Electron cooling and the connection between expansion and flux-density
  evolution in radio supernovae
  Radio supernovae (RSNe) are weak and rare events. Their typical maximum radio
luminosities are of the order of only $10^{27}$\,erg\,s$^{-1}$\,Hz$^{-1}$.
There are, however, very few cases of relatively bright (and/or close) RSNe,
from which the expansion of the shock and the radio light curves at several
frequencies have been monitored covering several years. Applying the standard
model of radio emission from supernovae, it is possible to relate the defining
parameters of the modelled expansion curve to those of the modelled light
curves in a simple algebraic way, by assuming an evolution law for the magnetic
field and for the energy density of the population of synchrotron-emitting
electrons.
  However, cooling mechanisms of the electrons may affect considerably this
connection between light curves and expansion curve, and lead to wrong
conclusions on the details of the electron acceleration and/or on the CSM
radial density profile. In this paper, we study how electron cooling modifies
the flux-density decay rate of RSNe for a set of plausible/realistic values of
the magnetic field and for different expansion regimes. We use these results to
estimate the magnetic fields of different RSNe observed to date and compare
them to those obtained by assuming energy equipartition between particles and
magnetic fields. For some of the best monitored RSNe, for which deceleration
measurements, optically thin spectral index, and power-law time decay have been
observed (SN\,1979C, SN\,1986J, SN\,1993J, and SN\,2008iz), we find
self-consistent solutions for the index of the power-law circumstellar density
profile ($s=2$ for all cases), the index of the power-law relativistic electron
population (rather steep values, $ p = 2.3 - 3.0$) and the initial magnetic
field (ranging from $\sim 20$ to $> 100$\,G).
