The Acceleration of Electrons In Radio Supernova SN1986J
We propose a model for radio supernovae (RSN) based on the synchrotron emission from relativistic electrons which are diffusively accelerated at the expanding supernova shock. This model was originally developed for application to the optically thin emission observed from SN1987A. Here we generalise it by including the effects of free-free absorption from both an external screen and from material internal to the source, and by relaxing the restriction to an azimuthal B-field. We find a good fit to the entire set of radio data for the best observed highly-luminous RSN -- SN1986J -- with a reduced \chi^2 of 3.85. Applying the new model to SN1988Z, another intrinsically bright RSN, also yields a good fit (\chi^2_{\rm red}\approx 2) but this is less significant, because of the limited data on this distant (z=0.02) source. These fits suggest that the shock expands at constant speed, that the magnetic field within the source decreases with time according to t^{-2}, and that the compression ratio of the shock front is close to the value expected of a strong shock in an ideal gas of adiabatic index 5/3 -- indicating a relatively low value of the cosmic ray pressure compared with SN1987A. In the case of SN1986J we derive an explosion date in August/September 1982, a magnetic field at the position of the shock 1000 days after explosion of 4nT and a spatial diffusion coefficient of the electrons of 4 10^{19} cm^2/s, four orders of magnitude greater than the Bohm value. In addition, we obtain the optical depths to external and internal absorption, and derive an estimate of the mass-loss rate.