Radio emission models of colliding-wind binary systems

We present calculations of the spatial and spectral distribution of the radio emission from a wide WR + OB colliding-wind binary system based on high-resolution hydrodynamical simulations and solutions to the radiative transfer equation. We account for both thermal and synchrotron radio emission, free-free absorption in both the unshocked stellar wind envelopes and the shocked gas, synchrotron self-absorption, and the Razin effect. To calculate the synchrotron emission several simplifying assumptions are adopted: the relativistic particle energy density is a simple fraction of the thermal particle energy density, in equipartition with the magnetic energy density, and a power-law in energy. We also assume that the magnetic field is tangled such that the resulting emission is isotropic. The applicability of these calculations to modelling radio images and spectra of colliding-wind systems is demonstrated with models of the radio emission from the wide WR + OB binary WR147. Its synchrotron spectrum follows a power-law between 5 and 15 GHz but turns down to below this at lower and higher frequencies. We find that while free-free opacity from the circum-binary stellar winds can potentially account for the low-frequency turnover, models that also include a combination of synchrotron self-absorption and Razin effect are favoured. We argue that the high-frequency turn down is a consequence of inverse-Compton cooling. We present our resulting spectra and intensity distributions, along with simulated MERLIN observations of these intensity distributions. From these we argue that the inclination of the WR147 system to the plane of the sky is low. We summarise by considering extensions of the current model that are important for models of the emission from closer colliding wind binaries, in particular the dramatically varying radio emission of WR 140.