Maximum energies of shock-accelerated electrons in young shell supernova remnants

Young supernova remnants (SNRs) are often assumed to be the source of cosmi c rays up to energies approaching the slight steepening in the cosmic-ray s pectrum at around 1000 TeV, known as the "knee." We show that the observed X-ray emission of 14 radio-bright shell remnants, including all live histor ical shells, can be used to put limits on E-max, the energy at which the el ectron energy distribution must steepen from its slope at radio-emitting en ergies. Most of the remnants show thermal spectra, so any synchrotron compo nent must fall below the observed X-ray fluxes. We obtain upper limits on E -max by considering the most rapid physically plausible cutoff in the relat ivistic electron distribution, an exponential, which is as sharp or sharper than found in any more elaborate models. This maximally curved model then gives us the highest possible E-max consistent with not exceeding observed X-rays. Our results are thus independent of particular models for the elect ron spectrum in SNRs. Assuming homogeneous emitting volumes with a constant magnetic field strength of 10 mu G, no object could reach 1000 TeV, and on ly one, Kes 73, has an upper limit on E-max above 100 TeV. All the other re mnants have limits at or below 80 TeV. E-max is probably set by the finite remnant lifetime rather than by synchrotron losses for remnants younger tha n a few thousand years, so that an observed electron steepening should be a ccompanied by steepening at the same energy for protons. More complicated, inhomogeneous models could allow higher values of E-max in parts of the rem nant, but the emission-weighted average value, that characteristic of typic al electrons, should obey these limits. The young remnants are not expected to improve much over their remaining lives at producing the highest energy Galactic cosmic rays; if they cannot, this picture of cosmic-ray origin ma y need major alteration.