High-dynamic-range extinction mapping of infrared dark clouds Dependence of density variance with sonic Mach number in molecular clouds

Context. 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. Aims. 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. Methods. 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 (CO)-C-13 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. Results. 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) similar or equal to 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 >) approximate to (0.047 +/- 0.016) M-s, which is suggestive of the correlation coefficient between the volume density and sonic Mach number, sigma(rho/) approximate to (0.20(0.22)(+0.37))M-s, 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 proportional to rho(0.5)). While our results remain suggestive because of the small number of clouds in our demonstration sample, the analysis can be improved by extending the study to a larger number of clouds.