ON MOLECULAR CLOUD SCALING LAWS AND STAR FORMATION

In this paper I recall the physical explanation based on gravitationally driven turbulence for the scaling laws found observationally for molecular clouds. Using this hypothesis it is possible to reduce all known scaling laws to a knowledge of two dimensionless indices i1 and i2 which measure respectively the extent to which the ensemble of molecular clouds form a strict fractal hierarchy and the strength of the dynamical coupling between adjacent scales in the dynamical cascade. In addition the characteristic scale separation (linear or density) between distinct structures in the nested hierarchy is necessary for a complete discussion. The indices i1 and i2 are simply related to the fractal dimension D and the density scaling index D-rho introduced by Henriksen. The dynamical coupling is likely to be collisional, either hydrodynamic or tidal. So long as gravity provides a characteristic time for the cloud dynamics, they will scale as though they were virialized, but they need not be so exactly. This allows thermal pressure and magnetic fields to be present, although not dominant (greater than equipartition values). A new form of scaling suitable for compressible Kolmogorov turbulence is given as an example of the general technique, and earlier predictions for the star-formation rate and the law of sequential star formation with mass are presented in a form generalized to include both the fractal structure and the dynamical coupling. It is emphasized that the theory gives a reasonable star-formation efficiency in molecular clouds and that it predicts a star cluster mode of star formation. A new suggestion is made for relating the mass of a cluster to the mass of the eventual most massive star based on this model which is in accord with recent suggestions.