Based on theoretical spectra computed using Density Functional Theory we study the properties of Polycyclic Aromatic Hydrocarbons (PAH). In particular using bin-average spectra of PAH molecules with varying number of carbons we investigate how the intensity of the mid-infrared emission bands, 3.3, 6.2, 7.7 and 11.3 microns, respond to changes in the number of carbons, charge of the molecule, and the hardness of the radiation field that impinges the molecule. We confirm that the 6.2/7.7 band ratio is a good predictor for the size of the PAH molecule (based on the number of carbons present). We also investigate the efficacy of the 11.3/3.3 ratio to trace the size of PAH molecules and note the dependence of this ratio on the hardness of the radiation field. While the ratio can potentially also be used to trace PAH molecular size, a better understanding of the impact of the underlying radiation field on the 3.3 microns feature and the effect of the extinction on the ratio should be evaluated. The newly developed diagnostics are compared to band ratios measured in a variety of galaxies observed with the Infrared Spectrograph on board the Spitzer Space Telescope. We demonstrate that the band ratios can be used to probe the conditions of the interstellar medium in galaxies and differentiate between environments encountered in normal star forming galaxies and Active Galactic Nuclei. Our work highlights the immense potential that PAH observations with the James Webb Space Telescope will have on our understanding of the PAH emission itself and of the physical conditions in galaxies near and far.
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