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

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

Self-Similar Collisionless Shocks

Observations of gamma-ray burst afterglows suggest that the correlation length of magnetic field fluctuations downstream of relativistic non-magnetized collisionless shocks grows with distance from the shock to scales much larger than the plasma skin depth. We argue that this indicates that the plasma properties are described by a self-similar solution, and derive constraints on the scaling properties of the solution. For example, we find that the scaling of the characteristic magnetic field amplitude with distance from the shock is B \propto D^{s_B} with -1<s_B<=0, that the spectrum of accelerated particles is dn/dE \propto E^{-2/(s_B+1)}, and that the scaling of the magnetic correlation function is \propto x^{2s_B} (for x>>D). We show that the plasma may be approximated as a combination of two self-similar components: a kinetic component of energetic particles and an MHD-like component representing "thermal" particles. We argue that the latter may be considered as infinitely conducting, in which case s_B=0 and the scalings are completely determined (e.g. dn/dE \propto E^{-2} and B \propto D^0). Similar claims apply to non- relativistic shocks such as in supernova remnants, if the upstream magnetic field can be neglected. Self-similarity has important implications for any model of particle acceleration and/or field generation. For example, we show that the diffusion function in the angle \mu of momentum p in diffusive shock acceleration models must satisfy D_{\mu\mu}(p,D) = D^{-1}D'_{\mu\mu}(p/D), and that a previously suggested model for the generation of large scale magnetic fields through a hierarchical merger of current-filaments should be generalized. A numerical experiment testing our analysis is outlined (Abridged).Comment: 16 pages, 1 figure, accepted for publication in Ap

Ras-mediated phosphorylation of a conserved threonine residue enhances the transactivation activities of c-Ets1 and c-Ets2

The Ras oncogene products regulate the expression of genes in transformed cells, and members of the Ets family of transcription factors have been implicated in this process. To determine which Ets factors are the targets of Ras signaling pathways, the abilities of several Ets factors to activate Ras-responsive enhancer (RRE) reporters in the presence of oncogenic Ras were examined. In transient transfection assay, reporters containing RREs composed of Ets-AP-1 binding sites could be activated 30-fold in NIH 3T3 fibroblasts and 80-fold in the macrophage-like line RAW264 by the combination of Ets1 or Ets2 and Ras but not by several other Ets factors that were tested in the assay. Ets2 and Ras also superactivated an RRE composed of Ets-Ets binding sites, but the Ets-responsive promoter of the c-fms gene was not superactivated. Mutation of a threonine residue to alanine in the conserved amino-terminal regions of Ets1 and Ets2 (threonine 38 and threonine 72, respectively) abrogated the ability of each of these proteins to superactivate reporter gene expression. Phosphoamino acid analysis of radiolabeled Ets2 revealed that Ras induced normally absent threonine-specific phosphorylation of the protein. The Ras-dependent increase in threonine phosphorylation was not observed in Ets2 proteins that had the conserved threonine 72 residue mutated to alanine or serine. These data indicate that Ets1 and Ets2 are specific nuclear targets of Ras signaling events and that phosphorylation of a conserved threonine residue is a necessary molecular component of Ras-mediated activation of these transcription factors

Analytical Study of Diffusive Relativistic Shock Acceleration

Particle acceleration in relativistic shocks is studied analytically in the test-particle, small-angle scattering limit, for an arbitrary velocity-angle diffusion function D. Accurate analytic expressions for the spectral index s are derived using few (2-6) low-order moments of the shock-frame angular distribution. For isotropic diffusion, previous results are reproduced and justified. For anisotropic diffusion, s is shown to be sensitive to D, particularly downstream and at certain angles, and a wide range of s values is attainable. The analysis, confirmed numerically, can be used to test collisionless shock models and to observationally constrain D. For example, strongly forward- or backward-enhanced diffusion downstream is ruled out by GRB afterglow observations.Comment: 4 pages, 2 figures, PRL accepted, minor change

On the Interaction of the PKS B1358-113 Radio Galaxy with the Abell 1836 Cluster

[abridged] Here we present the analysis of multifrequency data gathered for the FRII radio galaxy PKS B1358-113, hosted in the brightest cluster galaxy of Abell 1836. The galaxy harbors one of the most massive black holes known to date and our analysis of the optical data reveals that this black hole is only weakly active. Based on new Chandra and XMM-Newton X-ray observations and archival radio data we derive the preferred range for the jet kinetic luminosity $\sim (0.5-3) \times 10^{45}$ erg s$^{-1}$. This is above the values implied by various scaling relations proposed for radio sources in galaxy clusters, being instead very close to the maximum jet power allowed for the given accretion rate. We constrain the radio source lifetime as $\sim 40-70$ Myrs, and the total amount of deposited jet energy $\sim (2-8) \times 10^{60}$\,ergs. The detailed analysis of the X-ray data provides indication for the presence of a bow-shock driven by the expanding radio lobes into the Abell 1836 cluster environment, with the corresponding Mach number $\sim 2-4$. This, together with the recently growing evidence that powerful FRII radio galaxies may not be uncommon in the centers of clusters at higher redshifts, supports the idea that jet-induced shock heating may indeed play an important role in shaping the properties of clusters, galaxy groups, and galaxies in formation. We speculate on a possible bias against detecting jet-driven shocks in poorer environments, resulting from an inefficient electron heating at the shock front, combined with a relatively long electron-ion equilibration timescale.Comment: Version accepted to Ap

Stochastic Acceleration in Relativistic Parallel Shocks

(abridged) We present results of test-particle simulations on both the first and the second order Fermi acceleration at relativistic parallel shock waves. We consider two scenarios for particle injection: (i) particles injected at the shock front, then accelerated at the shock by the first order mechanism and subsequently by the stochastic process in the downstream region; and (ii) particles injected uniformly throughout the downstream region to the stochastic process. We show that regardless of the injection scenario, depending on the magnetic field strength, plasma composition, and the employed turbulence model, the stochastic mechanism can have considerable effects on the particle spectrum on temporal and spatial scales too short to be resolved in extragalactic jets. Stochastic acceleration is shown to be able to produce spectra that are significantly flatter than the limiting case of particle energy spectral index -1 of the first order mechanism. Our study also reveals a possibility of re-acceleration of the stochastically accelerated spectrum at the shock, as particles at high energies become more and more mobile as their mean free path increases with energy. Our findings suggest that the role of the second order mechanism in the turbulent downstream of a relativistic shock with respect to the first order mechanism at the shock front has been underestimated in the past, and that the second order mechanism may have significant effects on the form of the particle spectra and its evolution.Comment: 14 pages, 11 figures (9 black/white and 2 color postscripts). To be published in the ApJ (accepted 6 Nov 2004