We follow the analysis of Koch et al. (2015) to compute the skewness and kurtosis, which are the third- and fourth- order statistical moments of the PDF, respectively. Skewness is a measure of the symmetry of the data distribution. Data that is symmetric around the center point have low skewness. If there is an excess of high values, the skewness will be positive, while an excess of low values produces negative skewness. Kurtosis quantifies the “peakiness" of the distribution. Normally distributed data will have a kurtosis of zero, peaky data will have positive kurtosis, and flatter data will exhibit negative kurtosis. For all positions in an integrated intensity map, we compute each higher-order moment within a small, circular region with a radius of five pixels. Figure 2 shows PDFs of the kurtosis and skewness. They are essentially histograms of the moment arrays (integrated intensity maps).
The kurtosis PDFs exhibit similar behavior: both are centered at zero and sharply decrease with increasing kurtosis magnitude. However, the T2t0 distribution falls off more quickly than that of W1T2t0.2. This likely occurs because the winds generate a more extreme range of high intensity values; the intensity distribution deviates further from a normal distribution.
The skewness PDFs have similar shapes, and both have a small tail at negative skewness. However, the W1T2t0.2 distribution center is shifted to positive skewness, while the T2t0 distribution is centered at zero. This makes sense since the winds in W1T2t0.2 create an excess of high-intensity values.
Simulations of pure turbulence find that as the Mach number increases, the skewness and kurtosis of the column density PDF also increase \citep{kowal07,burkhart09}. Higher Mach number flows have stronger shocks, which increase the fraction of high-density, and hence high-column density, material. This is consistent with our results, since the winds create density enhancements and the CO intensity is a proxy for underlying column density.