A Principal Component Analysis of polycyclic aromatic hydrocarbon emission in NGC 2023

We use the measured fluxes of polycyclic aromatic hydrocarbon (PAH) emission features at 6.2, 7.7, 8.6, 11.0 and 11.2 $\mu$m in the reflection nebula NGC 2023 to carry out a principal component analysis (PCA) as a means to study previously reported variations in the PAH emission. We find that almost all of the variations (99%) can be explained with just two parameters -- the first two principal components (PCs). We explore the characteristics of these PCs and show that the first PC ($PC_{1}$), which is the primary driver of the variation, represents the amount of emission of a mixture of PAHs with ionized species dominating over neutral species. The second PC ($PC_{2}$) traces variations in the ionization state of the PAHs across the nebula. Correlations of the PCs with various PAH ratios show that the 6.2 and 7.7 $\mu$m bands behave differently than the 8.6 and 11.0 $\mu$m bands, thereby forming two distinct groups of ionized bands. We compare the spatial distribution of the PCs to the physical conditions, in particular to the strength of the radiation field, $G_{0}$, and the $G_{0}/n_{H}$ ratio and find that the variations in $PC_{2}$, i.e. the ionization state of PAHs are strongly affected by $G_{0}$ whereas the amount of PAH emission (as traced by $PC_{1}$) does not depend on $G_0$.