Cosmic ray spectrum from diffusive shock acceleration

Nonthermal radiation from supernova remnants (SNRs) provides observational evidence and constraints on the diffusive shock acceleration (DSA) hypothesis for the origins of Galactic cosmic rays (CRs). Recently it has been recognized that a variety of plasma wave-particle interactions operate at astrophysical shocks and the detailed outcomes of DSA are governed by their complex and nonlinear interrelationships. Here we calculate the energy spectra of CR protons and electrons accelerated at Type Ia SNRs, using time-dependent, DSA simulations with phenomenological models for magnetic field amplification due to CR streaming instabilities, Alf<TEX>$\acute{e}$</TEX>enic drift, and free escape boundary. We show that, if scattering centers drift with the Alf<TEX>$\acute{e}$</TEX>en speed in the amplified magnetic fields, the CR energy spectrum is steepened and the acceleration efficiency is significantly reduced at strong CR modified SNR shocks. Even with fast Afv<TEX>$\acute{e}$</TEX>nic drift, DSA can still be efficient enough to develop a substantial shock precursor due to CR pressure feedback and convert about 20-30% of the SN explosion energy into CRs. Since the high energy end of the CR proton spectrum is composed of the particles that are injected in the early stages, in order to predict nonthermal emissions, especially in X-ray and <TEX>${\gamma}-ray$</TEX> bands, it is important to follow the time dependent evolution of the shock dynamics, CR injection process, magnetic field amplification, and particle escape. Thus it is crucial to understand the details of these plasma interactions associated with collisionless shocks in successful modeling of nonlinear DSA.

Cosmological shocks form as an inevitable consequence of gravitational collapse during the large scale structure formation and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration (DSA). We have calculated the evolution of CR modified shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of DSA in 1D quasi-parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc <TEX>$\ge$</TEX> 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that <TEX>$10^{-4} - 10^{-3}$</TEX> of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The CR acceleration efficiency increases with shock Mach number, but it asymptotes to <TEX>${\~}50\%$</TEX> in high Mach number shocks, regardless of the injection rate and upstream CR pressure. On the other hand, in moderate strength shocks (<TEX>$M_s {\le} 5$</TEX>), the pre-existing CRs increase the overall CR energy. We conclude that the CR acceleration at cosmological shocks is efficient enough to lead to significant nonlinear modifications to the shock structures.

Shocks are ubiquitous in astrophysical environments and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration. It is believed that the CR pressure is important in the evolution of the interstellar medium of our galaxy and most of galactic CRs with energies up to eV are accelerated by supernova remnant shocks. In this contribution we have studied the CR acceleration at shocks through numerical simulation of 1D, quasi-parallel shocks for a wide range of shock Mach numbers and shock speeds. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies, and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number, and high Mach number shocks all evolve towards efficiencies , regardless of the injection rate and upstream CR pressure. We conclude that the injection rates in strong quasi-parallel shocks are sufficient to lead to significant nonlinear modifications to the shock structures, implying the importance of the CR acceleration at astrophysical shocks.

A numerical scheme that incorporates a injection model into a combined gasdynamics and cosmic-ray (CR) diffusion-convection code has been developed. The hydro/CR code can follow in a very cost-effective way the evolution of CR-modified planar quasi-parallel shocks by adopting subzone shock tracking and multilevel adaptive mesh refinement techniques. An additional conservative quantity, S = Pg/ργg−1, is introduced to follow the adiabatic compression accurately in the precursor region, especially in front of strong, highly modified shocks. The thermal leakage injection model is based on the nonlinear interactions of the suprathermal particles with self-generated MHD waves in quasi-parallel shocks. The particle injection is followed numerically by filtering the diffusive flux of suprathermal particles across the shock to the upstream region according to a velocity-dependent transparency function that controls the fraction of leaking particles. This function is determined by a single parameter, , which should depend on the strength of postshock wave turbulence but is modeled as a constant parameter in our simulations. We have studied CR injection and acceleration efficiencies during the evolution of CR-modified planar shocks for a wide range of initial shock Mach numbers, M0, assuming a Bohm-like diffusion coefficient. For expected values of the injection process is very efficient when the subshock is strong, leading to fast and significant modification of the shock structure. As the CR pressure increases, the subshock weakens and the injection rate decreases accordingly so that the subshock does not disappear. Although some fraction of the particles injected early in the evolution continue to be accelerated to ever higher energies, the postshock CR pressure reaches an approximate time-asymptotic value because of a balance between fresh injection/acceleration and advection/diffusion of the CR particles away from the shock. In the strong shock limit of M0 30, the injection and acceleration processes are largely independent of the initial shock Mach number for a given , while they are sensitively dependent on M0 for M0 < 30. We conclude that the injection rates in strong parallel shocks are sufficient to lead to rapid nonlinear modifications to the shock structures and that self-consistent injection and time-dependent simulations are crucial to understanding the nonlinear evolution of CR-modified shocks.

