Observational constraints on energetic particle diffusion in young supernovae remnants: amplified magnetic field and maximum energy

Constraints on the diffusion and acceleration parameters in five young supernova remnants (SNRs) are derived from the observed thickness of their X-ray rims, as limited by the synchrotron losses of the highest energy electrons, assuming uniform and isotropic turbulence. From a joint study of the electrons diffusion and advection in the downstream medium of the shock, it is shown that the magnetic field must be amplified up to values between 250 and 500 mu G in the case of Cas A, Kepler, and Tycho, or similar to 100 mu G in the case of SN 1006 and G347.3- 0.5. The di. usion coe. cient at the highest electron energy can also be derived from the data, by relating the X- ray energy cuto. to the acceleration timescale. Values typically between 1 and 10 times the Bohm di. usion coe. cient are found to be required. We also find interesting constraints on the energy dependence of the diffusion coe. cient, by requiring that the di. usion coe. cient at the maximum proton energy be not smaller than the Bohm value in the amplified field. This favours di. usion regime between the Kraichnan and the Bohm regime, and rejects turbulence spectrum indices larger than similar or equal to 3/2. Finally, the maximum energy of the accelerated particles is found to lay between 10(13) and 5 x 10(13) eV for electrons, and around Z x 8 x 10(14) eV at most for nuclei ( or similar to 2.5 times less if a Bohm di. usion regime is assumed), roughly independently of the compression ratio assumed at the shock. Even by taking advantage of the uncertainties on the measured parameters, it appears very di. cult for the considered SNRs in their current stage of evolution to produce protons up to the knee of the cosmic- ray spectrum, at similar to 3 x 10(15) eV, and essentially impossible to accelerate Fe nuclei up to either the ankle at similar to 3 x 10(18) eV or the second knee at similar to 5 x 10(17) eV.