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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 efficiency. These controversies motivated us to investigate numerically by Monte Carlo simulations the particle acceleration efficiency in oblique modified shocks. The results show flatter spectra compared to the spectra of the pressumed sharp discontinuity shock fronts. The findings are in accordance with theoretical predictions, since the scattering inside the precursor confines high energy particles to further scattering, resulting in higher energies making the whole acceleration process more efficient.
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Supernova remnants (SNRs) are believed to accelerate particles up to high energies through the mechanism of diffusive shock acceleration (DSA). Except for direct plasma simulations, all modeling efforts must rely on a given form of the diffusion coefficient, a key parameter that embodies the interactions of energetic charged particles with the magnetic turbulence. The so-called Bohm limit is commonly employed. In this paper we revisit the question of acceleration at perpendicular shocks, by employing a realistic model of perpendicular diffusion. Our coefficient reduces to a power-law in momentum for low momenta (of index $alpha$), but becomes independent of the particle momentum at high momenta (reaching a constant value $kappa_{infty}$ above some characteristic momentum $p_{rm c}$). We first provide simple analytical expressions of the maximum momentum that can be reached at a given time with this coefficient. Then we perform time-dependent numerical simulations to investigate the shape of the particle distribution that can be obtained when the particle pressure back-reacts on the flow. We observe that, for a given index $alpha$ and injection level, the shock modifications are similar for different possible values of $p_{rm c}$, whereas the particle spectra differ markedly. Of particular interest, low values of $p_{rm c}$ tend to remove the concavity once thought to be typical of non-linear DSA, and result in steep spectra, as required by recent high-energy observations of Galactic SNRs.
The theory of diffusive particle acceleration explains the spectral properties of the cosmic rays below energies of approx. 10^6 GeV as produced at strong shocks in supernova remnants (SNRs). To supply the observed flux of cosmic rays, a significant fraction of the energy released by a supernova has to be transfered to cosmic rays. The key to the question of the efficiency of SNRs in producing cosmic rays is the injection process from thermal energies. A self-consistent model has to take into account the interaction of the accelerated particles with magneto-hydrodynamic waves, which generate the particle diffusion, a requisite for the acceleration process. Such a nonlinear model of the turbulent background plasma has been developed recently (Malkov, 1998, Phys. Rev. E 58, 4911). We use this model for the first numerical treatment of the gas dynamics and the diffusion-convection equation at a quasi-parallel strong shock, which incorporates a plasma-physical injection model to investigate the cosmic ray production.
Particle acceleration at non-relativistic shocks can be very efficient, leading to the appearance of non-linear effects due to the dynamical reaction of the accelerated particles on the shock structure and to the non-linear amplification of the magnetic field in the shock vicinity. The value of the maximum momentum $p_{max}$ in these circumstances cannot be estimated using the classical results obtained within the framework of test particle approaches. We provide here the first attempt at estimating $p_{max}$ in the cosmic ray modified regime, taking into account the non-linear effects mentioned above.
A novel diagnostic of cosmic-ray modified shocks by polarimetry of H $alpha$ emissions is suggested. In a cosmic-ray modified shock, the pressure of cosmic rays is sufficiently high compared to the upstream ram pressure to force the background plasma to decelerate (measured in the shock rest frame). Simultaneously, a fraction of the hydrogen atoms co-existing in the upstream plasma collide with the decelerated protons and undergo charge-exchange reactions. As a result, hydrogen atoms with the same bulk velocity of the decelerated protons are generated. We show that when the shock is observed from edge-on, the H $alpha$ radiated by these upstream hydrogen atoms is linearly polarized with a sizable degree of a few per cent as a result of resonant scattering of Ly $beta$. The polarization direction depends strongly on the velocity modification; the direction is parallel to the shock surface for the case of no modification, while the direction is parallel to the shock velocity for the case of a modified shock.
In the past few years, gamma-ray astronomy has entered a golden age. At TeV energies, only a handful of sources were known a decade ago, but the current generation of ground-based imaging atmospheric Cherenkov telescopes has increased this number to more than one hundred. At GeV energies, the Fermi Gamma-ray Space Telescope has increased the number of known sources by nearly an order of magnitude in its first 2 years of operation. The recent detection and unprecedented morphological studies of gamma-ray emission from shell-type supernova remnants is of great interest, as these analyses are directly linked to the long standing issue of the origin of the cosmic-rays. However, these detections still do not constitute a conclusive proof that supernova remnants accelerate the bulk of Galactic cosmic-rays, mainly due to the difficulty of disentangling the hadronic and leptonic contributions to the observed gamma-ray emission. In this talk, I will review the most relevant cosmic ray related results of gamma ray astronomy concerning supernova remnants.
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