Donald C. Ellison

The plasma physics of shock acceleration

The notion that plasma shocks in astrophysical settings can and do accelerate charged particles to high energies is not a new one. However, in recent years considerable progress has been achieved in understanding the role particle acceleration plays both in astrophysics and in the shock process itself. In this paper we briefly review the history and theory of shock acceleration, paying particular attention to theories of parallel shocks which include the backreaction of accelerated particles on the shock structure. We discuss in detail the work that computer simulations, both plasma and Monte Carlo, are playing in revealing how thermal ions interact with shocks and how particle acceleration appears to be an inevitable and necessary part of the basic plasma physics that governs collisionless shocks. We briefly describe some of the outstanding problems that still confront theorists and observers in this field.

Shock acceleration of electrons and ions in solar flares

The simultaneous first-order Fermi shock acceleration of electrons, protons, and alpha particles are compared to observations of solar energetic particle events. For each event, a unique shock compression ratio in the range of approximately 1.6-3 produces spectra in good agreement with observation. The range in compression ratios predicts that the more than five orders of magnitude spread in electron-to-proton intensity ratios observed at MeV energies is compressed to about three orders of magnitude at an assumed injection energy of 100 keV. The remaining spread can be accounted for with a modest range of injection conditions. The model predicts that the acceleration time to a given energy will be approximately equal for electrons and protons, and for reasonable solar parameters, can be on the order of 1 s to approximately 100 MeV. 37 references.

A Simple Model of Nonlinear Diffusive Shock Acceleration

We present a simple model of nonlinear diffusive shock acceleration (also called first-order Fermi shock acceleration) that determines the shock modification, spectrum, and efficiency of the process in the plane-wave, steady state approximation as a function of an arbitrary injection parameter, η. The model, which uses a three-power-law form for the accelerated particle spectrum and contains only simple algebraic equations, includes the essential elements of the full nonlinear model and has been tested against Monte Carlo and numerical kinetic shock models. We include both adiabatic and Alfven wave heating of the upstream precursor. The simplicity and ease of calculation make this model useful for studying the basic properties of nonlinear shock acceleration, as well as providing results accurate enough for many astrophysical applications. It is shown that the shock properties depend upon the shock speed u0 with respect to a critical value u ηp, which is a function of the injection rate η and maximum accelerated particle momentum pmax. For u0 MA0, or by rtot ≈ 1.5M in the opposite case (MS0 is the sonic Mach number and MA0 is the Alfven Mach number). If u0 > u, the shock, although still strong, becomes almost unmodified and accelerated particle production decreases inversely proportional to u0.

Galactic Cosmic Rays from Supernova Remnants. II. Shock Acceleration of Gas and Dust

We present a quantitative model of Galactic cosmic-ray (GCR) origin and acceleration, wherein a mixture of interstellar and/or circumstellar gas and dust is accelerated by a supernova remnant blast wave. The gas and dust are accelerated simultaneously, but differences in how each component is treated by the shock leave a distinctive signature, which we believe exists in the cosmic-ray composition data. A reexamination of the detailed GCR elemental composition, presented in a companion paper, has led us to abandon the long-held assumption that GCR abundances are somehow determined by first ionization potential. Instead, volatility and mass (presumably mass-to-charge ratio) seem to better organize the data: among the volatile elements, the abundance enhancements relative to solar increase with mass (except for the slightly high H/He ratio); the more refractory elements seem systematically overabundant relative to the more volatile ones in a quasi-mass-independent fashion. If this is the case, material locked in grains in the interstellar medium must be accelerated to cosmic-ray energies more efficiently than interstellar gas-phase ions. Here we present results from a nonlinear shock model that includes (1) the direct acceleration of interstellar gas-phase ions, (2) a simplified model for the direct acceleration of weakly charged grains to ~100 keV amu-1 energies, simultaneously with the acceleration of the gas ions, (3) the energy losses of grains colliding with the ambient gas, (4) the sputtering of grains, and (5) the simultaneous acceleration of the sputtered ions to GeV and TeV energies. We show that the model produces GCR source abundance enhancements of the volatile, gas-phase elements that are an increasing function of mass, as well as a net, mass-independent enhancement of the refractory, grain elements over protons, consistent with cosmic-ray observations. We also investigate the implications of the slightly high H/He ratio. The GCR22Ne excess may also be accounted for in terms of the acceleration of 22Ne-enriched presupernova Wolf-Rayet star wind material surrounding the most massive supernovae. We also show that cosmic-ray source spectra, at least below ~1014 eV, are well matched by the model.

