Understanding extragalactic ionized regions through emission-line diagnostics: the power of multidimensional diagnostic diagrams

Optical diagnostic diagrams are useful tools for identifying different extragalactic ionized regions. The state-of-the-art photoionization models provide the theoretical basis for understanding the distribution of the data in these diagrams, and serve as one of the important methods to calibrate the gas-phase metallicity and other physical parameters of ionized regions. However, the model-constraining power of the original two-dimensional diagrams is limited. As a result, inconsistent model predictions might occur for different diagnostic diagrams, and the measured physical properties of the ionized regions can have large systemic uncertainties. In this talk, I will introduce a three-dimensional diagnostic diagram to solve the above problems. I will show that the intrinsic shapes of photoionization model surfaces in three dimensions uniquely determine a new two-dimensional projection, which puts strong constraints on the model parameters, including the shape of the ionizing SED, the N/O abundance pattern, etc. Combined with a pair of AGN and SF models, the three-dimensional diagram can also be used to calculate the fractional contribution from AGN or SF ionization for composite regions. In addition, the best-fit SF model determined by this diagram yields consistent predictions on both metallicity and ionization parameter for SF regions in different line-ratio spaces, providing a potential solution to the debated correlation between these two quantities in the literature. Finally, I will briefly discuss the limitation of current photoionization models in reproducing the strength of certain emission lines, and what we can learn in these cases.