Dissecting the molecular structure of the Orion B cloud: insight from principal component analysis

Context. The combination of wideband receivers and spectrometers currently available in (sub-)millimeter observatories deliver wide-field hyperspectral imaging of the interstellar medium. Tens of spectral lines can be observed over degree wide fields in about 50 h. This wealth of data calls for restating the physical questions about the interstellar medium in statistical terms. Aims. We aim to gain information on the physical structure of the interstellar medium from a statistical analysis of many lines from different species over a large field of view, without requiring detailed radiative transfer or astrochemical modeling. Methods. We coupled a non-linear rescaling of the data with one of the simplest multivariate analysis methods, namely the principal component analysis, to decompose the observed signal into components that we interpret first qualitatively and then quantitatively based on our deep knowledge of the observed region and of the astrochemistry at play. Results. We identify three principal components, linear compositions of line brightness temperatures, that are correlated at various levels with the column density, the volume density and the UV radiation field. Conclusions. When sampling a sufficiently diverse mixture of physical parameters, it is possible to decompose the molecular emission in order to gain physical insight on the observed interstellar medium. This opens a new avenue for future studies of the interstellar medium.