Why is it that we think ultra high energy cosmic rays are emitted from supernovae.
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Do you have a link to a document which discusses ultra-high energy (UHE)* cosmic rays (CR) being emitted from supernovae? This page, from the Adelaide High Energy Astrophysics Group, and this from the University of Utah's Hi-Res group both state that supernovae are unlikely to be sources of UHE CRs; e.g. (from the second source) "However, it is difficult to explain the existence of cosmic rays above 1018 eV, because supernovae are simply not large enough to maintain acceleration to the UHE regime."
However, the huge energies generated in gamma ray bursts (GRB) suggested to many that they might be a source of UHE CR. Recently, the link between at least some "long duration" GRBs and supernovae was established.
These lecture notes give a flavour of some current work and thinking.
*the term "ultra-high energy" here means above ~1018 eV.
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