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Register a new userEffect of energy losses and interactions during diffusive shock acceleration: applications to SNR, AGN and UHE Cosmic Rays
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R.J. Protheroe
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I discuss the shape of the high energy end of the spectrum of particles arising from diffusive shock acceleration in the presence of (i) additional diffusive escape from the accelerator, (ii) continuous energy losses, (iii) energy changes arising from interactions. The form of the spectrum near cut-off is sensitive to these processes as well as to the momentum-dependence of the diffusion coefficients and the compression ratio, and so the spectrum of any radiation emitted by the accelerated particles may reflect the physical conditions of the acceleration region. Results presented in this paper have applications in interpreting the spectral energy distributions of many types of astrophysical object including supernova remnants (SNR), active galactic nuclei (AGN) and acceleration sources of ultra high energy cosmic rays (UHE CR). Except for extremely nearby sources, spectral features imprinted on the spectrum of UHE CR during the acceleration process will be largely eroded during propagation, but the spectrum of UHE neutrinos produced in interactions of UHE CR with radiation, both during cosmic ray acceleration and subsequent propagation through the cosmic microwave background radiation, contains sufficient information to determine the cut-off momentum of the UHE CR just after acceleration for reasonable assumptions. Observation of these UHE neutrinos by the Pierre Auger Observatory may help in identifying the sources of the highest energy cosmic rays.
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In this paper, we study the diffusive shock acceleration of cosmic-ray protons and nuclei, taking into account all the relevant interaction processes with photon backgrounds. We investigate how the competition between protons and nuclei is modified by the acceleration parameters such as the acceleration rate, its rigidity dependence, the photon density and the confinement capability of the sources. We find that in the case of interaction-limited acceleration processes protons are likely to be accelerated to higher energies than nuclei, whereas for confinement-limited acceleration nuclei are accelerated to higher energies than protons. Finally, we discuss our results in the context of possible astrophysical accelerators, and in the light of recent cosmic-ray data.
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.
The energy losses and spectra of Ultra High Energy Cosmic Rays (UHECR) are calculated for protons as primary particles. The attention is given to the energy losses due to electron-positron production in collisions with the microwave 2.73 K photons. The energy spectra are calculated for several models, which differ by production spectra and by source distribution, namely: (i) Uniform distribution of the sources with steep generation spectra with indices 2.4 - 2.7, with cosmological evolution and without it. In this case it is possible to fit the shape of the observed spectrum up to 8.10^{19} eV, but the required CR emissivity is too high and the GZK cutoff is present. (ii) Uniform distribution of the sources with flat generation spectrum dE/E^2 which is relevant to GRBs. The calculated spectrum is in disagreement with the observed one. The agreement at Elesssim 8.10^{19} eV can be reached using a complex generation spectrum, but the required CR emissivity is three orders of magnitude higher than that of GRBs, and the predicted spectrum has the GZK cutoff. (iii) The case of local enhancement within region of size 10 - 30 Mpc with overdensity given by factor 3- 30. The overdensity larger than 10 is needed to eliminate the GZK cutoff.
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.
The galactic cosmic rays are generally believed to be originated in supernova remnants (SNRs), produced in diffusive shock acceleration (DSA) process in supernova blast waves driven by expanding SNRs. One of the key unsettled issue in SNR origin of cosmic ray model is the maximum attainable energy by a cosmic ray particle in the supernova shock. Recently it has been suggested that an amplification of effective magnetic field strength at the shock may take place in young SNRs due to growth of magnetic waves induced by accelerated cosmic rays and as a result the maximum energy achieved by cosmic rays in SNR may reach the knee energy instead of $sim 200$ TeV as predicted earlier under normal magnetic field situation. In the present work we investigate the implication of such maximum energy scenarios on TeV gamma rays and neutrino fluxes from the molecular clouds interacting with the SNR W28. The authors compute the gamma-ray and neutrino flux assuming two different values for the maximum energy reached by cosmic rays in the SNR, from CR interaction in nearby molecular clouds. Both protons and nuclei are considered as accelerated particles and as target material. Our findings suggest that the issue of the maximum energy of cosmic rays in SNRs can be observationally settled by the upcoming gamma-ray experiment the Large High Altitude Air Shower Observatory (LHAASO). The estimated neutrino fluxes from the molecular clouds are , however, out of reach of the present/near future generation of neutrino telescopes.
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