2021A&A...646A..97T

Context. The traditional approach to characterize the structure of molecular clouds is to map their line emission.
Aims. We aim to test and apply a stratified random sampling technique that can characterize the line emission from molecular clouds more efficiently than mapping.
Methods. We sampled the molecular emission from the Perseus cloud using the H₂ column density as a proxy. We divided the cloud into ten logarithmically spaced column density bins, and we randomly selected ten positions from each bin. The resulting 100 cloud positions were observed with the IRAM 30 m telescope, covering the 3 mm-wavelength band and parts of the 2 and 1 mm bands.
Results. We focus our analysis on the 11 molecular species (plus isotopologs) detected toward most column density bins. In all cases, the line intensity is tightly correlated with the H₂ column density. For the CO isotopologs, the trend is relatively flat, while for high-dipole moment species such as HCN, CS, HCO⁺, and HNC, the trend is approximately linear. To reproduce this behavior, we developed a cloud model in which the gas density increases with column density, and where most species have abundance profiles characterized by an outer photodissociation edge and an inner freeze-out drop. With this model, we determine that the intensity behavior of the high-dipole moment species arises from a combination of excitation effects and molecular freeze out, with some modulation from optical depth. This quasi-linear dependence with the H₂ column density makes the gas at low column densities dominate the cloud-integrated emission. It also makes the emission from most high-dipole moment species proportional to the cloud mass inside the photodissociation edge.
Conclusions. Stratified random sampling is an efficient technique for characterizing the emission from whole molecular clouds. When applied to Perseus, it shows that despite the complex appearance of the cloud, the molecular emission follows a relatively simple pattern. A comparison with available studies of whole clouds suggests that this emission pattern may be common.