrotron and curvature regimes, the variability plays a key role in the formation of the synchro-curvature radiation. Using the Hamiltonian formalism, we find that the particle trajectory has the form of a helix wound around the drift trajectory. This allows us to calculate analytically the intensity and energy distribution of prompt radiation in the general case of magnetic bremsstrahlung in the curved magnetic field. We show that the transition to the limit of the synchrotron and curvature radiation regimes is determined by the relation between the drift velocity and the component of the particle velocity perpendicular to the drift trajectory. The detailed numerical calculations, which take into account the energy losses of particles, confirm the principal conclusions based on the simplified analytical treatment of the problem, and allow us to analyze quantitatively the transition between different radiation regimes for a broad range of initial pitch angles. We argue that in the case of realization of specific configurations of the electric and magnetic fields, the gamma-ray emission of the pulsar magnetospheres can be dominated by the component radiated in the synchro-curvature regime., Comment: this article supersedes arXiv:1207.6903 and arXiv:1305.0783

The beaming pattern of radiation emitted by a relativistically moving source like jets in microquasars, AGN and GRBs, is a key issue for understanding of acceleration and radiation processes in these objects. In this paper we introduce a formalism based on a solution of the photon transfer equation to study the beaming patterns for emission produced by electrons accelerated in the jet and upscattering photons of low-energy radiation fields of external origin (the so-called External Compton scenario). The formalism allows us to treat non-stationary, non-homogeneous and anisotropic distributions of electrons, but assuming homogeneous/isotropic and non-variable target photon fields. We demonstrate the non-negligible impact of the anisotropy in the electron distribution on angular and spectral characteristics of the EC radiation., Comment: 7 pages, 2 figures

The details of trajectories of charged particles become increasingly important for proper understanding of processes of formation of radiation in strong and curved magnetic fields. Because of damping of the perpendicular component of motion, the particle's pitch angle could be decreased by many orders of magnitude leading to the change of the radiation regime -- from synchrotron to the curvature mode. To explore the character of this transition, we solve numerically the equations of motion of a test particle in a dipole magnetic field, and calculate the energy spectrum of magnetic bremsstrahlung self-consistently, i.e. without a priori assumptions on the radiation regime. In this way we can trace the transitions between the synchrotron and curvature regimes, as well as study the third (intermediate or the so-called synchro-curvature) regime. We briefly discuss three interesting astrophysical scenarios, the radiation of electrons in the pulsar magnetosphere in the polar cap and outer gap models, as well as the radiation of ultrahigh energy protons in the magnetosphere of a massive black hole, and demonstrate that in these models the synchrotron, synchro-curvature and curvature regimes can be realized with quite different relative contributions to the total emission., Comment: the reprocessed version of this article merged with arXiv:1207.6903 can be found in arXiv:1501.04994

The spectral shape of radiation due to Inverse Compton Scattering is analyzed, in the Thomson and the Klein-Nishina regime, for electron distributions with exponential cut-off. We derive analytical, asymptotic expressions for the spectrum close to the maximum cut-off region. We consider monoenergetic, Planckian and Synchrotron photons as target photon fields. These approximations provide a direct link between the distribution of parent electrons and the up-scattered spectrum at the cut-off region., Comment: 27 pages, 15 figures, accepted for publication in ApJ

Using the standard canonical formalism, the equations of mechanics and kinetics in the Friedmann-Lemaitre-Robertson-Walker (FLRW) space-times in Cartesian coordinates have been obtained. The transformation law of the generalized momentum under the shift of the origin of the coordinate system has been found, and the form invariance of the Hamiltonian function relative to the shift transformation has been proved. The general solution of the collisionless Boltzmann equation has been found. In the case of the homogeneous distribution the solutions of the kinetic equation for several simple, but important for applications, cases have been obtained.

