Principal component analysis of molecular clouds: Can CO reveal the dynamics?

We use principal component analysis (PCA) to study the gas dynamics in numerical simulations of typical molecular clouds (MCs). Our simulations account for the non-isothermal nature of the gas and include a simplified treatment of the time-dependent gas chemistry.We model the CO line emission in a post-processing step using a 3D radiative transfer code. We consider mean number densities n₀ = 30, 100, 300 cm^-3 that span the range of values typical for MCs in the solar neighbourhood and investigate the slope αPCA of the pseudo-structure function computed by PCA for several components: the total density, H₂ density, ¹²CO density, ¹²CO J = 1 → 0 intensity and ¹³CO J = 1 → 0 intensity. We estimate power-law indices αPCA for different chemical species that range from 0.5 to 0.9, in good agreement with observations, and demonstrate that optical depth effects can influence the PCA. We show that when the PCA succeeds, the combination of chemical inhomogeneity and radiative transfer effects can influence the observed PCA slopes by as much as ̃±0.1. The method can fail if the CO distribution is very intermittent, e.g. in low-density clouds where CO is confined to small fragments.