On the role of injection in kinetic approaches to nonlinear particle acceleration at non-relativistic shock waves

The dynamical reaction of the particles accelerated at a shock front by the first order Fermi process can be determined within kinetic models that account for both the hydrodynamics of the shocked fluid and the transport of the accelerated particles. These models predict the appearance of multiple solutions, all physically allowed. We discuss here the role of injection in selecting the real solution, in the framework of a simple phenomenological recipe, which is a variation of what is sometimes referred to as thermal leakage. In this context we show that multiple solutions basically disappear and when they are present they are limited to rather peculiar values of the parameters. We also provide a quantitative calculation of the efficiency of particle acceleration at cosmic ray modified shocks and we identify the fraction of energy which is advected downstream and that of particles escaping the system from upstream infinity at the maximum momentum. The consequences of efficient particle acceleration for shock heating are also discussed

On the Structure and Scale of Cosmic Ray Modified Shocks

Strong astrophysical shocks, diffusively accelerating cosmic rays (CR) ought to develop CR precursors. The length of such precursor $L_{p}$ is believed to be set by the ratio of the CR mean free path $\lambda$ to the shock speed, i.e., $L_{p}\sim c\lambda/V_{sh}\sim cr_{g}/V_{sh}$, which is formally independent of the CR pressure $P_{c}$. However, the X-ray observations of supernova remnant shocks suggest that the precursor scale may be significantly shorter than $L_{p}$ which would question the above estimate unless the magnetic field is strongly amplified and the gyroradius $r_{g}$ is strongly reduced over a short (unresolved) spatial scale. We argue that while the CR pressure builds up ahead of the shock, the acceleration enters into a strongly nonlinear phase in which an acoustic instability, driven by the CR pressure gradient, dominates other instabilities (at least in the case of low $\beta$ plasma). In this regime the precursor steepens into a strongly nonlinear front whose size scales with \emph{the CR pressure}as $L_{f}\sim L_{p}\cdot(L_{s}/L_{p})^{2}(P_{c}/P_{g})^{2}$, where $L_{s}$ is the scale of the developed acoustic turbulence, and $P_{c}/P_{g}$ is the ratio of CR to gas pressure. Since $L_{s}\ll L_{p}$, the precursor scale reduction may be strong in the case of even a moderate gas heating by the CRs through the acoustic and (possibly also) the other instabilities driven by the CRs.Comment: EPS 2010 paper, to appear in PPC

New insights on hadron acceleration at supernova remnant shocks

We outline the main features of nuclei acceleration at supernova remnant forward shocks, stressing the crucial role played by self-amplified magnetic fields in determining the energy spectrum observed in this class of sources. In particular, we show how the standard predictions of the non-linear theory of diffusive shock acceleration has to be completed with an additional ingredient, which we propose to be the enhanced velocity of the magnetic irregularities particles scatter against, to reconcile the theory of efficient particle acceleration with recent observations of gamma-ray bright supernova remnants.Comment: 7 pages, 2 figures. To apper in "Cosmic-ray induced phenomenology in star-forming environments: Proceedings of the 2nd Session of the Sant Cugat Forum of Astrophysics" (April 16-19, 2012), Olaf Reimer and Diego F. Torres (eds.

Proton-Helium Spectral Anomaly as a Signature of Cosmic Ray Accelerator

The much-anticipated proof of cosmic ray (CR) acceleration in supernova remnants (SNR) must hinge on full consistency of acceleration theory with the observations; direct proof is impossible because of the orbit scrambling of CR particles. The PAMELA orbital telescope revealed deviation between helium and proton CR spectra deemed inconsistent with the theory, since the latter does not differentiate between elements of ultrarelativistic rigidity. By considering an initial (injection-) phase of the diffusive shock acceleration (DSA), where elemental similarity does not apply, we demonstrate that the spectral difference is, in fact, a unique signature of the DSA. Collisionless plasma SNR shocks inject more He2+ relative to protons when they are stronger and so produce harder helium spectra. The injection bias is due to Alfven waves driven by the more abundant protons, so the He2+ ions are harder to trap by these waves because of the larger gyroradii. By fitting the p/He ratio to the PAMELA data, we bolster the DSA-case for resolving the century-old mystery of CR origin.Comment: PRL Accepted version: reformatted figures, references added, minor correction

Non-thermal high-energy emission from colliding winds of massive stars

Colliding winds of massive star binary systems are considered as potential sites of non-thermal high-energy photon production. This is motivated merely by the detection of synchrotron radio emission from the expected colliding wind location. Here we investigate the properties of high-energy photon production in colliding winds of long-period WR+OB-systems. We found that in the dominating leptonic radiation process anisotropy and Klein-Nishina effects may yield spectral and variability signatures in the gamma-ray domain at or above the sensitivity of current or upcoming gamma-ray telescopes. Analytical formulae for the steady-state particle spectra are derived assuming diffusive particle acceleration out of a pool of thermal wind particles, and taking into account adiabatic and all relevant radiative losses. For the first time we include their advection/convection in the wind collision zone, and distinguish two regions within this extended region: the acceleration region where spatial diffusion is superior to convective/advective motion, and the convection region defined by the convection time shorter than the diffusion time scale. The calculation of the Inverse Compton radiation uses the full Klein-Nishina cross section, and takes into account the anisotropic nature of the scattering process. This leads to orbital flux variations by up to several orders of magnitude which may, however, be blurred by the geometry of the system. The calculations are applied to the typical WR+OB-systems WR 140 and WR 147 to yield predictions of their expected spectral and temporal characteristica and to evaluate chances to detect high-energy emission with the current and upcoming gamma-ray experiments. (abridged)Comment: 67 pages, 24 figures, submitted to Ap

