Stellar winds in H II regions – II. Turbulent mixing between an H II layer and a stellar wind bubble in the presence of a magnetic field

We discuss the turbulent mixing between an ionization bounded H II layer, and a hot shocked stellar wind (HSSW) which keeps it under pressure. The turbulence is driven by the acoustic instability described in an earlier paper (Breitschwerdt & Kahn). We calculate the stretching of fluid elements and of a frozen-in magnetic field, and derive a condition under which turbulence can decay to small enough length-scales so that effective mixing takes place. We use these arguments to describe the evolution of a wind-driven bubble around an early-type star and conclude that, when there is a uniform ambient magnetic field, mixing occurs freely below a critical polar angle θcrit. We calculate the total mass that is added to the HSSW in this way during the dynamical evolution and derive critical time-scales for which cooling becomes catastrophic. Finally we apply these results to NGC 6334(A) and find an estimate for the ambient magnetic field B0.