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

Abstract

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. It is shown that the magnetic field must be amplified up to values between 250 and 500 microGauss in the case of Cas A, Kepler, and Tycho, or ~ 100 microGauss in the case of SN 1006 and G347.3-0.5. The diffusion coefficient at the highest electron energy can also be derived from the data, by relating the X-ray energy cutoff to the acceleration timescale. Values typically between 1 and 10 times the Bohm diffusion coefficient are found to be required. We also find interesting constraints on the energy dependence of the diffusion coefficient. This favours diffusion regimes between the Kraichnan and the Bohm regime, and rejects turbulence spectrum indices larger than ~ 3/2. Finally, the maximum energy of the accelerated particles is found to lay between 10^13 and 5 10^13 eV for electrons, and around Z \times 8 10^14 eV at most for nuclei (or ~ 2.5 times less if a Bohm diffusion 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 difficult for the considered SNRs in their current stage of evolution to produce protons up to the knee of the cosmic-ray spectrum, at ~ 3 10^15 eV, and essentially impossible to accelerate Fe nuclei up to either the ankle at ~ 3 10^18 eV or the second knee at ~ 5 10^17 eV.