Radio Emission and Particle Acceleration in SN 1993J

The radio light curves of SN 1993J are discussed. We find that a fit to the individual spectra by a synchrotron spectrum, suppressed by external free-free absorption and synchrotron self-absorption, gives a superior fit to models based on pure free-free absorption. A standard r-2 circumstellar medium is assumed and is found to be adequate. From the flux and cutoff wavelength, the magnetic field in the synchrotron-emitting region behind the shock is determined to B ≈ 64(Rs/1015 cm)-1 G. The strength of the field argues strongly for turbulent amplification behind the shock. The ratio of the magnetic and thermal energy density behind the shock is ~0.14. Synchrotron losses dominate the cooling of the electrons, whereas inverse Compton losses due to photospheric photons are less important. For most of the time also Coulomb cooling affects the spectrum. A model where a constant fraction of the shocked, thermal electrons are injected and accelerated, and subsequently lose their energy due to synchrotron losses, reproduces the observed evolution of the flux and number of relativistic electrons well. The injected electron spectrum has dn/dγ ∝ γ-2.1, consistent with diffusive shock acceleration. The injected number density of relativistic electrons scales with the thermal electron energy density, ρV2, rather than the density, ρ. The evolution of the flux is strongly connected to the deceleration of the shock wave. The total energy density of the relativistic electrons, if extrapolated to γ ~ 1, is ~5 × 10-4 of the thermal energy density. The free-free absorption required is consistent with previous calculations of the circumstellar temperature of SN 1993J, Te ~ (2-10) × 105 K, which failed in explaining the radio light curves by pure free-free absorption. Implications for the injection of the relativistic electrons, and the relative importance of free-free absorption, Razin suppression, and the synchrotron self-absorption effect for other supernovae, are also briefly discussed. It is argued that especially the expansion velocity, both directly and through the temperature, is important for determining the relative importance of the free-free absorption and synchrotron self-absorption. Some guidelines for the modeling and interpretation of VLBI observations are also given.