Cosmic-Ray Acceleration at Ultrarelativistic Shock Waves: Effects of Downstream Short-Wave Turbulence

The present paper is the last of a series studying the first-order Fermi acceleration processes at relativistic shock waves with the method of Monte Carlo simulations applied to shocks propagating in realistically modeled turbulent magnetic fields. The model of the background magnetic field structure of Niemiec & Ostrowski (2004, 2006) has been augmented here by a large-amplitude short-wave downstream component, imitating that generated by plasma instabilities at the shock front. Following Niemiec & Ostrowski (2006), we have considered ultrarelativistic shocks with the mean magnetic field oriented both oblique and parallel to the shock normal. For both cases simulations have been performed for different choices of magnetic field perturbations, represented by various wave power spectra within a wide wavevector range. The results show that the introduction of the short-wave component downstream of the shock is not sufficient to produce power-law particle spectra with the "universal" spectral index 4.2. On the contrary, concave spectra with cutoffs are preferentially formed, the curvature and cutoff energy being dependent on the properties of turbulence. Our results suggest that the electromagnetic emission observed from astrophysical sites with relativistic jets, e.g. AGN and GRBs, is likely generated by particles accelerated in processes other than the widely invoked first-order Fermi mechanism.Comment: 9 pages, 8 figures, submitted to Ap

Cosmic Ray Acceleration at Relativistic Shock Waves with a "Realistic" Magnetic Field Structure

The process of cosmic ray first-order Fermi acceleration at relativistic shock waves is studied with the method of Monte Carlo simulations. The simulations are based on numerical integration of particle equations of motion in a turbulent magnetic field near the shock. In comparison to earlier studies, a few "realistic" features of the magnetic field structure are included. The upstream field consists of a mean field component inclined at some angle to the shock normal with finite-amplitude sinusoidal perturbations imposed upon it. The perturbations are assumed to be static in the local plasma rest frame. Their flat or Kolmogorov spectra are constructed with randomly drawn wave vectors from a wide range $(k_{min}, k_{max})$. The downstream field structure is derived from the upstream one as compressed at the shock. We present particle spectra and angular distributions obtained at mildly relativistic sub- and superluminal shocks and also parallel shocks. We show that particle spectra diverge from a simple power-law, the exact shape of the spectrum depends on both the amplitude of the magnetic field perturbations and the wave power spectrum. Features such as spectrum hardening before the cut-off at oblique subluminal shocks and formation of power-law tails at superluminal ones are presented and discussed. At parallel shocks, the presence of finite-amplitude magnetic field perturbations leads to the formation of locally oblique field configurations at the shock and the respective magnetic field compressions. This results in the modification of the particle acceleration process, introducing some features present in oblique shocks, e.g., particle reflections from the shock. We demonstrate for parallel shocks a (nonmonotonic) variation of the particle spectral index with the turbulence amplitude.Comment: revised version (37 pages, 13 figures

Cosmic-ray Acceleration at Ultrarelativistic Shock Waves: Effects of a "Realistic" Magnetic Field Structure

First-order Fermi acceleration processes at ultrarelativistic shocks are studied with Monte Carlo simulations. The accelerated particle spectra are derived by integrating the exact particle trajectories in a turbulent magnetic field near the shock. ''Realistic'' features of the field structure are included. We show that the main acceleration process at superluminal shocks is the particle compression at the shock. Formation of energetic spectral tails is possible in a limited energy range only for highly perturbed magnetic fields, with cutoffs occuring at low energies within the resonance energy range considered. These spectral features result from the anisotropic character of particle transport in the downstream magnetic field, where field compression produces effectively 2D perturbations. Because of the downstream field compression, the acceleration process is inefficient in parallel shocks for larger turbulence amplitudes, and features observed in oblique shocks are recovered. For small-amplitude turbulence, wide-energy range particle spectra are formed and modifications of the process due to the existence of long-wave perturbations are observed. In both sub- and superluminal shocks, an increase of \gamma leads to steeper spectra with lower cut-off energies. The spectra obtained for the ``realistic'' background conditions assumed here do not converge to the ``universal'' spectral index claimed in the literature. Thus the role of the first-order Fermi process in astrophysical sources hosting relativistic shocks requires serious reanalysis.Comment: submitted to Ap

Efficiency of cosmic ray reflections from an ultrarelativistic shock wave

The process of cosmic ray acceleration up to energies in excess of $10^{20}$ eV at relativistic shock waves with large Lorentz factors, $\Gamma \gg 1$ requires $\sim \Gamma^2$ particle energy gains at single reflections from the shock (cf. Gallant & Achterberg 1999). In the present comment, applying numerical simulations we address an efficiency problem arising for such models. The actual efficiency of the acceleration process is expected to be substantially lower than the estimates of previous authors.Comment: 3 pages, 3 figures, accepted for publication in MNRAS (Letters

On the Green and Wald formalism

Backreaction in the cosmological context is a longstanding problem that is especially important in the present era of precise cosmology. The standard model of a homogeneous background plus density perturbations is most probably oversimplified and is expected to fail to fully account for the near-future observations of sub-percent precision. From a theoretical point of view, the problem of backreaction is very complicated and deserves careful examination. Recently, Green and Wald claimed in a series of papers to have developed a formalism to properly describe the influence of density inhomogeneities on average properties of the Universe, i.e., the backreaction effect. A brief discussion of this framework is presented, focussing on its drawbacks and on misconceptions that have arisen during the "backreaction debate".Comment: Contribution to the proceedings of MG1