tokens: found by Colombo et al. ( 2014 ). Their results, furthermore, impose a cautionary warning for the study of the mass–size relationship of our own Galaxy: if we are unable to distinguish whether an observed Galactic cloud is in one or another environment, we might be producing a mass–size relationship that arises from clouds in different physical environments. It is convenient to stress that, although Colombo et al. ( 2014 ) made an effort to avoid line blending in their cloud decomposition, the situation can be quite complex, since even at the smallest scales where coherent structures can be found (i.e. cores, fibres), substantial superposition along the line of sight can occur (Ballesteros-Paredes Mac Low 2002 ; Gammie et al. 2003 ; Shetty et al. 2010 ; Zamora-Avilés et al. 2017 ; Clarke et al. 2018 ). The situation for clouds in external galaxies might deserve a full further study, since the resolution is substantially different in external Galaxies (typically, 30–50 pc; see e.g.Sun et al. 2018 ; Utomo et al. 2018 ), with only one study (Faesi et al. 2018 ) achieving resolutions of ∼10 pc. A first puzzling challenge is to understand, for instance, the origin of mass–size relation with q 2 in the interarm region of M51, since q = 2 is the limit when clouds are defined via thresholds in column density. 4.3 Fractal dimension? Different studies have interpreted the exponent of the power-law mass–size relation as representative of the fractal dimension (e.g. Elmegreen Falgarone 1996 ; Roman-Duval et al. 2010 ; Beattie, Federrath Klessen 2019 ). This approach has two hypotheses: First, the mass can be a proxy for the area. Secondly, the linear size is related also to the area in a quadratic way, since in the observational studies the size is typically considered to be proportional to the square root of the area of the cloud. In principle, the first hypothesis seems plausible: observed molecular clouds exhibit rapidly decaying N -PDFs (Kainulainen et al. 2009 ). The same is found for MCs in numerical simulations (e.g. Vázquez-Semadeni García 2001 ; Tassis et al. 2010 ; Ballesteros-Paredes et al. 2011b ; Kritsuk, Norman Wagner 2011 ). This means that the filling factor of the dense structures is quite small, which in turn, implies that the mass should be proportional to the area. However, for a collection of Galactic clouds, the superposition effects we discussed are not compatible with invoking mass as a proxy for the area. As shown in the present work, the same fact that the exponent in the mass–size relation is larger than 2 means that the mass is not proportional to the area. In addition, invoking the square root of the area as a proxy for the linear size does not tell us what will be the linear size–area correlation, which is precisely what is intended to be measured with the fractal dimension. A more appropriate estimation of the fractal dimension will be that of comparing the actual area of an ensemble of clouds with an independent estimation
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