Diffusive shock acceleration (DSA) at relativistic shocks is expected to be an important acceleration mechanism in a variety of astrophysical objects including extragalactic jets in active galactic nuclei and gamma ray bursts. These sources remain good candidate sites for the generation of ultra-high energy cosmic rays. In this paper, key predictions of DSA at relativistic shocks that are germane to production of relativistic electrons and ions are outlined. The technique employed to identify these characteristics is a Monte Carlo simulation of such diffusive acceleration in test-particle, relativistic, oblique, magnetohydrodynamic (MHD) shocks. Using a compact prescription for diffusion of charges in MHD turbulence, this approach generates particle angular and momentum distributions at any position upstream or downstream of the shock. Simulation output is presented for both small angle and large angle scattering scenarios, and a variety of shock obliquities including superluminal regimes when the de Hoffmann-Teller frame does not exist. The distribution function power-law indices compare favorably with results from other techniques. They are found to depend sensitively on the mean magnetic field orientation in the shock, and the nature of MHD turbulence that propagates along fields in shock environs. An interesting regime of flat spectrum generation is addressed; we provide evidence for it being due to shock drift acceleration, a phenomenon well-known in heliospheric shock studies. The impact of these theoretical results on blazar science is outlined. Specifically, Fermi-LAT gamma-ray observations of these relativistic jet sources are providing significant constraints on important environmental quantities for relativistic shocks, namely the field obliquity, the frequency of scattering and the level of field turbulence.
Collisionless magneto-hydrodynamic (MHD) shocks are found in diverse environments ranging from the inner heliosphere to the central regions of distant galaxies and other astrophysical objects. Particle acceleration at these collisionless shocks is believed to be a common phenomenon in space plasmas. In the heliosphere, direct measurements of accelerated non-thermal ions and electrons in various energy ranges at the Earth's bow shock (e.g. Scholer et al., 1980, Möbius et al., 1987and Gosling et al., 1989) and interplanetary shocks (e.g., Sarris & Van Allen, 1974;Decker et al. 1981;Tan et al. 1988;Baring et al. 1997) indicate energization processes that are intimately connected to shock environs. Outside the heliosphere, non-thermal particle distributions are inferred from observed photon spectra of supernova remnants, pulsar wind nebulae, blazars, and gamma-ray bursts (e.g. Blandford & Eichler, 1987, and references therein), all of which possess supersonic outflows that are readily shocked. Commonly, these non-thermal distributions take the form of power-law tails that can extend to thousands or millions of times the ambient thermal energies of the particles.
First-order Fermi acceleration, often called diffusive shock acceleration (DSA), is believed to be the primary acceleration mechanism in most collisionless MHD shocks. This phenomenon arises when charged particles interact quasi-elastically with tur-bulent fields in the shock layer, and are diffusively transported back and forth across the shock, each time achieving a net gain in energy on average. Monte Carlo simulations of this process (see Jones and Ellison, 1991, and references therein) have had great success in modeling shocks inside the heliosphere and comparing them directly with in-situ measurements from various spacecraft (e.g. Ellison et al., 1990b;Baring et al., 1997;Summerlin & Baring, 2006). It is quite likely that this same process is responsible for the power-law tails inferred in astrophysical shocks, including relativistic MHD discontinuites such as those believed to be associated with blazars (e.g. see Stecker, Baring & Summerlin 2007) and gamma-ray bursts (e.g. see reviews by Piran 1999;Mészáros, 2001).
Early work on relativistic shocks was mostly analytic in the test-particle approximation (e.g., Peacock 1981;Kirk & Schneider 1987;Heavens & Drury 1988;Kirk & Heavens 1989), where the accelerated particles do not contribute significantly to the global MHD structure of the shock. Since such systems are inherently anisotropic, due to rapid convection of particles through and away downstream of the shock, the diffusion approximation cannot be applied. This renders analytic approaches, such as solution of the diffusion-convection Fokker-Planck equation, more difficult for ultra-relativistic upstream flows, though advances can be made in special cases, such as the limit of extremely small angle scattering (e.g. Kirk & Schnei-1 der 1987;Kirk et al. 2000). Accordingly, complementary Monte Carlo techniques, first developed for non-relativistic shock applications by Ellison, Jones & Eichler (1981), have been employed for relativistic shocks by a number of authors, including testparticle analyses for steady-state shocks of parallel and oblique magnetic fields by Ellison et al. (1990a), Ostrowski (1991), Bednarz & Ostrowski (1998), Baring (1999), Niemiec & Ostrowski (2004), Ellison & Double (2004) and Stecker, Baring & Summerlin (2007). It is such a simulational approach that is highlighted here; its accessibility to broad dynamic ranges in momenta is extremely desirable, providing a niche for Monte Carlo techniques in connecting with observations of astronomical objects such as gamma-ray bursts (GRBs) and blazars.
It should be noted that the most comprehensive way to study dissipation, acceleration and wave generation in collisionless shocks is with particle-in-cell (PIC) simulations, where particle motion and field fluctuations are obtained as solutions of the Newton-Lorentz and Maxwell’s equations. Relativistic PIC codes have blossomed to model shocks in applications such as GRBs and pulsar wind termination shocks, focusing largely, but not exclusively, on perpendicular shocks (e.g. Gallant et al. 1992;Smolsky & Usov 1996;Silva et al. 2003;Hededal et al. 2004;Liang & Nishimura 2004;Medvedev et al. 2005;Nishikawa et al. 2005;and Spitkovsky 2008). These works have explored pair shocks, ion-doped shocks, Poynting flux-dominated outflows, and low-field systems with dissipation driven by the Weibel instability. PIC simulations are dynamic in nature, and rarely achieve a time-asymptotic state. None of these works has demonstrated the establishment of an extended power-law that is required in modeling emission from gamma-ray bursts and active galactic nuclei, though note the isolated recent suggestion (Spitkovsky, 2008;Sironi & Spitkovsky 2011) of a non-thermal tail generated by diffusive transport. The general difficulty with explicitly seeing ac
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