Determining the H⁺ region / PDR equation of state in star-forming regions

The emission-line regions of starburst galaxies and active nuclei reveal a wealth of spectroscopic information. A unified picture of the relationship among ionized, atomic, and molecular gas makes it possible to better understand these observations. We performed a series of calculations designed to determine the equation of state - the relationship among density, temperature, and pressure - through emission-line diagnostic ratios that form in the H⁺ region and the photodissociation region (PDR). We consider a wide range of physical conditions in the H⁺ region. We connect the H⁺ region to the PDR by considering two constant pressure cases: one with no magnetic field and one in which the magnetic field overwhelms the thermal pressure. We show that diagnostic ratios can yield the equation of state for single H⁺ regions adjacent to single PDRs, with the results being more ambiguous when considering observations of entire galaxies. As a test, we apply our calculations to the Orion H⁺/PDR region behind the Trapezium. We find the ratio of thermal to magnetic pressure in the PDR to be ∼1.2. If magnetic and turbulent energy are in equipartition, our results mean that the magnetic field is not the cause of the unexplained broadening in M42, but may significantly affect line broadening in the PDR. Since Orion is often used to understand physical processes in extragalactic environments, our calculations suggest that magnetic pressure should be considered in modeling such regions.