Tracing the general structure of Galactic molecular clouds using Planck data - I. The Perseus region as a test case

We present an analysis of probability distribution functions (pdfs) of column density in different zones of the star-forming region Perseus and its diffuse environment based on the map of dust opacity at 353 GHz available from the Planck archive. The pdf shape can be fitted by a combination of a lognormal function and an extended power-law tail at high densities, in zones centred at the molecular cloud Perseus. A linear combination of several lognormals fits very well the pdf in rings surrounding the cloud or in zones of its diffuse neighbourhood. The slope of the mean-density scaling law <rho > L proportional to L-alpha is steep (a = 1.93) in the former case and rather shallow (a = 0.77 0.11) in the rings delineated around the cloud. We interpret these findings as signatures of two distinct physical regimes: (i) a gravoturbulent one which is characterized by nearly linear scaling of mass and practical lack of velocity scaling; and (ii) a predominantly turbulent one which is best described by steep velocity scaling and by invariant for compressible turbulence (p)LullL, describing a scale-independent flux of the kinetic energy per unit volume through turbulent cascade. The gravoturbulent spatial domain can be identified with the molecular cloud Perseus while a relatively sharp transition to predominantly turbulent regime occurs in its vicinity.