Stochastic electron acceleration in the TeV supernova remnant RX J1713.7-3946: the high-energy cut-off

In the leptonic scenario for TeV emission from a few well-observed shell-type TeV supernova remnants (STTSNRs), very weak magnetic fields are inferred. If fast-mode waves are produced efficiently in the shock downstream, we show that they are viable agents for acceleration of relativistic electrons inferred from the observed spectra even in the subsonic phase, in spite that these waves are subject to strong damping by thermal background ions at small dissipation scales. Strong collisionless non-relativistic astrophysical shocks are studied with the assumption of a constant Alfven speed in the downstream. The turbulence evolution is modelled with both the Kolmogorov and Kraichnan phenomenology. Processes determining the high-energy cut-off of non-thermal electron distributions are examined. The Kraichnan models lead to a shallower high-energy cut-off of the electron distribution and require a lower downstream density than the Kolmogorov models to fit a given emission spectrum. With reasonable parameters, the model explains observations of STTSNRs, including recent data obtained with the Fermi gamma-ray telescope. More detailed studies of the turbulence generation and dissipation processes, supernova explosions and progenitors are warranted for better understanding of the nature of supernova shocks.