On Radiation Pressure in Static, Dusty HII Regions

Radiation pressure acting on gas and dust causes HII regions to have central densities that are lower than the density near the ionized boundary. HII regions in static equilibrium comprise a family of similarity solutions, parametrized by 3 parameters: beta, gamma, and the product (Q_0 n_rms); beta characterizes the stellar spectrum, gamma characterizes the dust/gas ratio, Q_0 is the ionizing output from the star (photons/s), and n_rms is the rms density within the ionized region. Adopting standard values for beta and gamma, varying (Q_0 n_rms) generates a one-parameter family of density profiles, ranging from nearly uniform density (small Q_0 n_rms), to hollow-sphere HII regions (large Q_0 n_rms). When (Q_0 n_rms) exceeds 10^{52} cm^{-3} s^{-1}, dusty HII regions have conspicuous central cavities, even if no stellar wind is present. For given beta, gamma and (Q_0 n_rms), a fourth quantity, which can be Q_0, determines the overall size and density of the HII region. Examples of density and emissivity profiles are given. We show how quantities of interest -- such as the peak-to-center emissivity ratio, the rms-to-mean density ratio, the edge-to-rms density ratio, and the fraction of the ionizing photons absorbed by the gas -- depend on the 3 parameters beta, gamma, and (Q_0 n_rms). For dusty HII regions, compression of the gas and dust into an ionized shell results in a substantial increase in the fraction of the >13.6 eV photons that actually ionize H (relative to a uniform density HII region with the same dust/gas ratio and density n=n_rms). We discuss the extent to which radial drift of dust grains in HII regions can alter the dust-to-gas ratio. The applicability of these solutions to real HII regions is discussed.