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Mid-Infrared Extinction Mapping of Infrared Dark Clouds II. The Structure of Massive Starless Cores and Clumps

(abridged) We develop the mid-infrared extinction (MIREX) mapping technique of Butler & Tan (2009, Paper I), presenting a new method to correct for the Galactic foreground emission based on observed saturation in independent cores. Using Spitzer GLIMPSE 8 micron images, this allows us to accurately probe mass surface densities, Sigma, up to ~0.5g/cm^2 with 2" resolution. We then characterize the structure of 42 massive starless and early-stage IRDC cores and their surrounding clumps, measuring Sigma_cl(r) from the core/clump centers. We first assess the properties of the core/clump at a scale where the total enclosed mass as projected on the sky is M_cl=60Msun. We find these objects have a mean radius of R_cl~0.1pc, mean Sigma_cl=0.3g/cm^2 and, if fit by a power law density profile rho_cl ~ r^{-k_{rho,cl}}, a mean value of k_{rho,cl}=1.1. If we assume a core is embedded in each clump and subtract the surrounding clump envelope to derive the core properties, we find a mean core density power law index of k_{rho,c} = 1.6. We repeat this analysis as a function of radius and derive the best-fitting power law plus uniform clump envelope model for each of the 42 core/clumps. The cores have typical masses of M_c~100Msun and mean Sigma_c~0.1g/cm^2, and are embedded in clumps with comparable mass surface densities. We conclude massive starless cores exist and are well-described by singular polytropic spheres. Their relatively low values of Sigma and the fact that they are IR dark may imply that their fragmentation is inhibited by magnetic fields rather than radiative heating. Comparing to massive star-forming cores, there is tentative evidence for an evolution towards higher densities and steeper density profiles as star formation proceeds.