16 pages, 3 figures. Proceedings of the conference "Supernovae: lights in the darkness" (XXIII Trobades Cientifiques de la Mediterrania), October 3-5, 2007, Mao, Menorca (Spain). Published by PoS. v2: two minor changes in Sect. 3
Galactic cosmic rays are widely believed to be accelerated in expanding shock waves initiated by supernova explosions. The theory of diffusive shock acceleration of cosmic rays is now well established, but two fundamental questions remain partly unanswered: what is the acceleration efficiency, i.e. the fraction of the total supernova energy converted to cosmic-ray energy, and what is the maximum kinetic energy achieved by particles accelerated in supernova explosions? Recent observations of supernova remnants, in X-rays with the Chandra and XMM-Newton satellites and in very-high-energy gamma rays with several ground-based atmospheric Cerenkov telescopes, have provided new pieces of information concerning these two questions. After a review of these observations and their current interpretations, I show that complementary information on the diffusive shock acceleration process can be obtained by studying the radio emission from extragalactic supernovae. As an illustration, a nonlinear model of diffusive shock acceleration is applied to the radio light curves of the supernova SN 1993J, which exploded in the nearby galaxy M81. The results of the model suggest that most of the Galactic cosmic rays may be accelerated during the early phase of interaction between the supernova ejecta and the wind lost from the progenitor star.
Using the Monte Carlo simulations we apply a method of discrete small amplitude particle momentum scattering to reproduce highly anisotropic conditions at relativistic shocks. We discusse acceleration times scales in relativistic shocks. Next, we describe newly found acceleration mechanism at ultrarelativistic shocks. The universal spectral index and the acceleration time for the shocks are given. In the end reflections from ultrarelativistic shocks are considered.
Reconnection shocks in a magnetically dominated plasma must be compressive. Non-thermal ion acceleration can occur across built-in slow shocks, and across outflow fast shocks when the outflow is supermagnetosonic and the field is line-tied. Electron acceleration may be initiated by injection from the dissipation region. Reconnection and shock acceleration thus cooperate and non-thermal acceleration should be a characteristic feature.
The acceleration mechanism at ultrarelativistic shocks is investigated using the Monte Carlo simulations. We apply a method of discrete small amplitude particle momentum scattering to reproduce highly anisotropic conditions at the shock and carefully describe the acceleration mechanism. The obtained acceleration times equal $1.0 r_{g}/c$ if the spectral index reach the value of 2.2, independent of physical conditions in the shock. Some other parameters of the acceleration process are also provided.
A comprehensive review is given of the various processes proposed for accelerating particles by shocks to high energies. These energies are limited by several bounds: the non-relativistic nature of the heliospheric collisionless shocks to which this review restricts, the finite size of these shocks, the finite width of the downstream region, and to the nature of turbulence. In general, collisionless shocks in the heliosphere cannot accelerate particles to very high energies. As a fundamental problem of the acceleration mechanism the injection of see particles is identified. Some mecchanisms fo…
Electron acceleration mechanism at high Mach number collisionless shocks propagating in a weakly magnetized medium is investigated by a self-consistent two-dimensional particle-in-cell simulation. Simulation results show that strong electrostatic waves are excited via the electron-ion electrostatic two-stream instability at the leading edge of the shock transition region as in the case of earlier one-dimensional simulations. We observe strong electron acceleration that is associated with the turbulent electrostatic waves in the shock transition region. The electron energy spectrum in the shock…
Theoretical studies of cosmic ray particle acceleration in the first-order Fermi process at relativistic shocks are reviewed. At the beginning we discuss the acceleration processes acting at mildly relativistic shock waves. An essential role of oblique field configurations and field perturbations in forming the particle energy spectrum and changing the acceleration time scale is discussed. Then, we report on attempts to consider particle acceleration at ultra-relativistic shocks, often yielding an asymptotic spectral index sigma = 2.2 at large shock Lorentz factors. We explain why this result …
The first-order cosmic ray acceleration at ultrarelativistic shocks is investigated using the Monte Carlo method. We apply a method of discrete particle momentum scattering as a model of particle pitch angle diffusion to reproduce highly anisotropic conditions at the shock wave. Shocks with Lorentz factors $γ$ up to 320 and varying magnetic field inclinations $ψ$ are considered. Values of diffusion coefficients upstream in the point where energy spectral indices stabilize to the limit 2.2 were calculated. The obtained acceleration time does not depend on shock conditions.
