Ionization Parameter as a Diagnostic of Radiation and Wind Pressures in
  H II Regions and Starburst Galaxies
  The ionization parameter U is potentially useful for measuring radiation
pressure feedback from massive star clusters, as it reflects the
radiation-to-gas-pressure ratio and is readily derived from mid-infrared line
ratios. We consider several effects which determine the apparent value of U in
HII regions and galaxies. An upper limit is set by the compression of gas by
radiation pressure. The pressure from stellar winds and the presence of neutral
clumps both reduce U for a given radiation intensity. The most intensely
irradiated regions are selectively dimmed by internal dust absorption of
ionizing photons, inducing observational bias on galactic scales. We explore
these effects analytically and numerically, and use them to interpret previous
observational results.
  We find that radiation confinement sets the upper limit log_10 U = -1 seen in
individual regions. Unresolved starbursts display a maximum value of ~ -2.3.
While lower, this is also consistent with a large portion of their HII regions
being radiation dominated, given the different technique used to interpret
unresolved regions, and given the bias caused by dust absorption. We infer that
many individual, strongly illuminated regions cannot be dominated by stellar
winds, and that even when averaged on galactic scales, shocked wind pressures
cannot be large compared to radiation pressure. Therefore, most HII regions
cannot be adiabatic wind bubbles. Our models imply a metallicity dependence in
the physical structure and dust attenuation of radiation-dominated regions,
both of which should vary strongly across a critical metallicity of about
one-twentieth solar.
