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Register a new userEfficiency limits of diffusive shock acceleration
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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.
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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.
Radio, X-ray, and gamma-ray observations provide us with strong evidence of particle acceleration to multi-TeV energies in various astrophysical sources. Diffusive shock acceleration is one of the most successful models explaining the presence of such high-energy particles. We discuss the impact of inverse Compton losses on the shock acceleration of electrons that takes place in radiation dominated environments, i.e. in regions where the radiation energy density exceeds that of the magnetic field. We perform a numerical calculation, including an energy-loss term in the transport equation of accelerated particles. We discuss the implications of this effect on the hard X-ray synchrotron and gamma-ray inverse Compton radiation, produced by shock-accelerated electrons in young supernova remnants in the presence of large radiation fields (e.g. in the Galactic centre). We also discuss possible implications of our results for clusters of galaxies and gamma-ray binaries. We demonstrate that the inverse Compton losses of electrons, in the Klein-Nishina regime, lead to spectra of ultra-relativistic electrons that may significantly differ from classical diffusive shock acceleration solution. The most prominent feature is the appearance of a pile-up in the spectrum around the cut-off energy.
Radio relics in galaxy clusters are giant diffuse synchrotron sources powered in cluster outskirts by merger shocks. Although the relic-shock connection has been consolidated in recent years by a number of observations, the details of the mechanisms leading to the formation of relativistic particles in this environment are still not well understood. The diffusive shock acceleration (DSA) theory is a commonly adopted scenario to explain the origin of cosmic rays at astrophysical shocks, including those in radio relics in galaxy clusters. However, in a few specific cases it has been shown that the energy dissipated by cluster shocks is not enough to reproduce the luminosity of the relics via DSA of thermal particles. Studies based on samples of radio relics are required to further address this limitation of the mechanism. In this paper, we focus on ten well-studied radio relics with underlying shocks observed in the X-rays and calculate the electron acceleration efficiency of these shocks that is necessary to reproduce the observed radio luminosity of the relics. We find that in general the standard DSA cannot explain the origin of the relics if electrons are accelerated from the thermal pool with an efficiency significantly smaller than 10%. Our results show that other mechanisms, such as shock re-acceleration of supra-thermal seed electrons or a modification of standard DSA, are required to explain the formation of radio relics.
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.
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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