Shocks in nova outflows. II. Synchrotron radio emission

The discovery of GeV gamma-rays from classical novae indicates that shocks and relativistic particle acceleration are energetically key in these events. Further evidence for shocks comes from thermal keV X-ray emission and an early peak in the radio light curve on a timescale of months with a brightness temperature which is too high to result from freely expanding photo-ionized gas. Paper I developed a one dimensional model for the thermal emission from nova shocks. This work concluded that the shock-powered radio peak cannot be thermal if line cooling operates in the post-shock gas at the rate determined by collisional ionization equilibrium. Here we extend this calculation to include non-thermal synchrotron emission. Applying our model to three classical novae, we constrain the amplification of the magnetic field $\epsilon_B$ and the efficiency $\epsilon_e$ of accelerating relativistic electrons of characteristic Lorentz factor $\gamma \sim 100$. If the shocks are radiative (low velocity $v_{\rm sh} \lesssim 1000$ km s$^{-1}$) and cover a large solid angle of the nova outflow, as likely characterize those producing gamma-rays, then values of $\epsilon_e \sim 0.01-0.1$ are required to achieve the peak radio brightness for $\epsilon_B = 10^{-2}$. Such high efficiencies exclude secondary pairs from pion decay as the source of the radio-emitting particles, instead favoring the direct acceleration of electrons at the shock. If the radio-emitting shocks are instead adiabatic (high velocity), as likely characterize those responsible for the thermal X-rays, then much higher brightness temperatures are possible, allowing the radio-emitting shocks to cover a smaller outflow solid angle.