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Luminosity indicators in dusty photoionized environments

The luminosity of the central source in ionizing radiation is an essential parameter in a photoionized environment, and one of the most fundamental physical quantities one can measure. We outline a method of determining luminosity for any emission-line region using only infrared data. In dusty environments, grains compete with hydrogen in absorbing continuum radiation. Grains produce infrared emission, and hydrogen produces recombination lines. We have computed a very large variety of photoionization models, using ranges of abundances, grain mixtures, ionizing continua, densities, and ionization parameters. The conditions were appropriate for such diverse objects as H II regions, planetary nebulae, starburst galaxies, and the narrow and broad line regions of active nuclei. The ratio of the total thermal grain emission relative to H$β$ (IR/H$β$) is the primary indicator of whether the cloud behaves as a classical Strömgren sphere (a hydrogen-bounded nebula) or whether grains absorb most of the incident continuum (a dust-bounded nebula). We find two global limits: when $IR/Hβ<100$ infrared recombination lines determine the source luminosity in ionizing photons; when $IR/Hβ\gg100$ the grains act as a bolometer to measure the luminosity.