Measuring the mass distribution of infrared dark clouds (IRDCs) over the wide dynamic range of their column densities is a fundamental obstacle in determining the initial conditions of high-mass star formation and star cluster formation. We present a
new technique to derive high-dynamic-range, arcsecond-scale resolution column density data for IRDCs and demonstrate the potential of such data in measuring the density variance - sonic Mach number relation in molecular clouds. We combine near-infrared data from the UKIDSS/Galactic Plane Survey with mid-infrared data from the Spitzer/GLIMPSE survey to derive dust extinction maps for a sample of ten IRDCs. We then examine the linewidths of the IRDCs using 13CO line emission data from the FCRAO/Galactic Ring Survey and derive a column density - sonic Mach number relation for them. For comparison, we also examine the relation in a sample of nearby molecular clouds. The presented column density mapping technique provides a very capable, temperature independent tool for mapping IRDCs over the column density range equivalent to A_V=1-100 mag at a resolution of 2. Using the data provided by the technique, we present the first direct measurement of the relationship between the column density dispersion, sigma_{N/<N>}, and sonic Mach number, M_s, in molecular clouds. We detect correlation between the variables with about 3-sigma confidence. We derive the relation sigma_{N/<N>} = (0.047 pm 0.016) Ms, which is suggestive of the correlation coefficient between the volume density and sonic Mach number, sigma_{rho/<rho>} = (0.20^{+0.37}_{-0.22}) Ms, in which the quoted uncertainties indicate the 3-sigma range. When coupled with the results of recent numerical works, the existence of the correlation supports the picture of weak correlation between the magnetic field strength and density in molecular clouds (i.e., B ~ rho^{0.5}).
Aims: We derive the probability density functions (PDFs) of column density for a complete sample of prominent molecular cloud complexes closer than 200 pc. Methods: We derive near-infrared dust extinction maps for 23 molecular cloud complexes, using
the nicest colour excess mapping technique and data from the 2MASS archive. The extinction maps are then used to examine the column density PDFs in the clouds. Results: The column density PDFs of most molecular clouds are well-fitted by log-normal functions at low column densities (0.5 mag < A_v < 3-5 mag). However, at higher column densities prominent, power-law-like wings are common. In particular, we identify a trend among the PDFs: active star-forming clouds always have prominent non-log-normal wings. In contrast, clouds without active star formation resemble log-normals over the whole observed column density range, or show only low excess of higher column densities. This trend is also reflected in the cumulative PDFs, showing that the fraction of high column density material is significantly larger in star-forming clouds. These observations are in agreement with an evolutionary trend where turbulent motions are the main cloud-shaping mechanism for quiescent clouds, but the density enhancements induced by them quickly become dominated by gravity (and other mechanisms) which is strongly reflected by the shape of the column density PDFs. The dominant role of the turbulence is restricted to the very early stages of molecular cloud evolution, comparable to the onset of active star formation in the clouds.