The acceleration of charged particles at astrophysical collisionless shock waves is one of the best studied processes for the energization of particles to ultrarelativistic energies, required by multifrequency observations in a variety of astrophysical situations. In this paper we discuss some work aimed at describing one of the main progresses made in the theory of shock acceleration, namely the introduction of the non-linear backreaction of the accelerated particles onto the shocked fluid. The implications for the investigation of the origin of ultra high energy cosmic rays will be discussed…
We suggest that non-thermal emission can be produced by multiple scatterings of the photons between the supernova ejecta and pre-shock material in supernova shock breakout. Such bulk-Comptonization process may significantly change the original thermal photon spectrum, forming a power-law non-thermal component at higher energies. We then show that the luminous X-ray outburst XRO081009 associated with SN2008D is likely to be such shock breakout emission from an ordinary type Ib/c supernova.
I review the current status of Fermi acceleration theory at relativistic shocks. I first discuss the relativistic shock jump conditions, then describe the non-relativistic Fermi mechanism and the differences introduced by relativistic flows. I present numerical calculations of the accelerated particle spectrum, and examine the maximum energy attainable by this process. I briefly consider the minimum energy for Fermi acceleration, and a possible electron pre-acceleration mechanism.
Cosmic ray particles are more rapidly accelerated in oblique shocks, with the magnetic field inclined with respect to the shock normal direction, than in parallel shocks, as a result of mirror reflection at the shock surface and slower diffusion in the shock normal direction. We investigate quantitatively how these effects contribute to reducing the acceleration time over the whole range of magnetic field inclinations. It is shown that, for quasi-perpendicular inclination, the mirror effect plays a remarkable role in reducing the acceleration time; whereas, at relatively small inclination, the…
We present both numerical and semi-analytical results on test-particle acceleration in multiple parallel shocks. We apply a kinetic Monte Carlo code and an eigenfunction expansion method to calculate the distribution functions for electron populations accelerated in subsequent parallel shocks with speeds ranging from non- to fully-relativistic. We examine the levels of particle anisotropy at the shocks and discuss the implications for AGN and microquasar jets.
We report studies on first-order Fermi acceleration in parallel modified shock waves with a large scattering center compression ratio expected from turbulence transmission models. Using a Monte Carlo technique we have modeled particle acceleration in shocks with a velocity ranging from nonrelativistic to ultrarelativistic and a thickness extending from nearly steplike to very wide structures exceeding the particle diffusion length by orders of magnitude. The nonrelativistic diffusion approximation is found to be surprisingly accurate in predicting the spectral index of a thick shock with large…
Theory of the first-order Fermi acceleration of cosmic ray particles at relativistic shock waves is reviewed. We consider shocks with parallel and oblique, sub- and super-luminal magnetic field configurations and with finite-amplitude magnetic field perturbations. A role of oblique field configurations and field perturbations in forming the cosmic ray energy spectrum and changing the acceleration time scale is discussed.
