  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. We use a three-dimensional,
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. To obtain good agreement with the X-ray
observations, our initial mass-loss rate estimates require a down-shift by a
factor of roughly 7.7 to $6.5\times10^{-7}$ and $7.5\times10^{-7}$ solar mass
per year 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 $\simeq 0.1$ 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. 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 $\approx 0.3-52\;$G.
(Abridged)
