Maximum Energies of Electron Acceleration in Young Supernova Remnants

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Young supernova remnants are often assumed to be the source of cosmic rays up to energies approaching the slight steepening at around 1000 TeV known as the ``knee'' in the cosmic-ray energy spectrum. We show that the observed X-ray emission of seven shell remnants, including all five historical shells, can be used to put limits on E_m, the energy at which the electron energy distribution must steepen from its slope at radio-emitting energies. Six of the remnants show thermal spectra, so any nonthermal component must fall below the observed X-ray fluxes. Assuming homogeneous emitting volumes with a mean magnetic-field strength of 10 \ mu G, no object could reach 1000 TeV, and only one, Cas A, has an upper limit on E_m near 100 TeV. All the other historical shells have limits at or below 50 TeV. These limits scale as B(-1/2) , so absurdly low magnetic fields would be required to get E_m much higher. E_m is probably set by the finite remnant lifetime rather than by synchrotron losses for remnants younger than a few thousand years, so that an observed electron steepening implies that the proton spectrum should steepen at that energy as well. More complicated, inhomogeneous models could allow higher values of E_m in parts of the remnant, but the emission-weighted average value, that characteristic of typical electrons, should obey these limits. The historical remnants should be among the best in the Galaxy at producing the highest-energy Galactic cosmic rays; if they cannot do it, this picture of cosmic-ray origin may need major alteration.

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