In this entry we derive relations between different properties of molecular clouds. We assume that the velocity dispersion in molecular clouds is the result of turbulent cascade, so there is a power law relation between the velocity dispersion and the size of the cloud . We can use this relation to estimate the relation between the virial mass and the size of the cloud The relation between the density and size of the cloud is given by We can consider two extreme cases for turbulence. In the limit of a very subsonic turbulence we get Kolmogorov spectrum, so . In the limit of a very supersonic turbulence, we get Burgers turbulence, so . The power law index of the velocity dispersion - size relation is therefore bounded by
The value inferred from observations, 0.38, is within these limits.
The density - size power law index is bounded by
The value inferred from observations, -1.1, is within these limits.