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

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Table 1:

Best power-law fits $M = a \pi R^\gamma$ for various extinction thresholds.
Threshold A₀	a	$\gamma$	Scatter	c
(mag)	( ${M}_\odot ~{\rm pc}^{-\gamma}$ )		(percent)
0.1	$\phantom{0}41.2$	1.99	$11\%$	2.25
0.2	$\phantom{0}73.1$	1.96	$12\%$	2.00
0.5	149.0	2.01	$14\%$	1.63
1.0	264.2	2.06	$12\%$	1.44
1.5	379.8	2.07	$14\%$	1.38

Notes. Note that because $\gamma \simeq 2$ in all cases, the quantity a can be interpreted as the average mass column density of the cloud above the corresponding extinction threshold. The last two columns show the standard deviation of the cloud column densities divided by their average (relative scatter) and the ratio between the average column densities and the minimum column density set by the extinction threshold (c).

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