  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.