Motivated by the suggestion of Kang, Ryu \& Jones (1996) that particles can be accelerated to high energies via diffusive shock acceleration process at the accretion shocks formed by the infalling flow toward the clusters of galaxies, we have calculated the expected particle flux from a cosmological ensemble of clusters. We use the observed temperature distribution of local clusters and assume a simple power-law evolutionary model for the comoving density of the clusters. The shock parameters such as the shock radius and velocity are deduced from the ICM temperature using the self-similar solutions for secondary infall onto the clusters. The magnetic field strength is assume to be in equipartition with the postshock thermal energy behind the accretion shock. We also assume that the injected energy spectrum is a power-law with the exponential cutoff at the maximum energy which is calculated from the condition that the energy gain rate for diffusive shock acceleration is balanced by the loss rate due to the interactions with the cosmic background radiation. In contrast to the earlier paper we have adopted here the description of the cosmic ray diffusion by Jokipii (1987) which leads to considerably higher particle energies. Finally the injected particle spectrum at the clusters is integrated over the cosmological distance to earth by considering the energy loss due to the interactions with the cosmic background radiation. Our calculations show that the expected spectrum of high-energy protons from the cosmological ensemble of the cluster accretion shocks could match well the observed cosmic ray spectrum near $10^{19}$eV with reasonable parameters and models if about $10^{-4}$ of the infalling kinetic energy can be injected into the intergalactic space as the high energy particles.

Shock waves propagating in collisionless heliospheric and astrophysical plasmas have been studied extensively over the decades. One prime motivation is to understand the nonthermal particle acceleration at shocks. Although the theory of diffusive shock acceleration (DSA) has long been the standard for cosmic-ray acceleration at shocks, plasma physical understanding of particle acceleration remains elusive. In this review, we discuss nonthermal electron acceleration mechanisms at quasi-perpendicular shocks, for which substantial progress has been made in recent years. The discussion presented in this review is restricted to the following three specific topics: The first is stochastic shock drift acceleration (SSDA), which is a relatively new mechanism for electron injection into DSA. The basic mechanism, related in-situ observations and kinetic simulations results, and how it is connected with DSA will be discussed. Second, we discuss shock surfing acceleration (SSA) at very high Mach number shocks relevant to young supernova remnants (SNRs). While the original proposal under the one-dimensional assumption is unrealistic, SSA has now been proven efficient by a fully three-dimensional kinetic simulation. We discuss the multidimensional nature of SSA and its role in electron injection. Finally, we discuss the current understanding of the magnetized Weibel-dominated shock. It is essentially a magnetized shock in which the reflected-gyrating ions dominate the formation of the shock structure but with a substantial magnetic field amplification by the ion-Weibel instability. Spontaneous magnetic reconnection of self-generated current sheets within the shock structure is an interesting consequence of Weibel-generated strong magnetic turbulence. Although the exact condition for active magnetic reconnection has not been clarified, we argue that high Mach number shocks with both Alfvén and sound Mach numbers exceeding 20–40 will likely behave as a Weibel-dominated shock. Despite a number of interesting recent findings, the relative roles of SSDA, SSA, and magnetic reconnection for electron acceleration at collisionless shocks and how the dominant particle acceleration mechanisms change depending on shock parameters remain to be answered.

