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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.