Supernova remnants in molecular clouds: on cosmic ray electron spectra

The particle acceleration process at a shock wave, in the presence of the second-order Fermi acceleration in the turbulent medium near the shock, is discussed as an alternative explanation for the observed flat synchrotron spectra of supernova remnants (SNRs) in molecular clouds. We argue that medium Alfv'en Mach number shocks considered by Chevalier (1999, ApJ, in press) for such SNRs can naturally lead to the observed spectral indices.