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 \langle \rho \rangle _ { L } \propto L ^ { \alpha } is steep ( \alpha = -1.93 ) in the former case and rather shallow ( \alpha = -0.77 \pm 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 \langle \rho \rangle _ { L } u _ { L } ^ { 3 } / L , 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 .