  Shell-type supernova remnants (SNRs) exhibit correlations between radio
surface brightness, SNR diameter, and ambient medium density. We investigate
these correlations, to extract useful information about the typical
evolutionary stage of radio SNRs, and to obtain insight into the origin of the
relativistic electrons and magnetic fields responsible for the radio emission.
We propose a scenario, according to which the observed correlations are the
combined effect of SNRs evolving in a wide range of ambient conditions, rather
than the evolutionary track of a "typical" SNR. We then develop a parametric
approach to interpret the statistical data, and apply it to the data sample
previously published by Berkhuijsen, as well as to a sample of SNRs in the
galaxy M33. We find that SNRs cease to emit effectively in radio at a stage
near the end of their Sedov evolution, and that models of synchrotron emission
with constant efficiencies in particle acceleration and magnetic field
amplification do not provide a close match to the data. We discuss the problem
of the cumulative distribution in size, showing that the slope of this
distribution does not relate to the expansion law of SNRs, as usually assumed,
but only to the ambient density distribution. This solves a long-standing
paradox: the almost linear cumulative distribution of SNRs led several authors
to conclude that these SNRs are still in free expansion, which also implies
very low ambient densities. Within this framework, we discuss the case of the
starburst galaxy M82. Statistical properties of SNR samples may be used to shed
light on both the physics of electron acceleration and the evolution of SNRs.
More precise results could be obtained by combining data of several surveys of
SNRs in nearby galaxies.
