Observed distributions of as a functionof the column density , which is normalized to its maximum value , for all the cores, and for other cases we tried, including separating high- and low-luminosity cores, as well as outflow cavity walls versus envelope emission. The solid lines are the running means, and the shaded areas are ± the standard deviation of each bin of points. The error bars correspond to these standard deviation values divided by the square root of the number of points in each bin.