Mioduszewski, Amy J.; Dwarkadas, Vikram V.; Ball, Lewis, ApJ, 562, 869

Abstract: We present calculations of the radio emission from supernovae based on high-resolution simulations of the hydrodynamics and radiation     transfer, using simple energy density relations that link the properties of the radiating electrons and the magnetic field to the hydrodynamics. As a specific example we model the emission from SN 1993J, which cannot be adequately fitted with the often-used analytic minishell model, and present a good fit to the radio evolution at a single frequency. Both free-free absorption and synchrotron self-absorption are needed to fit the light curve at early times, and a circumstellar density profile of r^{-1.7} provides the best fit to the later data. We show that the interaction of density structures in the ejecta with the reverse supernova shock may produce features in the radio light curves such as have been observed. We discuss the use of high-resolution radio images of supernovae to distinguish between different absorption mechanisms and determine the origin of specific light curve features. Comparisons of VLBI images of SN 1993J with synthetic model images suggest that internal free-free absorption completely obscures emission at 8.4 GHz passing through the center of the supernova for the first few tens of years after explosion. We predict that at 8.4 GHz the internal free-free absorption is currently declining, and that over the next ~40 yr the surface brightness of the center of the source should increase relative to the bright ring of emission seen in VLBI images. Similar absorption in a nearby supernova would make the detection of a radio pulsar at 1 GHz impossible for ~150 yr after explosion.

Simulations: Here's an MPEG simulation showing the evolution of the radio supernova with time in the simulations. The upper frame contains the simulated images, and the lower frame the flux density profile from the supernova. At early times, the SN is dominated by synchrotron self-absorption, and the flux profile is flat over the entire surface. But once the SN becomes optically thin the radio emission peaks in the thin shell between the inner and outer shocks. The simulations shows that the width of the radio emission region grows with time, as expected. These simulations compare quite well with the observations.
(Please note that the scale on the image is inverted. Red is actually the maximum flux.)

You can compare these simulated images to the observed ones. Norbert Bartel and his group have some fascinating VLBI observations of 1993J, shown here.

Dwarkadas, Vikram V., Mioduszewski, Amy J., Ball, Lewis,

in the proccedings of IAU Colloquium 192, "SUPERNOVAE (10 years of SN1993J)", edited by J.M. Marcaide and K.W. Weiler, Springer Verlag 2004

Abstract : We present calculations of the radio images and light curves from supernovae, based on high-resolution numerical simulations of the hydrodynamics and radiation transfer in a spherically symmetric medium. As a specific example we model the emission from SN1993J. This supernova does not appear to be expanding in a self-similar fashion, and cannot be adequately fitted with the often-used analytic mini-shell model. We present a good fit to the radio evolution at a single frequency. Both free-free absorption and synchrotron self-absorption are needed to fit the light curve at early times, and a circumstellar density profile of $\rho \sim r ^{-1.7}$ provides the best fit to the later data. Comparisons of VLBI images of SN1993J with synthetic model images suggest that internal free-free absorption completely obscures emission at 8.4~GHz passing through the center of the supernova for the first few tens of years after explosion

SN 1993J VLBI. IV. A Geometric Distance to M81 with the Expanding Shock Front Method

N. Bartel, M. F. Bietenholz, M. P. Rupen and V. V. Dwarkadas

The Astrophysical Journal, Volume 668, Issue 2, pp. 924-940, 2007

We compare the angular expansion velocities, determined with VLBI, with the linear expansion velocities measured from optical spectra for supernova 1993J in the galaxy M81, over the period from 7 days to ~9 yr after shock breakout, and estimate the distance to SN 1993J using the expanding shock front method (ESM). We find that the best distance estimate is obtained by fitting the angular velocity of a point halfway between the contact surface and outer shock front to the maximum observed hydrogen gas velocity. We obtain a direct, geometric, distance estimate for M81 of D=3.96+/-0.05+/-0.29 Mpc with statistical and systematic error contributions, respectively, which combine to a total standard error of +/-0.29 Mpc. The upper limit of 4.25 Mpc corresponds to the hydrogen gas with the highest observed velocity just reaching out to the contact surface a few days after shock breakout. The lower limit of 3.67 Mpc corresponds to this gas reaching as far out as the forward shock for the whole observing period, which would mean that Rayleigh-Taylor fingers have grown to the forward shock already a few days after shock breakout. Our distance estimate is 9%+/-13% larger than that of 3.63+/-0.34 Mpc from the HST Key Project. The radio shell and the Hα absorbing and emitting gas are similarly decelerated on average, but the latter slightly less so than the former several years after shock breakout. This may indicate developing Rayleigh-Taylor fingers, extending progressively further into the shocked circumstellar medium.