On radiation pressure in static, dusty H II 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 with three parameters: β, γ, and the product Q ₀ n _rms; β characterizes the stellar spectrum, γ characterizes the dust/gas ratio, Q ₀ is the stellar ionizing output (photons/s), and n _rms is the rms density within the ionized region. Adopting standard values for β and γ, varying Q ₀ n _rms generates a one-parameter family of density profiles, ranging from nearly uniform density (small Q ₀ n _rms) to shell-like (large Q ₀ n _rms). When Q ₀ n _rms ≳ 10⁵² cm^-3 s^-1, dusty HII regions have conspicuous central cavities, even if no stellar wind is present. For given β, γ, 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-central emission measure 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 β, γ, 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 stellar 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.