The colliding winds in a massive binary system generate synchrotron emission due to a fraction of electrons that have been accelerated to relativistic speeds around the shocks in the colliding-wind region. We studied the radio light curve of 9 Sgr = HD 164794, a massive O-type binary with a 9.1-yr period. We investigated whether the radio emission varies consistently with orbital phase and we determined some parameters of the colliding-wind region. We reduced a large set of archive data from the Very Large Array (VLA) to determine the radio light curve of 9 Sgr at 2, 3.6, 6 and 20 cm. We also constructed a simple model that solves the radiative transfer in the colliding-wind region and both stellar winds. The 2-cm radio flux shows clear phase-locked variability with the orbit. The behaviour at other wavelengths is less clear, mainly due to a lack of observations centred on 9 Sgr around periastron passage. The high fluxes and nearly flat spectral shape of the radio emission show that synchrotron radiation dominates the radio light curve at all orbital phases. The model provides a good fit to the 2-cm observations, allowing us to estimate that the brightness temperature of the synchrotron radiation emitted in the colliding-wind region at 2 cm is at least 4 x 10^8 K. The simple model used here already allows us to derive important information about the colliding-wind region. We propose that 9 Sgr is a good candidate for more detailed modelling, as the colliding-wind region remains adiabatic during the whole orbit thus simplifying the hydrodynamics.
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