The cosmic-ray streaming instability creates strong magnetohydrodynamic turbulence in the precursor of a SN shock. The level of turbulence determines the maximum energy of cosmic-ray particles accelerated by the diffusive shock accelera- tion mechanism. In this paper we present the continuation of previous work (Ptuskin & Zirakashvili 2003). We assume that Kolmogorov type nonlinear wave interactions together with ion-neutral collisions restrict the amplitude of the random mag- netic field. As a result, the maximum energy of the accelerated particles strongly depends on the age of a SNR. The average spectrum of cosmic rays injected in the interstellar medium in the course of the adiabatic SNR evolution (the Sedov stage) is approximately Q(p)p 2 ∝ p −2 at energies larger than 10−30 GeV/nucleon and with a maximum particle energy that is close to the position of the knee in the cosmic-ray spectrum observed at ∼4 × 10 15 eV. At an earlier stage of SNR evolution - the ejecta-dominated stage described by the Chevalier-Nadyozhin solution, the particles are accelerated to higher energies and have a rather steep power-law distribution. These results suggest that the knee may mark the transition from the ejecta-dominated to the adiabatic evolution of SNR shocks which accelerate cosmic rays.

The direct measurements of cosmic rays (CRs), after correction for the propagation effects in the interstellar medium, indicate that their source spectra are likely to be significantly steeper than the canonical E −2 spectrum predicted by the standard diffusive shock acceleration (DSA) mechanism. The DSA has long been held responsible for the production of galactic CRs in supernova remnant (SNR) shocks. The γ-ray “probes” of the acceleration spectra of CRs on the spot, inside the SNRs, lead to the same conclusion. We show that the steep acceleration spectrum can be attributed to the combination of (i) spherical expansion, (ii) tilting of the magnetic field along the shock surface, and (iii) shock deceleration. Because of (i) and (ii), the DSA is efficient only on two “polar caps” of a spherical shock where the local magnetic field is within ≃45° to its normal. The shock-produced spectrum observed edge-on steepens with the particle energy because the number of freshly accelerated particles with lower energies continually adds up to a growing acceleration region. We demonstrate the steepening effect by obtaining an exact self-similar solution for the particle acceleration at an expanding shock surface with an arbitrary energy dependence of particle diffusivity κ. We show that its increase toward higher energy steepens the spectrum, which deeply contrasts with the standard DSA spectrum where κ cancels out.

The bi-annual International Cosmic Ray Conferences have become the most central meetings for discussing new results and recent progress in the field of cosmic ray research. The contributions to these conferences cover a wide range of subjects extending from the physics of the sun and heliosphere, over gamma-ray observations to direct and indirect cosmic ray measurements and their interpretation. Many new results are announced for the first time at these meetings. The present volume is a compilation of the contributions of Institutes of Forschungszentrum Karlsruhe and University Karlsruhe to the 30 th International Cosmic Ray Conference (ICRC), held in Merida, Mexico from July 3 to 11, 2007. The collection of contributions provides an up-to-date review of the current activities and research projects related to cosmic rays that are pursued in Karlsruhe. The articles also demonstrate the enormous progress that has been made during the last years, in particular in the field of ultra-high energy cosmic rays. Most of these contributions are the result of close and fruitful collaboration of many different groups worldwide, first of all within international collaborations such as the Pierre Auger, LOPES and KASCADE-Grande Collaborations, but also within smaller groups. The articles compiled in this report are sorted according to the main research foci of the Karlsruhe groups. These include the physics of the knee in the cosmic ray spectrum, the transition between galactic and extra-galactic cosmic rays, and extragalactic cosmic rays of the highest energies. Cosmic rays in the energy range from just below the knee in the cosmic ray spectrum (10 14.5 eV) to the energy of the conjectured transition between galactic and extra-galactic cosmic rays are studied with the KASCADE-Grande detector at the site of Forschungszentrum Karlsruhe. KASCADE-Grande is a multi-detector air shower array, which combines the electron and muon detectors of the KASCADE (KArlsruhe Shower Core and Array Detector) array with a 0.5 km 2 array of scintillators. Based on a data set from about 3 years of operation, first shower size spectra have been derived and limits on the anisotropy of the cosmic ray flux were presented at the conference. An alternative method of air shower detection is the measurement of radio signals produced by the particles showers in the atmosphere. The physics potential of this detection technique is investigated with the LOPES (LOFAR PrototypE Station) array of dipole antennas at the site of the KASCADE-Grande installation. Measuring the electric field strength in the frequency range from 40 to 80 MHz, a very good correlation between the shower energy reconstructed with KASCADE-Grande and the radio signal was found. Important contributions presented at the conference include the investigation of the influence of thunderstorms on the measured field strength and the measurement of showers with large zenith angles as well as significant progress in the modelling of the emission processes of the radio signals during the shower development. The study of cosmic rays at the highest energies and the transition between galactic and extra-galactic cosmic rays is the aim of the Pierre Auger Project. The Pierre Auger Observatory is the largest cosmic ray detector with one installation in the northern and southern hemisphere to ensure full sky coverage. The southern detector is currently under construction in the Province of Mendoza, Argentina.