Galactic Cosmic Rays from Supernova Remnants. I. A Cosmic-Ray Composition Controlled by Volatility and Mass-to-Charge Ratio

We show that the Galactic cosmic-ray source (GCRS) composition is best described in terms of (1) a general enhancement of the refractory elements relative to the volatile ones, and (2) among the volatile elements, an enhancement of the heavier elements relative to the lighter ones. This mass dependence most likely reflects a mass-to-charge (A/Q) dependence of the acceleration efficiency; among the refractory elements, there is no such enhancement of heavier species, or only a much weaker one. We regard as coincidental the similarity between the GCRS composition and that of the solar corona, which is biased according to first ionization potential. In a companion paper, this GCRS composition is interpreted in terms of an acceleration by supernova shock waves of interstellar and/or circumstellar (e.g.,22Ne-rich Wolf-Rayet wind) gas-phase and, especially, dust material.

Radio to Gamma-Ray Emission from Shell-Type Supernova Remnants: Predictions from Nonlinear Shock Acceleration Models

Supernova remnants (SNRs) are widely believed to be the principal source of Galactic cosmic rays, produced by diffusive shock acceleration in the environs of the remnants expanding blast wave. Such energetic particles can produce gamma rays and lower energy photons via interactions with the ambient plasma. The recently reported observation of TeV gamma rays from SN 1006 by the Collaboration of Australia and Nippon for a Gamma-Ray Observatory in the Outback (CANGAROO), combined with the fact that several unidentified EGRET sources have been associated with known radio/optical/X-ray-emitting remnants, provides powerful motivation for studying gamma-ray emission from SNRs. In this paper, we present results from a Monte Carlo simulation of nonlinear shock structure and acceleration coupled with photon emission in shelllike SNRs. These nonlinearities are a by-product of the dynamical influence of the accelerated cosmic rays on the shocked plasma and result in distributions of cosmic rays that deviate from pure power laws. Such deviations are crucial to acceleration efficiency considerations and impact photon intensities and spectral shapes at all energies, producing GeV/TeV intensity ratios that are quite different from test particle predictions. The Sedov scaling solution for SNR expansions is used to estimate important shock parameters for input into the Monte Carlo simulation. We calculate ion (proton and helium) and electron distributions that spawn neutral pion decay, bremsstrahlung, inverse Compton, and synchrotron emission, yielding complete photon spectra from radio frequencies to gamma-ray energies. The cessation of acceleration caused by the spatial and temporal limitations of the expanding SNR shell in moderately dense interstellar regions can yield spectral cutoffs in the TeV energy range that are consistent with Whipples TeV upper limits on those EGRET unidentified sources that have SNR associations. Supernova remnants in lower density environments generate higher energy cosmic rays that produce predominantly inverse Compton emission observable at super-TeV energies, consistent with the SN 1006 detection. In general, sources in such low-density regions will be gamma-ray-dim at GeV energies.