Nonlinear shock acceleration beyond the Bohm limit

We suggest a physical mechanism whereby the acceleration time of cosmic rays by shock waves can be significantly reduced. This creates the possibility of particle acceleration beyond the knee energy at ~10^15eV. The acceleration results from a nonlinear modification of the flow ahead of the shock supported by particles already accelerated to the knee momentum at p ~ p_*. The particles gain energy by bouncing off converging magnetic irregularities frozen into the flow in the shock precursor and not so much by re-crossing the shock itself. The acceleration rate is thus determined by the gradient of the flow velocity and turns out to be formally independent of the particle mean free path (m.f.p.). The velocity gradient is, in turn, set by the knee-particles at p ~ p_* as having the dominant contribution to the CR pressure. Since it is independent of the m.f.p., the acceleration rate of particles above the knee does not decrease with energy, unlike in the linear acceleration regime. The reason for the knee formation at p ~ p_* is that particles with $p > p_*$ are effectively confined to the shock precursor only while they are within limited domains in the momentum space, while other particles fall into ``loss-islands'', similar to the ``loss-cone'' of magnetic traps. This structure of the momentum space is due to the character of the scattering magnetic irregularities. They are formed by a train of shock waves that naturally emerge from unstably growing and steepening magnetosonic waves or as a result of acoustic instability of the CR precursor. These losses steepen the spectrum above the knee, which also prevents the shock width from increasing with the maximum particle energy.Comment: aastex, 13 eps figure

A cosmic ray current driven instability in partially ionised media

We investigate the growth of hydromagnetic waves driven by streaming cosmic rays in the precursor environment of a supernova remnant shock. It is known that transverse waves propagating parallel to the mean magnetic field are unstable to anisotropies in the cosmic ray distribution, and may provide a mechanism to substantially amplify the ambient magnetic field. We quantify the extent to which temperature and ionisation fractions modify this picture. Using a kinetic description of the plasma we derive the dispersion relation for a collisionless thermal plasma with a streaming cosmic ray current. Fluid equations are then used to discuss the effects of neutral-ion collisions. We calculate the extent to which the environment into which the cosmic rays propagate influences the growth of the magnetic field, and determines the range of possible growth rates. If the cosmic ray acceleration is efficient, we find that very large neutral fractions are required to stabilise the growth of the non-resonant mode. For typical supernova parameters in our galaxy, thermal effects do not significantly alter the growth rates. For weakly driven modes, ion-neutral damping can dominate over the instability at more modest ionisation fractions. In the case of a supernova shock interacting with a molecular clouds, such as in RX J1713.7-3946, with high density and low ionisation, the modes can be rapidly damped.Comment: 5 pages, 2 figures, accepted to A&A. Corrections made. Applications adde

Shock Acceleration of Cosmic Rays - a critical review

Motivated by recent unsuccessful efforts to detect the predicted flux of TeV gamma-rays from supernova remnants, we present a critical examination of the theory on which these predictions are based. Three crucial problems are identified: injection, maximum achievable particle energy and spectral index. In each case significant new advances in understanding have been achieved, which cast doubt on prevailing paradigms such as Bohm diffusion and single-fluid MHD. This indicates that more realistic analytical models, backed by more sophisticated numerical techniques should be employed to obtain reliable predictions. Preliminary work on incorporating the effects of anomalous transport suggest that the resulting spectrum should be significantly softer than that predicted by conventional theory.Comment: 8 pages, invited review presented at the 17th ECRS, Lodz, July 2000; to appear in Journal of Physics G: Nuclear and Particle Physic

The high energy gamma-ray emission expected from Tycho's supernova remnant

A nonlinear kinetic model of cosmic ray (CR) acceleration in supernova remnants (SNRs) is used to describe the properties of Tycho's SNR. Observations of the expansion characteristics and of the nonthermal radio and X-ray emission spectra, assumed to be of synchrotron origin, are used to constrain the overall dynamical evolution and the particle acceleration parameters of the system, in addition to what is known from independent estimates of the distance and thermal X-ray observations. It is shown that a very efficient production of nuclear cosmic rays, leading to strong shock modification, and a large downstream magnetic field strength B_d approx 240muG are required to reproduce the observed synchrotron emission from radio to X-ray frequencies. This field strength is still well within the upper bound for the effective magnetic field, consistent with the acceleration process. The pi^0-decay gamma-ray flux turns out to be somewhat greater than the inverse Compton (IC) flux off the Cosmic Microwave Background at energies below 1 TeV, dominating it strongly at 10 TeV. The predicted TeV gamma-ray flux is consistent with but close to the very low upper limit recently obtained by HEGRA. A future detection at E_gamma ~ 10 TeV would clearly indicate hadronic emission.Comment: 8 pages, 6 figures. Accepted in Astronomy and Astrophyic

Dissipative Dynamics of Collisionless Nonlinear Alfven Wave Trains

The nonlinear dynamics of collisionless Alfven trains, including resonant particle effects is studied using the kinetic nonlinear Schroedinger (KNLS) equation model. Numerical solutions of the KNLS reveal the dynamics of Alfven waves to be sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field. The combined effects of both wave nonlinearity and Landau damping result in the evolutionary formation of stationaryOA S- and arc-polarized directional and rotational discontinuities. These waveforms are freqently observed in the interplanetary plasma.Comment: REVTeX, 6 pages (including 5 figures). This and other papers may be found at http://sdphpd.ucsd.edu/~medvedev/papers.htm