Bottling the Champagne: Dynamics and Radiation Trapping of Wind-Driven Bubbles around Massive Stars.

In this paper we make predictions for the behaviour of wind bubbles around young massive stars using analytic theory. We do this in order to determine why there is a discrepancy between theoretical models that predict that winds should play a secondary role to photoionisation in the dynamics of HII regions, and observations of young HII regions that seem to suggest a driving role for winds. In particular, regions such as M42 in Orion have neutral hydrogen shells, suggesting that the ionising radiation is trapped closer to the star. We first derive formulae for wind bubble evolution in non-uniform density fields, focusing on singular isothermal sphere density fields with a power law index of -2. We find that a classical "Weaver"-like expansion velocity becomes constant in such a density distribution. We then calculate the structure of the photoionised shell around such wind bubbles, and determine at what point the mass in the shell cannot absorb all of the ionising photons emitted by the star, causing an "overflow" of ionising radiation. We also estimate perturbations from cooling, gravity, magnetic fields and instabilities, all of which we argue are secondary effects for the conditions studied here. Our wind-driven model provides a consistent explanation for the behaviour of M42 to within the errors given by observational studies. We find that in relatively denser molecular cloud environments \around single young stellar sources, champagne flows are unlikely until the wind shell breaks up due to turbulence or clumping in the cloud.