Radio Emission and Particle Acceleration in SN 1993J

The radio light curves of SN 1993J are discussed. We nd that a t to the individual spectra by a synchrotron spectrum, suppressed by external free-free absorption and synchrotron self-absorption, gives a superior t to models based on pure free-free absorption. A standard r~2 circumstellar medium is assumed and is found to be adequate. From the ux and cuto wavelength, the magnetic eld in the synchrotron-emitting region behind the shock is determined to cm)~1 G. The strength of B B 64(R s /1015 the eld argues strongly for turbulent amplication behind the shock. The ratio of the magnetic and thermal energy density behind the shock is D0.14. 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 a ects 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 ux and number of relativistic electrons well. The injected electron spectrum has dn/dc P c~2.1, consistent with di usive shock acceleration. The injected number density of relativistic electrons scales with the thermal electron energy density, oV 2, rather than the density, o. The evolution of the ux is strongly connected to the deceleration of the shock wave. The total energy density of the relativistic electrons, if extrapolated to c D 1, is D5 ] 10~4 of the thermal energy density. The free-free absorption required is consistent with previous calculations of the circumstellar temperature of SN 1993J, K, which failed in explaining the radio light curves by T e D (210) ] 105 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 e ect for other supernovae, are also briey discussed. It is argued that especially the expansion velocity, both directly and through the temperature, is important for determining the relative importance of the freefree absorption and synchrotron self-absorption. Some guidelines for the modeling and interpretation of VLBI observations are also given.