PDFs derived from Herschel column density maps toward the low-mass star-forming regions Maddalena and Auriga. Left panel: PDF from the original map, right: one from the corrected map. The vertical dashed line indicates the approximate completeness limit. The left y-axis gives the normalized probability p(η), the right y-axis the number of pixels per log bin. The upper x-axis is the visual extinction and the lower x-axis the logarithm of the normalized column density. The green curve indicates the fitted PDF. For Auriga, diffuse LOS-contamination (or a well defined seperate cloud) shows up as an individual PDF at low extinctions. The red line indicates a power-law fit to the high Av tail. Inside each panel, we give the value where the PDF peaks (Av,pk), the deviation point from lognormal to power-law tail (DP), the dispersion of the fitted PDF (ση), the slope s and the X2 of the fit (linear regression), and the exponent α of an equivalent spherical density distribution. These values are also summarized in Table 1.
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