Radio emission from shell-type supernova remnants
  The evolution of the radio emission of shell-type Supernova remnants (SNRs) is modeled within the framework of the simple and commonly used assumptions that the mechanism of diffusive shock acceleration (DSA) is responsible for generating radio emitting electrons and that the magnetic field is the typical interstellar field compressed at the shock. It is considered that electrons are injected into the mechanism in test-particle regime directly from the high energy tail of the downstream Maxwellian distribution function. The model can be applied to most of the observed SNRs. It is shown that the model successfully explains the many averaged observational properties of evolved shell-type SNRs. In particular, the radio surface brightness ($\Sigma$) evolves with diameter as $\sim D^{-(0.3 \div 0.5)}$, while the bounding shock is strong (Mach number is ${\mathcal M} \geq10$), followed by steep decrease (steeper than $\sim D^{-4.5}$) for ${\cal M} <10$. Such evolution of the surface brightness with diameter and its strong dependence on the environmental parameters strongly reduce the usefulness of $\Sigma - D$ relations as a tool for determining the distances to SNRs. The model predicts no radio emission from SNRs in the late radiative stage of evolution and the existence of radio-quiet but relatively active SNRs is possible. Our model easily explains very large-diameter radio sources such as the Galactic Loops and the candidates for Hypernova radio remnants. The model predicts that most of the observed SNRs are located in a tenuous phase of the ISM. From the comparison of the model results with the statistics of evolved shell-type SNRs, we were able to estimate the fraction of electrons accelerated from the thermal pool in the range $(3\div 11) \times 10^{- 4}$. 
Abdul Asvarov