Abstract
We study the solutions of a modified version of the isothermal Lane-Emden equation, which incorporates the effect of the (owtwards directed) radiation pressure resulting from photoionizations. These solutions are relevant for HII regions around a cluster with over ≈500 O stars, which can photoionize gas out to ≈√{10{cm}^{-3}/n_0}pc (where n_0 is the central gas density), where the effects of the self-gravity and the radiation pressure become important. We find that the solutions have a transition from a “gravity dominated” regime (in which the solutions converge at large radii to the non-singular, isothermal sphere solution) to a “radiation pressure dominated” regime (in which the density diverges at a finite radius) for central HII region densities above n_{crit}=100 cm^{-3}. We argue that the high central density, radiation pressure dominated solutions will not occur in most astrophysically relevant situations, because of the absence of a possible confining environment with a high enough pressure.
