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Register a new userA more accurate numerical scheme for diffusive shock acceleration
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We present a more accurate numerical scheme for the calculation of diffusive shock acceleration of cosmic rays using Stochastic Differential Equations. The accuracy of this scheme is demonstrated using a simple analytical flow profile that contains a shock of finite width and a varying diffusivity of the cosmic rays, where the diffusivity decreases across the shock. We compare the results for the slope of the momentum distribution with those obtained from a perturbation analysis valid for finite but small shock width. These calculations show that this scheme, although computationally more expensive, provides a significantly better performance than the Cauchy-Euler type schemes that were proposed earlier in the case where steep gradients in the cosmic ray diffusivity occur. For constant diffusivity the proposed scheme gives similar results as the Cauchy-Euler scheme.
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Low sonic Mach number shocks form in the intracluster medium (ICM) during the formation of the large-scale structure of the universe. Nonthermal cosmic-ray (CR) protons are expected to be accelerated via diffusive shock acceleration (DSA) in those ICM shocks, although observational evidence for the $gamma$-ray emission of hadronic origin from galaxy clusters has yet to be established. Considering the results obtained from recent plasma simulations, we improve the analytic test-particle DSA model for weak quasi-parallel ($Q_parallel$) shocks, previously suggested by citet{kang2010}. In the model CR spectrum, the transition from the postshock thermal to CR populations occurs at the injection momentum, $p_{rm inj}$, above which protons can undergo the full DSA process. As the shock energy is transferred to CR protons, the postshock gas temperature should decrease accordingly and the subshock strength weakens due to the dynamical feed of the CR pressure to the shock structure. This results in the reduction of the injection fraction, although the postshock CR pressure approaches an asymptotic value when the CR spectrum extends to the relativistic regime. Our new DSA model self-consistently accounts for such behaviors and adopts better estimations for $p_{rm inj}$. With our model DSA spectrum, the CR acceleration efficiency ranges $etasim10^{-3}-0.01$ for supercritical, $Q_parallel$-shocks with sonic Mach number $2.25lesssim M_{rm s}lesssim5$ in the ICM. Based on citet{ha2018b}, on the other hand, we argue that proton acceleration would be negligible in subcritical shocks with $M_{rm s}<2.25$.
The present article investigates magnetic amplification in the upstream medium of SNR blast wave through both resonant and non-resonant regimes of the streaming instability. It aims at a better understanding of the diffusive shock acceleration (DSA) efficiency considering various relaxation processes of the magnetic fluctuations in the downstream medium. Multi-wavelength radiative signatures coming from the SNR shock wave are used in order to put to the test the different downstream turbulence relaxation models. We confirm the result of Parizot et al (2006) that the maximum CR energies should not go well beyond PeV energies in young SNRs where X-ray filaments are observed. In order to match observational data, we derive an upper limit on the magnetic field amplitude insuring that stochastic particle reacceleration remain inefficient. Considering then, various magnetic relaxation processes, we present two necessary conditions to achieve efficient acceleration and X-ray filaments in SNRs: 1/the turbulence must fulfil the inequality $2-beta-delta_{rm d} ge 0$ where $beta$ is the turbulence spectral index while $delta_d$ is the relaxation length energy power-law index; 2/the typical relaxation length has to be of the order the X-ray rim size. We identify that Alvenic/fast magnetosonic mode damping does fulfil all conditions while non-linear Kolmogorov damping does not. Confronting previous relaxation processes to observational data, we deduct that among our SNR sample, the older ones (SN1006 & G347.3-0.5) fail to verify all conditions which means that their X-ray filaments are likely controlled by radiative losses. The younger SNRs, Cas A, Tycho and Kepler, do pass all tests and we infer that the downstream magnetic field amplitude is lying in the range of 200-300 $mu$ Gauss.
We present a model for the non-thermal emission from a colliding-wind binary. Relativistic protons and electrons are assumed to be accelerated through diffusive shock acceleration (DSA) at the global shocks bounding the wind-wind collision region. The non-linear effects of the back-reaction due to the cosmic ray pressure on the particle acceleration process and the cooling of the non-thermal particles as they flow downstream from the shocks are included. We explore how the non-thermal particle distribution and the keV-GeV emission changes with the stellar separation and the viewing angle of the system, and with the momentum ratio of the winds. We confirm earlier findings that DSA is very efficient when magnetic field amplification is not included, leading to significantly modified shocks. We also find that the non-thermal flux scales with the binary separation in a complicated way and that the anisotropic inverse Compton emission shows only a moderate variation with viewing angle due to the spatial extent of the wind-wind collision.
It is well accepted today that diffusive acceleration in shocks results to the cosmic ray spectrum formation. This is in principle true for non-relativistic shocks, since there is a detailed theory covering a large range of their properties and the resulting power-law spectrum, which is nevertheless not as efficient to reach the very high energies observed in the cosmic ray spectrum. On the other hand, the cosmic ray maximum energy and the resulting spectra from relativistic shocks, are still under investigation and debate concerning their contribution to the features of the cosmic ray spectrum and the measured, or implied, cosmic ray radiation from candidate astrophysical sources. Here, we discuss the efficiency of the first order Fermi (diffusive) acceleration mechanism up to relativistic shock speeds, presenting Monte Carlo simulations.
We calculate the temporal evolution of distributions of relativistic electrons subject to synchrotron and adiabatic processes and Fermi-like acceleration in shocks. The shocks result from Kelvin-Helmholtz instabilities in the jet. Shock formation and particle acceleration are treated in a self-consistent way by means of a numerical hydrocode. We show that in our model the number of relativistic particles is conserved during the evolution, with no need of further injections of supra-thermal particles after the initial one. From our calculations, we derive predictions for values and trends of quantities like the spectral index and the cutoff frequency that can be compared with observations.
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