Inverse Compton gamma-ray models for remnants of Galactic type Ia supernovae?

We theoretically and phenomenologically investigate the question whether the gamma-ray emission from the remnants of the type Ia supernovae SN 1006, Tycho's SN and Kepler's SN can be the result of electron acceleration alone. The observed synchrotron spectra of the three remnants are used to determine the average momentum distribution of nonthermal electrons as a function of the assumed magnetic field strength. Then the inverse Compton emission spectrum in the Cosmic Microwave Background photon field is calculated and compared with the existing upper limits for the very high energy gamma-ray flux from these sources. It is shown that the expected interstellar magnetic fields substantially overpredict even these gamma-ray upper limits. Only rather strongly amplified magnetic fields could be compatible with such low gamma-ray fluxes. However this would require a strong component of accelerated nuclear particles whose energy density substantially exceeds that of the synchrotron electrons, compatible with existing theoretical acceleration models for nuclear particles and electrons. Even though the quantitative arguments are simplistic, they appear to eliminate simplistic phenomenological claims in favor of a inverse Compton gamma-ray scenario for these sources.