  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.
