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We present a far-IR survey of the entire Mon R2 GMC with $Herschel-SPIRE$cross-calibrated with $Planck-HFI$ data. We fit the SEDs of each pixel with agreybody function and an optimal beta value of 1.8. We find that mid-rangecolumn densities obtained from far-IR dust emission and near-IR extinction areconsistent. For the entire GMC, we find that the column density histogram, orN-PDF, is lognormal below $\sim$10$^{21}$ cm$^{-2}$. Above this value, thedistribution takes a power law form with an index of -2.16. We analyze the gasgeometry, N-PDF shape, and YSO content of a selection of subregions in thecloud. We find no regions with pure lognormal N-PDFs. The regions with acombination of lognormal and one power law N-PDF have a YSO cluster and acorresponding centrally concentrated gas clump. The regions with a combinationof lognormal and two power law N-PDF have significant numbers of typicallyyounger YSOs but no prominent YSO cluster. These regions are composed of anaggregate of closely spaced gas filaments with no concentrated dense gas clump.We find that for our fixed scale regions, the YSO count roughly correlates withthe N-PDF power law index. The correlation appears steeper for single power lawregions relative to two power law regions with a high column density cut-off,as a greater dense gas mass fraction is achieved in the former. A strongercorrelation is found between embedded YSO count and the dense gas mass amongour regions.

A $Herschel-SPIRE$ Survey of the Mon R2 Giant Molecular Cloud: Analysis of the Gas Column Density Probability Density Function