Larson's third law and the universality of molecular cloud structure

Larson (1981) first noted a scaling relation between masses and sizes in molecular clouds that implies that these objects have approximately constant column densities. This original claim, based upon millimeter observations of carbon monoxide lines, has been challenged by many theorists, arguing that the apparent constant column density observed is merely the result of the limited dynamic range of observations, and that in reality clouds have column density variations over two orders of magnitudes. In this letter we investigate a set of nearby molecular clouds with near-infrared excess methods, which guarantee very large dynamic ranges and robust column density measurements, to test the validity of Larson's third law. We verify that different clouds have almost identical average column densities above a given extinction threshold; this holds regardless of the extinction threshold, but the actual average surface mass density is a function of the specific threshold used. We show that a second version of Larson's third law, involving the mass-radius relation for single clouds and cores, does not hold in our sample, indicating that individual clouds are not objects that can be described by constant column density. Our results instead indicate that molecular clouds are characterized by a universal structure. Finally we point out that this universal structure can be linked to the log-normal nature of cloud column density distributions.