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 …
Studies of energetic particle acceleration at collisionless shocks by the diffusive shock acceleration process indicate that completely smooth cosmic ray dominated shock structures are possible. The existence of these is discussed and conditions for their existence derived. It is shown that such solutions cannot dominate the evolution of supernova remnants if the particle diffusion coefficient has the expected strong momentum dependence To appear in Astronomy and Astrophysics, July 1995, vol 299 pp 222-224
Electron injection process at high Mach number collisionless quasi-perpendicular shock waves is investigated by means of one-dimensional electromagnetic particle-in-cell simulations. We find that energetic electrons are generated through the following two steps: (1) electrons are accelerated nearly perpendicular to the local magnetic field by shock surfing acceleration at the leading edge of the shock transition region. (2) the preaccelerated electrons are further accelerated by shock drift acceleration. As a result, energetic electrons are preferentially reflected back to the upstream. Shock …
The linear theory of shock acceleration predicts the maximum particle energy to be limited only by the acceleration time and the size of the shock. We study the combined effect of acceleration nonlinearity (shock modification by accelerated particles, that must be present in strong astrophysical shocks) and propagation of Alfven waves that are responsible for particle confinement to the shock front. We show that wave refraction to larger wave numbers in the nonlinearly modified flow causes enhanced losses of particles in the momentum range p_max/R < p < p_max, where R>1 is the nonlinear pre-co…
We review the present status of the cosmic ray acceleration theory in mildly relativistic shock waves. Due to the involved substantial particle anisotropies analytical methods can tackle only simple situations involving weakly turbulent conditions near the shock. The numerical Monte Carlo methods are used to study the acceleration process in more general conditions. Contrary to non-relativistic shocks, the cosmic ray spectra at relativistic shock waves depend substantially on the magnetic field configurations and turbulence spectra. Depending on these conditions both very flat and very steep s…
Particle acceleration in collisionless astrophysical shocks, i.e., diffusive shock acceleration (DSA), is the most likely mechanism for producing cosmic rays, at least below 10^{15} eV. Despite the success of this theory, several key elements, including the injection of thermal particles, remains poorly understood. We investigate injection in strongly nonlinear shocks by comparing a semi-analytic model of DSA with a Monte Carlo model. These two models treat injection quite differently and we show, for a particular set of parameters, how these differences influence the overall acceleration effi…
Nonthermal particles can be produced due to incomplete thermalization at collisionless shocks and further accelerated to very high energies via diffusive shock acceleration. In a previous study we explored the cosmic ray (CR) acceleration at cosmic shocks through numerical simulations of CR modified, quasi-parallel shocks in 1D plane-parallel geometry with the physical parameters relevant for the shocks emerging in the large scale structure formation of the universe (Kang & Jones 2002). In order to consider the CR acceleration at shocks with a broader range of physical properties, in this cont…
Relativistic shocks provide an efficient method for high-energy particle acceleration in many astrophysical sources. Multiple shock systems are even more effective and of importance, for example, in the internal shock model of gamma-ray bursts. We investigate the reacceleration of pre-existing energetic particles at such relativistic internal shocks by the first order Fermi process of pitch angle scattering. We use a well established eigenfunction method to calculate the resulting spectra for infinitely thin shocks. Implications for GRBs and relativistic jets are discussed.
Particle acceleration at astrophysical shocks may be very efficient if magnetic scattering is self-generated by the same particles. This nonlinear process adds to the nonlinear modification of the shock due to the dynamical reaction of the accelerated particles on the shock. Building on a previous general solution of the problem of particle acceleration with arbitrary diffusion coefficients (Amato & Blasi, 2005), we present here the first semi-analytical calculation of particle acceleration with both effects taken into account at the same time: charged particles are accelerated in the backgrou…
First order Fermi acceleration at astrophysical shocks is often invoked as a mechanism for the generation of non-thermal particles. This mechanism is especially simple in the approximation that the accelerated particles behave like test particles, not affecting the shocked fluid. Many complications enter the calculations when the accelerated particles have a backreaction on the fluid, in which case we may enter the non linear regime of shock acceleration. In this paper we summarize the main features of a semi-analytical approach to the study of the non linearity in shock acceleration, and comp…
