Modern theory of Fermi acceleration: a new challenge to plasma physics

One of the main features of astrophysical shocks is their ability to accelerate particles to extremely high energies. The leading acceleration mechanism, the diffusive shock acceleration is reviewed. It is demonstrated that its efficiency critically depends on the injection of thermal plasma into acceleration which takes place at the subshock of the collisionless shock structure that, in turn, can be significantly smoothed by energetic particles. Furthermore, their inhomogeneous distribution provides free energy for MHD turbulence regulating the subshock strength and injection rate. Moreover, the MHD turbulence confines particles to the shock front controlling their maximum energy and bootstrapping acceleration. Therefore, the study of the MHD turbulence in a compressive plasma flow near a shock is a key to understanding of the entire process. The calculation of the injection rate became part of the collisionless shock theory. It is argued that the further progress in diffusive shock acceleration theory is impossible without a significant advance in these two areas of plasma physics.Comment: 12 pages, 4 figures, invited talk at APS/ICPP, Quebec 2000, to appear in Phys. of Plasma

Probing Nearby CR Accelerators and ISM Turbulence with Milagro Hot Spots

Both the acceleration of cosmic rays (CR) in supernova remnant shocks and their subsequent propagation through the random magnetic field of the Galaxy deem to result in an almost isotropic CR spectrum. Yet the MILAGRO TeV observatory discovered a sharp ($\sim10^{\circ})$ arrival anisotropy of CR nuclei. We suggest a mechanism for producing a weak and narrow CR beam which operates en route to the observer. The key assumption is that CRs are scattered by a strongly anisotropic Alfven wave spectrum formed by the turbulent cascade across the local field direction. The strongest pitch-angle scattering occurs for particles moving almost precisely along the field line. Partly because this direction is also the direction of minimum of the large scale CR angular distribution, the enhanced scattering results in a weak but narrow particle excess. The width, the fractional excess and the maximum momentum of the beam are calculated from a systematic transport theory depending on a single scale $l$ which can be associated with the longest Alfven wave, efficiently scattering the beam. The best match to all the three characteristics of the beam is achieved at $l\sim1$pc. The distance to a possible source of the beam is estimated to be within a few 100pc. Possible approaches to determination of the scale $l$ from the characteristics of the source are discussed. Alternative scenarios of drawing the beam from the galactic CR background are considered. The beam related large scale anisotropic CR component is found to be energy independent which is also consistent with the observations.Comment: 2 figures, ApJ accepted version2 minor changes and correction

Critical self-organization of astrophysical shocks

There are two distinct regimes of the first order Fermi acceleration at shocks. The first is a linear (test particle) regime in which most of the shock energy goes into thermal and bulk motion of the plasma. The second is an efficient regime when it goes into accelerated particles. Although the transition region between them is narrow, we identify the factors that drive the system to a {\it self-organized critical state} between those two. Using an analytic solution, we determine this critical state and calculate the spectra and maximum energy of accelerated particles.Comment: To appear in ApJL, Sec.3 extensively rewritten, 4 pages, Latex, emulateapj.sty, eps

On the mechanism for breaks in the cosmic ray spectrum

The proof of cosmic ray (CR) origin in supernova remnants (SNR) must hinge on full consistency of the CR acceleration theory with the observations; direct proof is impossible because of the orbit stochasticity of CR particles. Recent observations of a number of galactic SNR strongly support the SNR-CR connection in general and the Fermi mechanism of CR acceleration, in particular. However, many SNR expand into weakly ionized dense gases, and so a significant revision of the mechanism is required to fit the data. We argue that strong ion-neutral collisions in the remnant surrounding lead to the steepening of the energy spectrum of accelerated particles by \emph{exactly one power}. The spectral break is caused by a partial evanescence of Alfven waves that confine particles to the accelerator. The gamma-ray spectrum generated in collisions of the accelerated protons with the ambient gas is also calculated. Using the recent Fermi spacecraft observation of the SNR W44 as an example, we demonstrate that the parent proton spectrum is a classical test particle power law $\propto E^{-2}$, steepening to $E^{-3}$ at $E_{br}\approx7GeV$.Comment: APS talk to appear in PoP, 4 figure

Hadronic Gamma Rays from Supernova Remnants

A gas cloud near a supernova remnant (SNR) provides a target for pp-collisions leading to subsequent gamma-ray emission through neutral pion decay. The assumption of a power-law ambient spectrum of accelerated particles with index near -2 is usually built into models predicting the spectra of very-high energy (VHE) gamma-ray emission from SNRs. However, if the gas cloud is located at some distance from the SNR shock, this assumption is not necessarily correct. In this case, the particles which interact with the cloud are those leaking from the shock and their spectrum is approximately monoenergetic with the injection energy gradually decreasing as the SNR ages. In the GLAST energy range the gamma-ray spectrum resulting from particle interactions with the gas cloud will be flatter than expected, with the cutoff defined by the pion momentum distribution in the laboratory frame. We evaluate the flux of particles escaping from a SNR shock and apply the results to the VHE diffuse emission detected by the HESS at the Galactic centre.Comment: 4 pages, 3 figures. Contribution to the 30th ICRC, Merida, Mexico, 2007 (final version

Dynamics of Mesoscale Magnetic Field in Diffusive Shock Acceleration

We present a theory for the generation of mesoscale ($kr_{g}\ll 1$, where $r_{g}$ is the cosmic ray gyroradius) magnetic fields during diffusive shock acceleration. The decay or modulational instability of resonantly excited Alfven waves scattering off ambient density perturbations in the shock environment naturally generates larger scale fields. For a broad spectrum of perturbations, the physical mechanism of energy transfer is random refraction, represented by diffusion of Alfven wave packet in $k-$space. The scattering field can be produced directly by the decay instability or by the Drury instability, a hydrodynamic instability driven by the cosmic ray pressure gradient. This process is of interest to acceleration since it generates waves of longer wavelength, and so enables the confinement and acceleration of higher energy particles. This process also limits the intensity of resonantly generated turbulent magnetic field on $r_{g}$ scales.Comment: 38 page, 4 figures, submitted to Ap

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