Modelling the structure of molecular clouds: I. A multi-scale energy equipartition

We present a model for describing the general structure of molecular clouds (MCs) at early evolutionary stages in terms of their mass-size relationship. Sizes are defined through threshold levels at which equipartitions between gravitational, turbulent and thermal energy $|W| \sim f(E_{\rm kin} + E_{\rm th})$ take place, adopting interdependent scaling relations of velocity dispersion and density and assuming a lognormal density distribution at each scale. Variations of the equipartition coefficient $1\le f\le 4$ allow for modelling of star-forming regions at scales within the size range of typical MCs ($\gtrsim$4 pc). Best fits are obtained for regions with low or no star formation (Pipe, Polaris) as well for such with star-forming activity but with nearly lognormal distribution of column density (Rosette). An additional numerical test of the model suggests its applicability to cloud evolutionary times prior to the formation of first stars.