We investigate the diffusive shock acceleration in the presence of the non-resonant streaming instability introduced by Bell (2004). The numerical MHD simulations of the magnetic field amplification combined with the analytical treatment of cosmic ray acceleration permit us to calculate the maximum energy of particles accelerated by high-velocity supernova shocks. The estimates for Cas A, Kepler, SN1006, and Tycho historical supernova remnants are given. We also found that the amplified magnetic field is preferentially oriented perpendicular to the shock front downstream of the fast shock. Thi…
In the present paper we discuss the modifications introduced into the first-order Fermi shock acceleration process due to a finite extent of diffusive regions near the shock or due to boundary conditions leading to an increased particle escape upstream and/or downstream the shock. In the considered simple example of the planar shock wave we idealize the escape phenomenon by imposing a particle escape boundary at some distance from the shock. Presence of such a boundary (or boundaries) leads to coupled steepening of the accelerated particle spectrum and decreasing of the acceleration time scale…
We study the first-order Fermi acceleration process at parallel shock waves by means of Monte Carlo simulations. A 'realistic' model of the magnetic field turbulence is applied involving sinusoidal waves imposed on the background mean field parallel to the shock normal. The finite-amplitude magnetic field perturbations lead to locally oblique field configurations at the shock and the respective magnetic field compression. It results in modification of the particle acceleration process introducing some features observed in oblique shocks, e.g. particle reflections from the shock. For the parall…
Accretion flows onto supergalactic-scale structures are accompanied with large spatial scale shock waves. These shocks were postulated as possible sources of ultra-high energy cosmic rays. The highest particle energies were expected for perpendicular shock configuration in the so-called "Jokipii diffusion limit", involving weakly turbulent conditions in the large-scale magnetic field imbedded in the accreting plasma. For such configuration we discuss the process limiting the highest energy that particles can obtain in the first-order Fermi acceleration process due to finite shock extensions to…
Spectroscopic observations of the 2006 outburst of RS Oph at both infrared (IR) and X-ray wavelengths have shown that the blast wave has decelerated at a higher rate than predicted by the standard test-particle adiabatic shock-wave model. The observed blast-wave evolution can be explained, however, by the diffusive shock acceleration of particles at the forward shock and the subsequent escape of the highest energy ions from the acceleration region. Nonlinear particle acceleration can also account for the difference of shock velocities deduced from the IR and X-ray data. We discuss the evolutio…
Collisionless shocks play a role in many astrophysical phenomena, from coronal mass ejections (CMEs) in the heliosphere to supernova remnants. Their role in heating and accelerating particles is well accepted yet the exact mechanism for ion heating is not well understood. Two systems, CMEs and supernova remnants, were examined to determine the heating of heavy ions as they pass through collisionless shocks thus providing a seed population for cosmic ray acceleration processes. Three parameters are examined, the plasma beta, the Mach number of the shock and the magnetic angle of the shock. CMEs…
The non-linear back reaction of accelerated cosmic rays at the shock fronts, leads to the formation of a smooth precursor with a length scale corresponding to the diffusive scale of the energetic particles. Past works claimed that shocklets could be created in the precursor region of a specific shock width, which might energize few thermal particles to sufficient acceleration and furthermore this precursor region may act as confining large angle scatterer for very high energy cosmic rays. On the other hand, it has been shown that the smoothing of the shock front could lower the acceleration ef…
The observations of a nearby low-luminosity gamma-ray burst (GRB) 060218 associated with supernova SN 2006aj may imply an interesting astronomical picture where a supernova shock breakout locates behind a relativistic GRB jet. Based on this picture, we study neutrino emission for early afterglows of GRB 060218-like GRBs, where neutrinos are expected to be produced from photopion interactions in a GRB blast wave that propagates into a dense wind. Relativistic protons for the interactions are accelerated by an external shock, while target photons are basically provided by the incoming thermal em…
The effect of the shock propagation on neutrino oscillation in supernova is studied paying attention to evolution of average energy of $ν_{e}$ and $\barν_{e}$. We show that the effect appears as a decrease in average $ν_{e}$ (in case of inverted mass hierarchy, $\barν_{e}$) energy at stellar surface as the shock propagates. It is found that the effect is significant 2 seconds after bounce if $3 \times 10^{-5} < \sin^{2}{θ_{13}} < 10^{-2}$.
