Polycyclic Aromatic Hydrocarbon emission model in photodissociation
  regions I: Application to the 3.3, 6.2, and 11.2 $\mu$m bands
  We present a charge distribution based model that computes the infrared
spectrum of polycyclic aromatic hydrocarbon (PAH) molecules using recent
measurements or quantum chemical calculations of specific PAHs. The model is
applied to a sample of well-studied photodissociation regions (PDRs) with
well-determined physical conditions (the radiation field strength, $G_{0}$,
electron density $n_{e}$, and the gas temperature, $T_{\rm gas}$).
Specifically, we modelled the emission of five PAHs ranging in size from 18 to
96 carbon atoms, over a range of physical conditions characterized by the
ionization parameter $\gamma = G_{0}\times T_{\rm gas}^{1/2}/n_{e}$. The anions
emerge as the dominant charge carriers in low $\gamma $ ($< 2\times 10^{2}$)
environments, neutrals in the intermediate $\gamma$ ($10^{3} - 10^{4}$)
environments, and cations in the high $\gamma$ ($ > 10^{5}$) environments.
Furthermore, the PAH anions and cations exhibit similar spectral
characteristics. The similarity in the cationic and anionic spectra translates
into the interpretation of the 6.2/(11.0+11.2) band ratio, with high values of
this ratio associated with large contributions from either cations or anions.
The model's predicted values of 6.2/(11.0+11.2) and 3.3/6.2 compared well to
the observations in the PDRs NGC 7023, NGC 2023, the horsehead nebula, the
Orion bar, and the diffuse ISM, demonstrating that changes in the charge state
can account for the variations in the observed PAH emission. We also reassess
the diagnostic potential of the 6.2/(11.0+11.2) vs 3.3/(11.0+11.2) ratios and
show that without any prior knowledge about $\gamma$, the 3.3/(11.0+11.2) can
predict the PAH size, but the 6.2/(11.0+11.2) cannot predict the $\gamma$ of
the astrophysical environment.