Context. Supernova remnants are known to accelerate cosmic rays on account of their nonthermal emission of radio waves, X-rays, and gamma rays. Although there are many models for the acceleration of cosmic rays in supernova remnants, the escape of cosmic rays from these sources has not yet been adequately studied. Aims. We aim to use our time-dependent acceleration code RATPaC to study the acceleration of cosmic rays and their escape in post-adiabatic supernova remnants and calculate the subsequent gamma-ray emission from inverse-Compton scattering and Pion decay. Methods. We performed spherically symmetric 1D simulations in which we simultaneously solved the transport equations for cosmic rays, magnetic turbulence, and the hydrodynamical flow of the thermal plasma in a volume large enough to keep all cosmic rays in the simulation. The transport equations for cosmic rays and magnetic turbulence were coupled via the cosmic-ray gradient and the spatial diffusion coefficient of the cosmic rays, while the cosmic-ray feedback onto the shock structure can be ignored. Our simulations span 100 000 years, thus covering the free-expansion, the Sedov–Taylor, and the beginning of the post-adiabatic phase of the remnant’s evolution. Results. At later stages of the evolution, cosmic rays over a wide range of energy can reside outside of the remnant, creating spectra that are softer than predicted by standard diffusive shock acceleration, and feature breaks in the 10 − 100 GeV-range. The total spectrum of cosmic rays released into the interstellar medium has a spectral index of s ≈ 2.4 above roughly 10 GeV which is close to that required by Galactic propagation models. We further find the gamma-ray luminosity to peak around an age of 4000 years for inverse-Compton-dominated high-energy emission. Remnants expanding in low-density media generally emit more inverse-Compton radiation, matching the fact that the brightest known supernova remnants – RCW86, Vela Jr., HESS J1731−347 and RX J1713.7−3946 – are all expanding in low density environments.

Stellar winds from massive stars may be significant sources of cosmic rays (CRs). To investigate this connection, we report a detailed study of gamma-ray emission near the young Milky Way star cluster (≈0.5 Myr old) in the star-forming region RCW 38 and compare this emission to its stellar wind properties and diffuse X-ray emission. Using 15 yr of Fermi-LAT data in the 0.2–300 GeV band, we find a significant (σ > 22) detection coincident with the star cluster, producing a total gamma-ray luminosity (extrapolated over 0.1–500 GeV) of L γ =(2.66 ± 0.92) × 1034 erg s−1 adopting a power-law spectral model (Γ = 2.34 ± 0.04). Using an empirical relationship and STARBURST99, we estimate the total wind power to be 8 × 1036 erg s−1, corresponding to a CR acceleration efficiency of η CR ≃ 0.4 for an assumed diffusion coefficient consistent with D = 1028 cm2 s−1. Alternatively, a lower acceleration efficiency of 0.1 can produce this L γ if the diffusion coefficient is smaller, D ≃ 2.5 × 1027 cm2 s−1. Additionally, we analyze Chandra X-ray data from the region and compare the hot-gas pressure to the CR pressure. We find the former is 4 orders of magnitude greater, suggesting that the CR pressure is not dynamically important relative to stellar winds. As RCW 38 is too young for supernovae to have occurred, the high CR acceleration efficiency in RCW 38 demonstrates that stellar winds may be an important source of Galactic CRs.