Spectroscopic observations of the 2006 outburst of the recurrent nova RS Ophiuchi at both infrared (IR) and X-ray wavelengths have shown that the blast wave has decelerated at a higher rate than predicted by the standard test-particle adiabatic shock-wave model. Here we show that the observed evolution of the nova remnant can be explained by the diffusive shock acceleration of particles at the blast wave and the subsequent escape of the highest energy ions from the shock region. Nonlinear particle acceleration can also account for the difference of shock velocities deduced from the IR and X-ra…
In this paper we present an investigation of numerical Monte Carlo simulations of the diffusive shock acceleration in the test particle limit. Very high gamma flow astrophysical plasmas, have been used, from $γ_{up}$ $\sim50$ up to $γ_{up}$ $\sim1000$, which could be relevant to the suggested models of AGNs Jets and their Central Engines as well as the ultra-relativistic shock particle acceleration in Gamma Ray Burst (GRB) fireballs. Particularly the energy gain per shock crossing and the time constant for the above high relativistic processes is numerically calculated. We explicitly find a co…
We investigate the role of the form of the spatial diffusion coefficient in shock acceleration of fast particles. Referring to non-classical diffusion and using the results of numerical (hybrid) simulations tailored for the downstream shock population in quasi-perpendicualr high-Mach number collisionless shocks to which we apply the theory, we demonstrate that the inferred diffusion coefficients are in excellent agreement with the requirements of the theory and its predictions. Diffusion in the collisionless regime turns out to be non-classical Gibbsian (Lévy flight), time-dependent though wea…
Heliospheric shocks are excellent systems for testing theories of particle acceleration in their environs. These generally fall into two classes: (1) interplanetary shocks that are linear in their ion acceleration characteristics, with the non-thermal ions serving as test particles, and (2) non-linear systems such as the Earth's bow shock and the solar wind termination shock, where the accelerated ions strongly influence the magnetohydrodynamic structure of the shock. This paper explores the modelling of diffusive acceleration at a particular interplanetary shock, with an emphasis on explainin…
We present results from a fully relativistic Monte Carlo simulation of diffusive shock acceleration (DSA) in unmodified (i.e., test-particle) shocks. The computer code uses a single algorithmic sequence to smoothly span the range from nonrelativistic speeds to fully relativistic shocks of arbitrary obliquity, providing a powerful consistency check. We show the dependence of the particle spectrum, which can differ strongly from the canonical f(p) proportional to p^{-4.23} result, on the obliquity and on the strength and ``fineness'' of scattering for a range of shock Lorentz factors. The Monte …
We present results from a fully relativistic Monte Carlo simulation of diffusive shock acceleration (DSA) in unmodified shocks. The computer code uses a single algorithmic sequence to smoothly span the range from nonrelativistic speeds to fully relativistic shocks of arbitrary obliquity, providing a powerful consistency check. While known results are obtained for nonrelativistic and ultra-relativistic parallel shocks, new results are presented for the less explored trans- relativistic regime and for oblique, fully relativistic shocks. We find, for a wide trans-relativistic range extending to s…
Direct comparisons of diffusive particle acceleration numerical simulations have been made against Monte Carlo and hybrid plasma simulations by Ellison {\it et. al.} (1993) and against observations at the earth's bow shock presented by Ellison {\it et. al.} (1990). Toward this end we have introduced a new numerical scheme for injection of cosmic-ray particles out of the thermal plasma, modeled by way of the diffusive scattering process itself; that is, the diffusion and acceleration across the shock front of particles out of the suprathermal tail of the Maxwellian distribution. We find that al…
A full particle simulation study is carried out on the electron acceleration at a collisionless, relatively low Alfven Mach number (M_A=5), perpendicular shock. Recent self-consistent hybrid shock simulations have demonstrated that the shock front of perpendicular shocks has a dynamic rippled character along the shock surface of low-Mach-number perpendicular shocks. In this paper, the effect of the rippling of perpendicular shocks on the electron acceleration is examined by means of large-scale (ion-scale) two-dimensional full particle simulations. It has been shown that a large-amplitude elec…
The present work considers diffusive shock acceleration at non-relativistic shocks using a system of stochastic differential equations (SDE) equivalent to the Fokker-Planck equation. We compute approximate solutions of the transport of cosmic particles at shock fronts with a SDE numerical scheme. The momentum gain is given by implicit calculations of the fluid velocity gradients using a linear interpolation between two consecutive time steps. We validate our procedure in the case of single shock acceleration with different shock thickness, with or without synchrotron losses. A comparative disc…
The properties of cosmic shock waves are studied through numerical simulations in two cosmological scenarios (SCDM and LCDM). The scaling relations for the average radius and velocity associated with the accretion shocks are somewhat different, yet qualitatively similar to the self similar solutions for a flat Omega_M=1 universe. The energy supplied by infalling gas at accretion shock waves is large enough to sustain production of abundant cosmic ray populations if a viable acceleration mechanism can take place there. Finally, in addition to shocks created by the encounter of the merging ICMs …
Chandra X-ray observations of the 1 E0657-56 galaxy cluster diffuse emission reveal the existence of large scale cluster merger shock. We study the observed radio and X-ray data of this cluster as a possible result of the diffusive shock acceleration. This model can explain the observations within reasonable ranges of physical parameters for the shock and the intracluster medium. The expected nonthermal soft and hard X-ray fluxes are predicted.
