We analyse column density and temperature maps derived from Herschel dust continuum observations of a sample of massive infrared dark clouds (G11.11-0.12, G18.82-0.28, G28.37+0.07, G28.53-0.25). We disentangle the velocity structure of the clouds using 13CO 1-0 and 12CO 3-2 data, showing that these IRDCs are the densest regions in massive giant molecular clouds and not isolated features. The probability distribution function (PDF) of column densities for all clouds have a power-law distribution over all (high) column densities, regardless of the evolutionary stage of the cloud: G11.11-0.12, G18.82-0.28, and G28.37+0.07 contain (proto)-stars, while G28.53-0.25 shows no signs of star formation. This is in contrast to the purely log-normal PDFs reported for near/mid-IR extinction maps. We only find a log-normal distribution for lower column densities, if we perform PDFs of the column density maps of the whole GMC in which the IRDCs are embedded. By comparing the PDF slope and the radial column density profile, we attribute the power law to the effect of large-scale gravitational collapse and to local free-fall collapse of pre- and protostellar cores. Independent from the PDF analysis, we find infall signatures in the spectral profiles of 12CO for G28.37+0.07 and G11.11-0.12, supporting the scenario of gravitational collapse. IRDCs are the densest regions within GMCs, which may be the progenitors of massive stars or clusters. At least some of the IRDCs are probably the same features as ridges (high column density regions with N>1e23 cm-2 over small areas), which were defined for nearby IR-bright GMCs. Because IRDCs are only confined to the densest (gravity dominated) cloud regions, the PDF constructed from this kind of a clipped image does not represent the (turbulence dominated) low column density regime of the cloud.
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