We present a new method to accurately describe the ionization fraction and the size distribution of polycyclic aromatic hydrocarbons ( PAHs ) within astrophysical sources .
To this purpose , we have computed the mid-infrared emission spectra of 308 PAH molecules of varying sizes , symmetries , and compactness , generated in a range of radiation fields .
We show that the intensity ratio of the solo CH out-of-plane bending mode in PAH cations and anions ( referred to as the “11.0” \micron band , falling in the 11.0–11.3 \micron region for cations and anions ) to their 3.3 \micron emission , scales with PAH size , similarly to the scaling of the 11.2/3.3 ratio with the number of carbon atoms ( N _ { \mathrm { C } } ) for neutral molecules .
Among the different PAH emission bands , it is the 3.3 \micron band intensity which has the strongest correlation with N _ { \mathrm { C } } , and drives the reported PAH intensity ratio correlations with N _ { \mathrm { C } } for both neutral and ionized PAHs .
The 6.2/7.7 intensity ratio , previously adopted to track PAH size , shows no evident scaling with N _ { \mathrm { C } } in our large sample .
We define a new diagnostic grid space to probe PAH charge and size , using the ( 11.2+11.0 ) /7.7 and ( 11.2+11.0 ) /3.3 PAH intensity ratios respectively .
We demonstrate the application of the ( 11.2+11.0 ) /7.7 – ( 11.2+11.0 ) /3.3 diagnostic grid for galaxies M82 and NGC 253 , for the planetary nebula NGC 7027 , and the reflection nebulae NGC 2023 and NGC 7023 .
Finally , we provide quantitative relations for PAH size determination depending on the ionization fraction of the PAHs and the radiation field they are exposed to .