Relativistic Fermi acceleration with shock compressed turbulence

This paper presents numerical simulations of test particle Fermi acceleration at relativistic shocks of Lorentz factor Gamma_sh = 2-60, using a realistic downstream magnetic structure obtained from the shock jump conditions. The upstream magnetic field is described as pure Kolmogorov turbulence; the corresponding downstream magnetic field lies predominantly in the plane tangential to the shock surface and the coherence length is smaller along the shock normal than in the tangential plane. Acceleration is nonetheless efficient and leads to powerlaw spectra with index s = 2.6-2.7 at large shock Lorentz factor Gamma_sh >> 1, markedly steeper than for isotropic scattering downstream. The acceleration timescale t_acc in the upstream rest frame becomes a fraction of Larmor time t_L in the ultra-relativistic limit, t_acc ~ 10 t_L/Gamma_sh. Astrophysical applications are discussed, in particular the acceleration in gamma-ray bursts internal and external shocks.Comment: 11 pages; 10 figures; submitted to MNRA

Inhomogeneous extragalactic magnetic fields and the second knee in the cosmic ray spectrum

Various experiments indicate the existence of a second knee around energy E=3.10^{17} eV in the cosmic ray spectrum. This feature could be the signature of the end of the galactic component and of the emergence of the extragalactic one, provided that the latter cuts off at low energies. Recent analytical calculations have shown that this cut-off could be a consequence of the existence of extragalactic magnetic fields: low energy protons diffuse on extragalactic magnetic fields and cannot reach the observer within a given time. We study the influence of inhomogeneous magnetic fields on the magnetic horizon, using a new semi-analytical propagation code. Our results indicate that, at a fixed value of the volume averaged magnetic field , the amplitude of the low energy cut-off is mainly controled by the strength of magnetic fields in the voids of the large scale structure distribution.Comment: 15 pages, 10 figures. Version to appear in PRD (minor changes

Anisotropy vs chemical composition at ultra-high energies

This paper proposes and discusses a test of the chemical composition of ultra-high energy cosmic rays that relies on the anisotropy patterns measured as a function of energy. In particular, we show that if one records an anisotropy signal produced by heavy nuclei of charge Z above an energy E_{thr}, one should record an even stronger (possibly much stronger) anisotropy at energies >E_{thr}/Z due to the proton component that is expected to be associated with the sources of the heavy nuclei. This conclusion remains robust with respect to the parameters characterizing the sources and it does not depend at all on the modelling of astrophysical magnetic fields. As a concrete example, we apply this test to the most recent data of the Pierre Auger Observatory. Assuming that the anisotropy reported above 55EeV is not a statistical accident, and that no significant anisotropy has been observed at energies <10EeV, we show that the apparent clustering toward Cen A cannot be attributed to heavy nuclei. Similar conclusions are drawn regarding the apparent excess correlation with nearby active galactic nuclei. We then discuss a robust lower bound to the magnetic luminosity that a source must possess in order to be able to accelerate particles of charge Z up to 100EeV, L_B>10^{45}Z^{-2}erg/s. Using this bound in conjunction with the above conclusions, we argue that the current PAO data does not support the model of cosmic ray origin in active radio-quiet or even radio-loud galaxies. Finally, we demonstrate that the apparent clustering in the direction of Cen A can be explained by the contribution of the last few gamma-ray bursts or magnetars in the host galaxy thanks to the scattering of the cosmic rays on the magnetized lobes.Comment: 10 pages, 3 figure

Generation of gravitational waves during early structure formation between cosmic inflation and reheating

In the pre-reheating era, following cosmic inflation and preceding radiation domination, the energy density may be dominated by an oscillating massive scalar condensate, such as is the case for quadratic chaotic inflation. We have found in a previous paper that during this period, a wide range of sub-Hubble scale perturbations are subject to a preheating instability, leading to the growth of density perturbations ultimately collapsing to form non-linear structures. We compute here the gravitational wave signal due to these structures in the linear limit and present estimates for emission in the non-linear limit due to various effects: the collapse of halos, the tidal interactions, the evaporation during the conversion of the inflaton condensate into radiation and finally the ensuing turbulent cascades. The gravitational wave signal could be rather large and potentially testable by future detectors.Comment: 11 pages, 3 figure

On the efficiency of Fermi acceleration at relativistic shocks

It is shown that Fermi acceleration at an ultra-relativistic shock wave cannot operate on a particle for more than 1 1/2 Fermi cycle (i.e., u -> d -> u -> d) if the particle Larmor radius is much smaller than the coherence length of the magnetic field on both sides of the shock, as is usually assumed. This conclusion is shown to be in excellent agreement with recent numerical simulations. We thus argue that efficient Fermi acceleration at ultra-relativistic shock waves requires significant non-linear processing of the far upstream magnetic field with strong amplification of the small scale magnetic power. The streaming or transverse Weibel instabilities are likely to play a key role in this respect.Comment: 4 pages, 2 figures; to appear in ApJ Letter

Distortion of the ultrahigh energy cosmic ray flux from rare transient sources in inhomogeneous extragalactic magnetic fields

Detecting and characterizing the anisotropy pattern of the arrival directions of the highest energy cosmic rays are crucial steps towards the identification of their sources. We discuss a possible distortion of the cosmic ray flux induced by the anisotropic and inhomogeneous distribution of extragalactic magnetic fields in cases where sources of ultrahigh energy cosmic rays are rare transient phenomena, such as gamma-ray bursts and/or newly born magnetars. This distortion does not involve an angular deflection but the modulation of the flux related to the probability of seeing the source on an experiment lifetime. To quantify this distortion, we construct sky maps of the arrival directions of these highest energy cosmic rays for various magnetic field configurations and appeal to statistical tests proposed in the literature. We conclude that this distortion cannot affect present experiments but should be considered when performing anisotropy studies with future large-scale experiments that record as many as hundreds of events above 6x10^19 eV.Comment: 9 pages, 6 figures, accepted by A&

Relativistic Shocks: Particle Acceleration and Magnetization

We review the physics of relativistic shocks, which are often invoked as the sources of non-thermal particles in pulsar wind nebulae (PWNe), gamma-ray bursts (GRBs), and active galactic nuclei (AGN) jets, and as possible sources of ultra-high energy cosmic-rays. We focus on particle acceleration and magnetic field generation, and describe the recent progress in the field driven by theory advances and by the rapid development of particle-in-cell (PIC) simulations. In weakly magnetized or quasi parallel-shocks (where the magnetic field is nearly aligned with the flow), particle acceleration is efficient. The accelerated particles stream ahead of the shock, where they generate strong magnetic waves which in turn scatter the particles back and forth across the shock, mediating their acceleration. In contrast, in strongly magnetized quasi-perpendicular shocks, the efficiencies of both particle acceleration and magnetic field generation are suppressed. Particle acceleration, when efficient, modifies the turbulence around the shock on a long time scale, and the accelerated particles have a characteristic energy spectral index of ~ 2.2 in the ultra-relativistic limit. We discuss how this novel understanding of particle acceleration and magnetic field generation in relativistic shocks can be applied to high-energy astrophysical phenomena, with an emphasis on PWNe and GRB afterglows.Comment: 32 pages; 9 figures; invited topical review, comments welcome; submitted for publication in "The Strongest Magnetic Fields in the Universe" (Space Sciences Series of ISSI, Springer), Space Science Review