The 2.35 year itch of Cygnus OB2 #9 III. X-ray and radio emission analysis based on 3D hydrodynamical modelling

Context. The wind-wind collision in a massive star binary system leads to the generation of high temperature shocks that emit at X-ray wavelengths and, if particle acceleration is effective, may exhibit non-thermal radio emission. Cyg OB2#9 is one of a small number of massive star binary systems in this class. Aims. X-ray and radio data recently acquired as part of a project to study Cyg OB2#9 are used to constrain physical models of the binary system, providing in-depth knowledge about the wind-wind collision and the thermal, and non-thermal, emission arising from the shocks. Methods. We use a 3D, adaptive mesh refinement simulation (including wind acceleration, radiative cooling, and the orbital motion of the stars) to model the gas dynamics of the wind-wind collision. The simulation output is used as the basis for radiative transfer calculations considering the thermal X-ray emission and the thermal/non-thermal radio emission. Results. The flow dynamics in the simulation show that wind acceleration (between the stars) is inhibited at all orbital phases by the opposing star's radiation field, reducing pre-shock velocities below terminal velocities. To obtain good agreement with the X-ray observations, our initial mass-loss rate estimates require a down-shift by a factor of similar to 7.7 to 6.5 x 10(-7) M-circle dot yr(-1) and 7.5 x 10(-7) M-circle dot yr(-1) for the primary and secondary star, respectively. Furthermore, the low gas densities and high shock velocities in Cyg OB2 #9 are suggestive of unequal electron and ion temperatures, and the X-ray analysis indicates that an immediately post-shock electron-ion temperature ratio of similar or equal to 0.1 is also required. The radio emission is dominated by non-thermal synchrotron emission. A parameter space exploration provides evidence against models assuming equipartition between magnetic and relativistic energy densities. However, fits of comparable quality can be attained with models having stark contrasts in the ratio of magnetic-to-relativistic energy densities. Both X-ray and radio lightcurves are largely insensitive to viewing angle. The variations in X-ray emission with orbital phase can be traced back to an inverse relation with binary separation and pre-shock velocity. The radio emission also scales with pre-shock velocity and binary separation, but to positive powers (i.e. not inversely). The radio models also reveal a subtle effect whereby inverse Compton cooling leads to an increase in emissivity as a result of the synchrotron characteristic frequency being significantly reduced. Finally, using the results of the radio analysis, we estimate the surface magnetic field strengths to be approximate to 0.3-52 G.