2017ApJ...837..171Y

The so-called unidentified infrared emission (UIE) features at 3.3, 6.2, 7.7, 8.6, and 11.3 µm ubiquitously seen in a wide variety of astrophysical regions are generally attributed to polycyclic aromatic hydrocarbon (PAH) molecules. Astronomical PAHs may have an aliphatic component, as revealed by the detection in many UIE sources of the aliphatic C-H stretching feature at 3.4 µm. The ratio of the observed intensity of the 3.4 µm feature to that of the 3.3 µm aromatic C-H feature allows one to estimate the aliphatic fraction of the UIE carriers. This requires knowledge of the intrinsic oscillator strengths of the 3.3 µm aromatic C-H stretch (A_3.3) and the 3.4 µm aliphatic C-H stretch (A_3.4). Lacking experimental data on A_3.3 and A_3.4 for the UIE candidate materials, one often has to rely on quantum-chemical computations. Although the second-order Moller-Plesset (MP2) perturbation theory with a large basis set is more accurate than the B3LYP density functional theory, MP2 is computationally very demanding and impractical for large molecules. Based on methylated PAHs, we show here that, by scaling the band strengths computed at an inexpensive level (e.g., B3LYP/6-31G*), we are able to obtain band strengths as accurate as those computed at far more expensive levels (e.g., MP2/6-311+G(3df,3pd)). We calculate the model spectra of methylated PAHs and their cations excited by starlight of different spectral shapes and intensities. We find that (I_3.4/I_3.3)_mod, the ratio of the model intensity of the 3.4 µm feature to that of the 3.3 µm feature, is insensitive to the spectral shape and intensity of the exciting starlight. We derive a straightforward relation for determining the aliphatic fraction of the UIE carriers (i.e., the ratio of the number of C atoms in aliphatic units N_C,ali to that in aromatic rings N_C,aro) from the observed band ratios (I_3.4/I_3.3)_obs: N_C,ali/N_C,aro~0.57×(I_3.4/I_3.3)_obs for neutrals and N_C,ali/N_C,aro~0.26×(I_3.4/I_3.3)_obs for cations.