Momentum space of accelerated protons. Particle scattering zoneson the -plane of momentum space. Protons in the stripes are not scattered by waves (see text). Therefore, particles from the domains maintain their propagation direction and promptly escape from the dense gas region. This and Figs. 3 and 4 are adapted (in modified and extended form) from Ref. 30.
SNR shock propagating into dense gas environment. The filling factor of the gas clumps is small, while some of them may be larger than the thickness of the CR layer near the shock front.
Spectra of accelerated protons and electrons. The both particle distributions are calculated for a weakly modified shock and are shown in momentum normalization (f(p) is steeper by two powers than the spectra in energy normalization, used in the text). Both spectra are multiplied by , so that the test particle distribution is flat. Shock parameters: acoustic Mach number M = 30, shock velocity , the break momentum . Shock pre-compression (flow compression across the CR precursor) R = 1.8, injection parameter [defined as , with and being the ambient gas density and the shock speed, respectively]; injection momentum .
Gamma radiation spectra. Photon spectra resulting from decay and calculated for two different parent proton spectra compared against the Fermi (circles) and Agile (squares) data. Solid line: a test particle acceleration regime with the spectral index q = 2 below the break and q = 3 above the break at /c. Dashed line: a moderately nonlinear acceleration regime corresponding to the spectrum shown in Fig. 3 ( and below and above the break, respectively). Cut-offs are placed at 300 GeV for TP- and 100 GeV, for NL-spectrum. Fermi and Agile data are adopted from Refs. 4 and 9, respectively. Both curves are well within the error bars of Fermi and Agile (not shown for clarity), which, in turn, overlap.9
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