The acceleration cites of ultra-high-energy (UHE) protons can be traced by the footprint left by these particles propagating through cosmic microwave background (CMB) radiation. Secondary electrons produced in extended region of several tens of Mpc emit their energy via synchrotron radiation predominantly in the initial direction of the parent protons. It forms a non-variable and compact (almost point-like) source of high energy gamma rays. The importance of this effect is increased for cosmologically distant objects; because of severe energy losses, UHE protons cannot achieve us even in the case of extremely weak intergalactic magnetic fields. Moreover, at high redshifts the energy conversion from protons to secondary particles becomes significantly more effective due to the denser and more energetic CMB in the past. This increases the chances of UHE cosmic rays to be traced by the secondary synchrotron gamma radiation. We discuss the energy budget and the redshift dependence of the efficiency of energy transfer from UHE protons to synchrotron radiation. The angular and spectral distributions of radiation in the gamma- and X-ray energy bands are calculated and discussed in the context of their detectability by Fermi LAT and Chandra observatories.

The angular, spectral and temporal features of the highest energy protons and accompanying them secondary neutrinos and synchrotron gamma-rays propagating through the intergalactic magnetic and radiation fields are studied using the analytical solutions of the Boltzmann transport equation obtained in the limit of the small-angle and continuous-energy-loss approximation., Comment: 21 pages, 13 figures

Clusters of galaxies are believed to be capable to accelerate protons at accretion shocks to energies exceeding 10^18 eV. At these energies, the losses caused by interactions of cosmic rays with photons of the Cosmic Microwave Background Radiation (CMBR) become effective and determine the maximum energy of protons and the shape of the energy spectrum in the cutoff region. The aim of this work is the study of the formation of the energy spectrum of accelerated protons at accretion shocks of galaxy clusters and of the characteristics of their broad band emission. The proton energy distribution is calculated self-consistently via a time-dependent numerical treatment of the shock acceleration process which takes into account the proton energy losses due to interactions with the CMBR. We calculate the energy distribution of accelerated protons, as well as the flux of broad-band emission produced by secondary electrons and positrons via synchrotron and inverse Compton scattering processes. We find that the downstream and upstream regions contribute almost at the same level to the emission. For the typical parameters characterising galaxy clusters, the synchrotron and IC peaks in the spectral energy distributions appear at comparable flux levels. For an efficient acceleration, the expected emission components in the X-ray and gamma-ray band are close to the detection threshold of current generation instruments, and will be possibly detected with the future generation of detectors., Comment: 9 pages, 13 figures, submitted to Astronomy & Astrophysics

We derived simple analytical parametrizations for energy distributions of photons, electrons, and neutrinos produced in interactions of relativistic protons with an isotropic monochromatic radiation field. The results on photomeson processes are obtained using numerical simulations of proton-photon interactions based on the public available Monte-Carlo code SOPHIA. For calculations of energy spectra of electrons and positrons from the pair production (Bethe-Heitler) process we suggest a simple formalism based on the well-known differential cross-section of the process in the rest frame of the proton. The analytical presentations of energy distributions of photons and leptons provide a simple but accurate approach for calculations of broad-band energy spectra of gamma-rays and neutrinos in cosmic proton accelerators located in radiation dominated environments., Comment: 17 pages, 21 figures, published in Phys.Rev.D. We have corrected two misprints in the text. We note that the correct expressions were used for calculations in the previous versions of the paper, thus the misprints did not have an impact on the figures

We present new parametrisations of energy spectra of secondary particles, $\pi$-mesons, gamma-rays, electrons and neutrinos, produced in inelastic proton-proton collisions. The simple analytical approximations based on imulations of proton-proton interactions using the public available SIBYLL code, provide very good accuracy for energy distributions of secondary products in the energy range above 100 GeV. Generally, the recommended analytical formulae deviate from the simulated distributions within a few percent over a large range of $x=E_i/E_p$ - the fraction of energy of the incident proton transferred to the secondaries. Finally, we describe an approximate procedure of continuation of calculations towards low energies, down to the threshold of $\pi$-meson production., Comment: 16 pages, 14 figures, submitted to Phys ReV D (Dec 30, 2005), revised after the referee reports (Fig 3 and Appendix added)