Effects of low resolution on the column density probability distribution function of molecular clouds

Observational resolution significantly impacts the interpretation of column density probability distribution functions (N-PDFs) in molecular clouds, which are essential for understanding turbulent structures and star formation processes. This study quantifies how a low spatial resolution truncates the high-density power-law tails of N-PDFs by simulating distant observations (2--10 kpc) of 17 local massive molecular clouds and/or regions using Herschel-based column density maps. We propose a parameter-free model, assuming proportional embedding of dense regions within lower-density gas, to predict the truncation column density where the survival function equals the beam-to-threshold area ratio. Comparisons with simulations show good agreement, with deviations up to 0.3 dex attributed to cloud multiplicity in large complexes and flatter power-law tails in coherent structures. Characteristic cloud scales, derived from Δ-variance spectra, indicate that global smearing dominates when beam sizes exceed these scales. We further develop a reverse method of recovering the intrinsic high-density tail from low-resolution data. Our findings link N-PDF shapes to morphologies, suggesting that feedback-compressed extended structures resist smearing, while multiplicity accelerates truncation. These insights caution against biases in N-PDF decompositions and provide a framework for correcting resolution effects in distant cloud studies, enhancing constraints on star formation theories.