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 fifty hours. This wealth of data calls for
restating the physical questions about the interstellar medium in statistical
terms. Aims. We aim at gaining 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 nonlinear 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 3 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.
