  We present a theoretical model for the non-thermal radio emission from single
hot stars, in terms of synchrotron radiation from electrons accelerated in
wind-embedded shocks. The model is described by five independent parameters
each with a straightforward physical interpretation. Applying the model to a
high-quality observation of Cyg OB2 No. 9 (O5 If), we obtain meaningful
constraints on most parameters. The most important result is that the outer
boundary of the synchrotron emission region must lie between 500 and 2200
stellar radii. This means that shocks must persist up to that distance. We also
find that relatively weak shocks (with a compression ratio < 3) are needed to
produce the observed radio spectrum. These results are compatible with current
hydrodynamical predictions. Most of our models also show a relativistic
electron fraction that increases outwards. This points to an increasing
efficiency of the acceleration mechanism, perhaps due to multiple acceleration,
or an increase in the strength of the shocks. Implications of our results for
non-thermal X-ray emission are discussed.

Astrophysics