3 An alternative model

Recently, Waxman & Loeb (1998) have produced an alternative sub-relativistic model to explain the radio curve shown in Fig. 1. In their model, the radio emission arises in the post-shocked gas (shock speed of 60000 km s^-1). They assume rapid equilibration between the electrons and protons and a modest compressed magnetic field. In this model, the energy in the magnetic field is many orders of magnitude smaller than that in the energetic particles. The curious result is that Waxman & Loeb (1999) are able to reproduce the observed spectrum (save for a high frequency point) and an energy estimate comparable to that of Kulkarni et al. This is curious because it is a general result that the total energy is minimized only when there is equipartition between the electrons and magnetic field strength.

The Waxman & Loeb analysis is based on the assumption of mono-energetic electrons. Sari et al. (1999) have carried out a detailed analysis using a thermal energy spectrum and find that for a non-equipartition plasma (as envisaged by Waxman & Loeb) the total energy is much higher than 10⁴⁹ erg. Thus it appears that the simplification used by Waxman & Loeb does grossly underestimate

the total energy. Thus we conclude that either the energy of the radio emitting plasma is 10⁵² erg or that there exists a relativistic shock in this SN.