Numerical results for particle acceleration at multiple oblique shocks are presented. We calculate the steady state spectral slope of test particles accelerated by the first order Fermi process. The results are compared to analytical treatments, for parameters, where the diffusion approximation does apply. Effects of injection and finite shock extend are included phenomenologically. We find the spectrum of accelerated particles to harden substantially at multiple oblique shocks and discuss the influence of the number of shocks compared to the obliquity itself.
First-order Fermi acceleration processes at ultrarelativistic shocks are studied with Monte Carlo simulations. The accelerated particle spectra are obtained by integrating the exact particle trajectories in a turbulent magnetic field near the shock, with a few ``realistic'' features of the field structure included. We show that the main acceleration process at oblique shocks is the particle compression at the shock. Formation of energetic spectral tails is possible in a limited energy range for highly perturbed magnetic fields. Cut-offs in the spectra occur at low energies in the resonance ran…
A review of the main issues in the field of particle acceleration in Supernova Remnants is provided in the context of future X-ray observations with Simbol-X. After a summary of the nonthermal acceleration mechanisms at work, I briefly review the observations of supernova remnants in hard X-rays and in gamma rays. Open issues are discussed in this framework.
The rate at which particles are accelerated by the first-order Fermi mechanism in shocks depends on the angle, \teq{\Tbone}, that the upstream magnetic field makes with the shock normal. The greater the obliquity the greater the rate, and in quasi-perpendicular shocks rates can be hundreds of times higher than those seen in parallel shocks. In many circumstances pertaining to evolving shocks (\eg, supernova blast waves and interplanetary traveling shocks), high acceleration rates imply high maximum particle energies and obliquity effects may have important astrophysical consequences. However, …
We study the suprathermal electron acceleration mechanism in a perpendicular magnetosonic shock wave in a high Mach number regime by using a particle-in-cell simulation. We find that shock surfing/surftron acceleration producing the suprathermal electrons occurs in the shock transition region where a series of large amplitude electrostatic solitary waves (ESWs) are excited by Buneman instability under the interaction between the reflected ions and the incoming electrons. It is shown that the electrons are likely to be trapped by ESWs, and during the trapping phase they can be effectively accel…
The limits imposed on diffusive shock acceleration by upstream ion-neutral Alfven wave damping, and by ionisation and Coulomb losses of low energy particles, are calculated. Analytic solutions are given for the steady upstream wave excitation problem with ion-neutral damping and the resulting escaping upstream flux calculated. The time dependent problem is discussed and numerical solutions presented. Finally the significance of these results for possible observational tests of shock acceleration in supernova remnants is discussed.
