Evolution of column density distributions within Orion A

We compare the structure of star-forming molecular clouds in different regions of Orion A to determine how the column density probability distribution function (N-PDF) varies with environmental conditions such as the fraction of young protostars. A correlation between the N-PDF slope and Class 0 protostar fraction has been previously observed in a low-mass star-formation region (Perseus); here we test whether a similar correlation is observed in a high-mass star-forming region. We used Herschel PACS and SPIRE cold dust emission observations to derive a column density map of Orion A. We used the Herschel Orion Protostar Survey catalog to accurately identify and classify the Orion A young stellar object content, including the cold and relatively short-lived Class 0 protostars (with a lifetime of similar to 0.14 Myr). We divided Orion A into eight independent regions of 0.25 square degrees (13.5 pc(2)); in each region we fit the N-PDF distribution with a power law, and we measured the fraction of Class 0 protostars. We used a maximum-likelihood method to measure the N-PDF power-law index without binning the column density data. We find that the Class 0 fraction is higher in regions with flatter column density distributions. We tested the effects of incompleteness, extinction-driven misclassification of Class 0 sources, resolution, and adopted pixel-scales. We show that these effects cannot account for the observed trend. Our observations demonstrate an association between the slope of the power-law N-PDF and the Class 0 fractions within Orion A. Various interpretations are discussed, including timescales based on the Class 0 protostar fraction assuming a constant star-formation rate. The observed relation suggests that the N-PDF can be related to an evolutionary state of the gas. If universal, such a relation permits evaluating the evolutionary state from the N-PDF power-law index at much greater distances than those accessible with protostar counts.