Diffuse Galactic Gamma Rays from Shock-Accelerated Cosmic Rays

A shock-accelerated particle flux \propto p^-s, where p is the particle momentum, follows from simple theoretical considerations of cosmic-ray acceleration at nonrelativistic shocks followed by rigidity-dependent escape into the Galactic halo. A flux of shock-accelerated cosmic-ray protons with s ~ 2.8 provides an adequate fit to the Fermi-LAT gamma-ray emission spectra of high-latitude and molecular cloud gas when uncertainties in nuclear production models are considered. A break in the spectrum of cosmic-ray protons claimed by Neronov, Semikoz, & Taylor (PRL, 108, 051105, 2012) when fitting the gamma-ray spectra of high-latitude molecular clouds is a consequence of using a cosmic-ray proton flux described by a power law in kinetic energy.Comment: Version to correspond to published letter in PRL; corrected Fig.

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

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

On The Origin of Very High Energy Cosmic Rays

We discuss the most recent developments in our understanding of the acceleration and propagation of cosmic rays up to the highest energies. In particular we specialize our discussion to three issues: 1) developments in the theory of particle acceleration at shock waves; 2) the transition from galactic to extragalactic cosmic rays; 3) implications of up-to-date observations for the origin of ultra high energy cosmic rays (UHECRs).Comment: Invited Review Article to appear in Modern Physics Letters A, Review Sectio

Particle acceleration at shock waves: particle spectrum as a function of the equation of state of the shocked plasma

We determine the spectrum of particles accelerated at shocks with arbitrary speed and arbitrary scattering properties for different choices of the equation of state of the downstream plasma. More specifically we consider the effect of energy exchange between the electron and proton thermal components downstream, and the effect of generation of a turbulent magnetic field in the downstream plasma. The slope of the spectrum turns out to be appreciably affected by all these phenomena, especially in the Newtonian and trans-relativistic regime, while in the ultra-relativistic limit the universal spectrum $s\approx 4.3$ seems to be a very solid prediction.Comment: 21 pages, 8 fig

Particle Diffusion and Acceleration by Shock Wave in Magnetized Filamentary Turbulence

We expand the off-resonant scattering theory for particle diffusion in magnetized current filaments that can be typically compared to astrophysical jets, including active galactic nucleus jets. In a high plasma beta region where the directional bulk flow is a free-energy source for establishing turbulent magnetic fields via current filamentation instabilities, a novel version of quasi-linear theory to describe the diffusion of test particles is proposed. The theory relies on the proviso that the injected energetic particles are not trapped in the small-scale structure of magnetic fields wrapping around and permeating a filament but deflected by the filaments, to open a new regime of the energy hierarchy mediated by a transition compared to the particle injection. The diffusion coefficient derived from a quasi-linear type equation is applied to estimating the timescale for the stochastic acceleration of particles by the shock wave propagating through the jet. The generic scalings of the achievable highest energy of an accelerated ion and electron, as well as of the characteristic time for conceivable energy restrictions, are systematically presented. We also discuss a feasible method of verifying the theoretical predictions. The strong, anisotropic turbulence reflecting cosmic filaments might be the key to the problem of the acceleration mechanism of the highest energy cosmic rays exceeding 100 EeV (10^{20} eV), detected in recent air shower experiments.Comment: 39 pages, 2 figures, accepted for publication in Ap

The spectrum of particles accelerated in relativistic, collisionless shocks

We analytically study diffusive particle acceleration in relativistic, collisionless shocks. We find a simple relation between the spectral index s and the anisotropy of the momentum distribution along the shock front. Based on this relation, we obtain s = (3beta_u - 2beta_u*beta_d^2 + beta_d^3) / (beta_u - beta_d) for isotropic diffusion, where beta_u (beta_d) is the upstream (downstream) fluid velocity normalized to the speed of light. This result is in agreement with previous numerical determinations of s for all (beta_u,beta_d), and yields s=38/9 in the ultra-relativistic limit. The spectrum-anisotropy connection is useful for testing numerical studies and for constraining non-isotropic diffusion results. It implies that the spectrum is highly sensitive to the form of the diffusion function for particles travelling along the shock front.Comment: 4 pages, 1 figur

The origin of ultra high energy cosmic rays

We briefly discuss some open problems and recent developments in the investigation of the origin and propagation of ultra high energy cosmic rays (UHECRs).Comment: Invited Review Talk at TAUP 2005 (Zaragoza - September 10-14, 2005). 7 page

Proton-Helium Spectral Anomaly as a Signature of Cosmic Ray Accelerator

The much-anticipated proof of cosmic ray (CR) acceleration in supernova remnants (SNR) must hinge on full consistency of acceleration theory with the observations; direct proof is impossible because of the orbit scrambling of CR particles. The PAMELA orbital telescope revealed deviation between helium and proton CR spectra deemed inconsistent with the theory, since the latter does not differentiate between elements of ultrarelativistic rigidity. By considering an initial (injection-) phase of the diffusive shock acceleration (DSA), where elemental similarity does not apply, we demonstrate that the spectral difference is, in fact, a unique signature of the DSA. Collisionless plasma SNR shocks inject more He2+ relative to protons when they are stronger and so produce harder helium spectra. The injection bias is due to Alfven waves driven by the more abundant protons, so the He2+ ions are harder to trap by these waves because of the larger gyroradii. By fitting the p/He ratio to the PAMELA data, we bolster the DSA-case for resolving the century-old mystery of CR origin.Comment: PRL Accepted version: reformatted figures, references added, minor correction

ION ACCELERATION AT THE QUASI-PARALLEL BOW SHOCK: DECODING THE SIGNATURE OF INJECTION

Collisionless shocks are efficient particle accelerators. At Earth, ions with energies exceeding 100 keV are seen upstream of the bow shock when the magnetic geometry is quasi-parallel, and large-scale supernova remnant shocks can accelerate ions into cosmic rays energies. This energization is attributed to diffusive shock acceleration, however, for this process to become active the ions must first be sufficiently energized. How and where this initial acceleration takes place has been one of the key unresolved issues in shock acceleration theory. Using Cluster spacecraft observations, we study the signatures of ion reflection events in the turbulent transition layer upstream of the terrestrial bow shock, and with the support of a hybrid simulation of the shock, we show that these reflection signatures are characteristic of the first step in the ion injection process. These reflection events develop in particular in the region where the trailing edge of large-amplitude upstream waves intercept the local shock ramp and the upstream magnetic field changes from quasi-perpendicular to quasi-parallel. The dispersed ion velocity signature observed can be attributed to a rapid succession of ion reflections at this wave boundary. After the ions' initial interaction with the shock, they flow upstream along the quasi-parallel magnetic field. Each subsequent wave front in the upstream region will sweep the ions back toward the shock, where they gain energy with each transition between the upstream and the shock wave frames. Within three to five gyroperiods, some ions have gained enough parallel velocity to escape upstream, thus completing the injection process.Comment: 30 pages, 10 figures. Accepted for publication in The Astrophysical Journa