Abstract. It is generally believed that the cosmic ray spectrum below the knee is of Galactic origin, although the exact sources making up the entire cosmic ray energy budget are still unknown. Including effects of magnetic amplification, Supernova Remnants (SNR) could be capable of accelerating cosmic rays up to a few PeV and they represent the only source class with a sufficient non-thermal energy budget to explain the cosmic ray spectrum up to the knee. Now, gamma-ray measurements of SNRs for the first time allow to derive the cosmic ray spectrum at the source, giving us a first idea of the concrete, possible individual contributions to the total cosmic ray spectrum. In this contribution, we use these features as input parameters for propagating cosmic rays from its origin to Earth using GALPROP in order to investigate if these supernova remnants reproduce the cosmic ray spectrum and if supernova remnants in general can be responsible for the observed energy budget.

Effect of energy losses and interactions during diffusive shock acceleration: applications to SNR, AGN and UHE cosmic rays

Diffusive shock acceleration is the theory of particle acceleration through multiple shock crossings. In order for this process to proceed at a rate that can be reconciled with observations of high-energy electrons in the vicinity of the shock, and for cosmic rays protons to be accelerated to energies up to observed galactic values, significant magnetic field amplification is required. In this review we will discuss various theories on how magnetic field amplification can proceed in the presence of a cosmic ray population. On both short and long scales, cosmic ray streaming can induce instabilities that act to amplify the magnetic field. Developments in this area that have occurred over the past decade are the main focus of this paper.

Galactic cosmic-ray source compositions, (Z/H)GCRS from H to Pb and ~10^8 -\n10^14 eV, differ from solar-local interstellar, (Z/H)SS or (Z/H)ISM by\n~20-200x. Both are mostly just mixes of core collapse (CCSN) and thermonuclear\n(SN Ia) supernova ejecta. The (Z/H)ISM come from steady unbiased accumulation\nover Gyrs. But the cosmic ray mass mixing ratio, universal ISM/CCSN ~4:1 of\nswept-up ISM and ~10x metallicity ejecta show that (Z/H)GCRS come from basic\nSedov-Taylor bulk mixing of homologous, expanding CCSN in their OB cluster\nself-generated superbubbles, further enriched by highly biased grain-sputtering\ninjection during diffusive shock acceleration (DSA). Moreover, this mixing\nratio now reveals that the cosmic rays are primarily accelerated as their\nevolving reverse shock radius and energy passes through their maxima.\nRefractories and volatiles, first deposited in fast ejecta and ISM grains in\nfreely expanding ejecta, are simultaneously Coulomb-sputtered FCS by turbulent\nH and He as suprathermal ions into DSA that carries them to cosmic-ray\nenergies. This bulk mixing selectively increases source mix abundancies (Z/H)SM\n/ (Z/H)SS by ~2-10; and injection by grain condensation and implantation\nfractions FGC, by another ~6, while Z^0.67 Coulomb grain sputtering enrichments\nFCS give an added ~4-20. Applying these basic processes of mixing and injection\nto solar system (Z/H)SS produces grain-injected, source-mix (Z/H)SMGI that\nmatch major cosmic ray abundances (Z/H)GCRS to within 35 % with no free\nparameters. Independently confirming grain injection, (Z/H)GCRS shows no\ndetectable contribution of Fe from SN Ia, although producing ~1/2 Fe in ISM,\nbut there is also no dust in SN Ia remnants, unlike CCSN.\n