We show that the inter-cloud Larson scaling relation between mean volume density and size \rho \propto R ^ { -1 } , which in turn implies that mass M \propto R ^ { 2 } , or that the column density N is constant , is an artifact of the observational methods used .
Specifically , setting the column density threshold near or above the peak of the column density probability distribution function N -pdf ( N \sim 10 ^ { 21 } cm ^ { -2 } ) produces the Larson scaling as long as the N -pdf decreases rapidly at higher column densities .
We argue that the physical reasons behind local clouds to have this behavior are that ( 1 ) this peak column density is near the value required to shield CO from photodissociation in the solar neighborhood , and ( 2 ) gas at higher column densities is rare because it is susceptible to gravitational collapse into much smaller structures in specific small regions of the cloud .
Similarly , we also use previous results to show that if instead a threshold is set for the volume density , the density will appear to be constant , implying thus that M \propto R ^ { 3 } .
Thus , the Larson scaling relation does not provide much information on the structure of molecular clouds , and does not imply either that clouds are in Virial equilibrium , or have a universal structure .
We also show that the slope of the M - R curve for a single cloud , which transitions from near-to-flat values for large radii to \alpha = 2 as a limiting case for small radii , depends on the properties of the N -pdf .