Luminosity indicators in dusty photoionized environments

The luminosity of the central source in ionizing radiation is an essential parameter in a photoionized environment and is one of the most fundamental physical quantities one can measure. We outline a method of determining the 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 Dhotoionization models, using ranges of abundances,grain mixtures, ionizing continua, densities, and ionization parameters. The conditions were appropriate for such diverse objects as H rr 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 beta (IR/H beta) is the primary indicator of whether the cloud behaves as a classical Stromgren 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/H beta < 100, infrared recombination lines determine the source luminosity in ionizing photons; when IR/H beta much greater than 100, the grains act as a bolometer to measure the luminosity.