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

Non-linear shock acceleration and high energy gamma rays from clusters of galaxies

Merger and accretion shocks in clusters of galaxies can accelerate particles via first order Fermi process. Since this mechanism is believed to be intrinsically efficient, shocks are expected to be modified by the backreaction of the accelerated particles. Such a modification might induce appreciable effects on the non--thermal emission from clusters and a suppression of the heating of the gas at strong shocks. Here we consider in particular the gamma ray emission and we discuss the capability of Cherenkov telescopes such as HESS to detect clusters at TeV energies.Comment: 6 pages, to appear in the proceedings of the Gamma 2004 Symposium on High Energy Gamma Ray Astronomy, Heidelberg, July 2004 (AIP Proceedings Series

Dynamics and High Energy Emission of the Flaring HST-1 Knot in the M 87 Jet

Stimulated by recent observations of a radio-to-X-ray synchrotron flare from HST-1, the innermost knot of the M 87 jet, as well as by a detection of a very high energy gamma-ray emission from M 87, we investigated the dynamics and multiwavelength emission of the HST-1 region. We study thermal pressure of the hot interstellar medium in M 87 and argue for a presence of a gaseous condensation in its central parts. Interaction of the jet with such a feature is likely to result in formation of a converging reconfinement shock in the innermost parts of the M 87 jet. We show that for a realistic set of the outflow parameters, a stationary and a flaring part of the HST-1 knot located \~100 pc away from the active center can be associated with the decelerated portion of the jet matter placed immediately downstream of the point where the reconfinement shock reaches the jet axis. We discuss a possible scenario explaining a broad-band brightening of the HST-1 region related to the variable activity of the central core. We show that assuming a previous epoch of the high central black hole activity resulting in ejection of excess particles and photons down along the jet, one may first expect a high-energy flare of HST-1 due to inverse-Comptonisation of the nuclear radiation, followed after a few years by an increase in the synchrotron continuum of this region. If this is the case, then the recently observed increase in the knot luminosity in all spectral bands could be regarded as an unusual echo of the outburst that had happened previously in the active core of the M 87 radio galaxy.Comment: 30 pages, 7 figures included. Accepted for publication in MNRA

The X-ray Jet in Centaurus A: Clues on the Jet Structure and Particle Acceleration

We report detailed studies of the X-ray emission from the kpc scale jet in the nearest active galaxy, Cen A. 41 compact sources were found within the jet, 13 of which were newly identified. We construct the luminosity function for the detected jet-knots and argue that the remaining emission is most likely to be truly diffuse, rather than resulting from the pile-up of unresolved faint knots. The transverse jet profile reveals that the extended emission has the intensity peak at the jet boundaries. We note that limb-brightened jet morphologies have been observed previously at radio frequencies in some jet sources, but never so clearly at higher photon energies. Our result therefore supports a stratified jet model, consisting of a relativistic outflow including a boundary layer with a velocity shear. In addition, we found that the X-ray spectrum of the diffuse component is almost uniform across and along the jet. We discuss this spectral behavior within a framework of shock and stochastic particle acceleration processes. We note some evidence for a possible spectral hardening at the outer sheath of the jet. Due to the limited photon statistics of the present data, further deep observations of Cen A are required to determine the reality of this finding, however we note that the existence of the hard X-ray features at outer jet boundaries would provide an important challenge to theories for the evolution of ultra-relativistic particles within the jets.Comment: 27page, 8 figures, ver2, accepted for publication in the Ap

On the characterization of Shannon's entropy by Shannon's inequality

1. In [2,5,6,7] a.o. several interpretations of the inequality for all such that were given and the following was prove

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

A cosmic ray cocoon along the X-ray jet of M87?

Relativistic jets propagating through an ambient medium must produce some observational effects along their side boundaries because of interactions across the large velocity gradient. One possible effect of such an interaction would be a sheared magnetic field structure at the jet boundaries, leading to a characteristic radio polarization pattern. As proposed by Ostrowski, another effect can come from the generation of a high energy cosmic ray component at the boundary, producing dynamic effects on the medium surrounding the jet and forming a cocoon dominated by cosmic rays with a decreased thermal gas emissivity. We selected this process for our first attempt to look for the effects of this type of interaction. We analyzed the Chandra X-ray data for the radio galaxy M87 in order to verify if the expected regions of diminished emissivity may be present near the spectacular X-ray jet in this source. The detailed analysis of the data, merged from 42 separate observations, shows signatures of lower emissivity surrounding the jet. In particular we detect an intensity dip along the part of the jet, which would be approximately 150 pc x 2 kpc in size, if situated along the jet which is inclined toward us. Due to a highly non-uniform X-ray background in the central region we are not able to claim the discovery of a cosmic ray cocoon around the M87 jet: we only have demonstrated that the data show morphological structures which could be accounted for if a cosmic ray cocoon exists.Comment: 8 pages, 8 pictures accepted for publication in MNRA