Particle injection and acceleration at earth's bow shock - Comparison of upstream and downstream events

The injection and acceleration of thermal solar wind ions at the quasi-parallel earths bow shock during radial interplanetary magnetic field conditions is investigated. Active Magnetospheric Particle Tracer Explorers/Ion Release Module satellite observations of complete proton spectra, and of heavy ion spectra above 10 keV/Q, made on September 12, 1984 near the nose of the shock, are presented and compared to the predictions of a Monte Carlo shock simulation which includes diffusive shock acceleration. It is found that the spectral observations are in good agreement with the predictions of the simulation when it is assumed that all accelerated ions originate in the solar wind and are injected into the acceleration mechanism by thermal leakage from the downstream plasma. The efficiency, which is determined directly from the downstream observations, is high, with at least 15 percent of the solar wind energy flux going into accelerated particles. The comparisons allow constraints to be placed on the rigidity dependence of the scattering mean free path and suggest that the upstream solar wind must be slowed substantially by backstreaming accelerated ions prior to undergoing a sharp transition in the viscous subshock. 75 refs.

Nonlinear Shock Acceleration and Photon Emission in Supernova Remnants

We have extended a simple model of nonlinear diffusive shock acceleration (Berezhko & Ellison 1999: Ellison &, Berezhko 1999a) to include the injection and acceleration of electrons and the production of photons from bremsstrahlung, synchrotron, inverse Compton, and pion-decay processes. We argue that, the results of this model, which is simpler to use than more elaborate ones, offer a significant improvement, over test-particle, power-law spectra which are often used in astrophysical applications of diffusive shock acceleration. With an evolutionary supernova remnant (SNR) model to obtain shock parameters as functions of ambient interstellar medium parameters and time, we predict broad-band continuum photon emission from supernova remnants in general, and SN1006 in particular, showing that our results compare well with the more complete time-dependent and spherically symmetric nonlinear model of Berezhko, Ksenofontov, & Petukhov (1999a). We discuss the implications nonlinear shock acceleration has for X-ray line emission, and use our model to describe how ambient conditions determine the TeV/radio flux ratio, an important parameter for gamma-ray observations of radio SNRs.

Efficient Cosmic Ray Acceleration, Hydrodynamics, and Self-Consistent Thermal X-Ray Emission Applied to Supernova Remnant RX J1713.7–3946

We model the broadband emission from supernova remnant (SNR) RX J1713.7-3946 including, for the first time, a consistent calculation of thermal X-ray emission together with non-thermal emission in a nonlinear diffusive shock acceleration model. Our model tracks the evolution of the SNR including the plasma ionization state between the forward shock and the contact discontinuity. We use a plasma emissivity code to predict the thermal X-ray emission spectrum assuming the initially cold electrons are heated either by Coulomb collisions with the shock-heated protons (the slowest possible heating), or come into instant equilibration with the protons. For either electron heating model, electrons reach 107 K rapidly and the X-ray line emission near 1 keV is more than 10 times as luminous as the underlying thermal bremsstrahlung continuum. Since recent Suzaku observations show no detectable line emission, this places strong constraints on the unshocked ambient medium density and on the relativistic electron-to-proton ratio. For the uniform circumstellar medium (CSM) models that we consider, the low densities and high relativistic electron-to-proton ratios required to match the Suzaku X-ray observations definitively rule out pion decay as the emission process producing GeV-TeV photons. We show that leptonic models, where inverse-Compton scattering against the cosmic background radiation dominates the GeV-TeV emission, produce better fits to the broadband thermal and non-thermal observations in a uniform CSM.

Acceleration rates and injection efficiencies in oblique shocks

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, as is demonstrated here, the efficiency for injecting thermal particles into the acceleration mechanism also depends strongly on obliquity and, in general, varies inversely with \teq{\Tbone}. The degree of turbulence and the resulting cross-field diffusion strongly influences both injection efficiency and acceleration rates. The test particle \mc simulation of shock acceleration used here assumes large-angle scattering, computes particle orbits exactly in shocked, laminar, non-relativistic flows, and calculates the injection efficiency as a function of obliquity, Mach number, and degree of turbulence. We find that turbulence must be quite strong for high Mach number, highly oblique shocks to inject significant numbers of thermal particles and that only modest gains in acceleration rates can be expected for strong oblique shocks over parallel ones if the only source of seed particles is the thermal background.