The nonthermal radiation observed from a handfull of clusters of Galaxies is the proof that particle acceleration occurs in the intracluster medium. It is often believed that shock surfaces associated with either mergers of clusters of galaxies, or with the cosmological inflow of matter onto clusters during structure formation may be the sites for acceleration. We discuss here the effectiveness of shock acceleration in the intracluster medium, stressing that merger related shocks are typically weak, at least for the so-called major mergers. We investigate the implications of shock strengths fo…
Fermi acceleration can take place at ultra-relativistic shock waves if the upstream or downstream magnetic field has been remodeled so that most of the magnetic power lies on short spatial scales. The relevant conditions under which Fermi acceleration become efficient in the presence of both a coherent and a short scale turbulent magnetic field are addressed. Within the MHD approximation, this paper then studies the amplification of a pre-existing magnetic field through the streaming of cosmic rays upstream of a relativistic shock wave. The magnetic field is assumed to be perpendicular in the …
We perform Monte Carlo simulations of diffusive shock acceleration at highly relativistic oblique shock waves. High upstream flow Lorentz gamma factors are used, which are relevant to models of ultra relativistic particle shock acceleration in Active Galactic Nuclei (AGN) central engines and relativistic jets and Gamma Ray Burst (GRB) fireballs. We investigate numerically the acceleration properties -in the ultra relativistic flow regime of $Γ\sim 10-10^{3}$- such as angular distribution, acceleration time constant, particle energy gain versus number of crossings and spectral shapes. We perfor…
The mechanism of diffusive Fermi acceleration at collisionless plasma shock waves is widely invoked in astrophysics to explain the appearance of non-thermal particle populations in a variety of environments, including sites of cosmic ray production, and is observed to operate at several sites in the heliosphere. This review outlines the principal results from the theory of diffusive shock acceleration, focusing first on how it produces power-law distributions in test-particle regimes, where the shock dynamics are dominated by the thermal populations that provide the seed particles for the acce…
Diffusive acceleration at collisionless shock waves remains one of the most promising acceleration mechanisms for the description of the origin of cosmic rays at all energies. A crucial ingredient to be taken into account is the reaction of accelerated particles on the shock, which in turn determines the efficiency of the process. Here we propose a semi-analytical kinetic method that allows us to calculate the shock modification induced by accelerated particles together with the efficiency for particle acceleration and the spectra of accelerated particles. The shock modification is calculated …
The Supernova Acceleration Probe (SNAP) will use Type Ia supernovae (SNe Ia) as distance indicators to measure the effect of dark energy on the expansion history of the Universe. (SNAP's weak-lensing program is described in a companion White Paper.) The experiment exploits supernova distance measurements up to their fundamental systematic limit; strict requirements on the monitoring of each supernova's properties lead to the need for a space-based mission. Results from pre-SNAP experiments, which characterize fundamental SN Ia properties, will be used to optimize the SNAP observing strategy to…
We present results of test-particle simulations on both the first- and the second-order Fermi acceleration for relativistic parallel shock waves. Our studies suggest that the role of the second-order mechanism in the turbulent downstream of a relativistic shock may have been underestimated in the past, and that the stochastic mechanism may have significant effects on the form of the particle spectra and its time evolution.
The theory of particle acceleration at shock fronts is briefly reviewed, with special emphasis on the production of the particles responsible for the nonthermal emission from blazars. The flat radio/IR spectra of these sources cannot be produced by diffusive acceleration at a simple nonrelativistic shock front propagating in a homogeneous medium. It can, however, be produced by a single unmodified mildly relativistic shock, if the pressure in the shocked gas is provided by the leptonic component, or, independently of the equation of state, by a relativistic shock which is oblique to the magnet…
The outflows from gamma ray bursts, active galactic nuclei and relativistic jets in general interact with the surrounding media through collisionless shocks. With three dimensional relativistic particle-in-cell simulations we investigate such shocks. The results from these experiments show that small--scale magnetic filaments with strengths of up to percents of equipartition are generated and that electrons are accelerated to power law distributions N(E)~E^{-p} in the vicinity of the filaments through a new acceleration mechanism. The acceleration is locally confined, instantaneous and differs…
Cosmological hydrodynamic simulations of large scale structure in the universe have shown that accretion shocks and merger shocks form due to flow motions associated with the gravitational collapse of nonlinear structures. Estimated speed and curvature radius of these shocks could be as large as a few 1000 km/s and several Mpc, respectively. According to the diffusive shock acceleration theory, populations of cosmic-ray particles can be injected and accelerated to very high energy by astrophysical shocks in tenuous plasmas. In order to explore the cosmic ray acceleration at the cosmic shocks, …
