Ryan Boyden edited subsection_Intensity_statistics_We_show__.tex  almost 8 years ago

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\subsection{Intensity statistics}  We show the colorplots for all intensity statistics in Figure ???. With the exception of the Cramer statistic, we find that these statistics exhibit strong sensitivities to changes in stellar mass-loss rates. As seen in their colorplots, the largest distances%(given by the darkest colors--include?)  appear when any strong wind model (W1) is compared to either a weak wind model (W2) or a purely turbulent model (TXt0).The Kurtosis Kurtosis, Skewness,  and Skewness SCF  are our clearest clear  examples of this, as they display a sensitivity hierarchy/trend trend  among pairings. These statistics yield the largest distances between pairs of W1 and TXt0, followed by pairs of W1 and W2.%(should I include: This sort of ordering confirms the notion that a cloud with strong winds is most different from a purely turbulent cloud, followed by a weaker winded one.--Not the best wording but I'm wondering if this sort of blunt statement is necessary, especially since it also slightly addresses time sensitivities.)  And, they capture similar, weaker sensitivities between pairs of W2 and TXt0. The sensitivity hierarchy/trend with wind strength is less clear for the PDF, SCF, PDF  and PCA. We find that time evolution randomly impacts the magnitude of these statistics' strong wind distances. Weaker wind comparisons among the PDF appear to be correlated to magnetic field strength, given their structure. This does not occur in the PCA and SCF, PCA.  since their its  distances for W2are quite small. Thus, they are it is  only weakly sensitive to magnetic field strength. %Weaker wind comparisons appear correlated to changes in magnetic field strength, given their distance trends.   %this blurring is not only noticeable in comparisons involving W1, but also structured in those between weaker wind models. We find the blurring to be associated with time evolution, %(and potentially magnetic field strength),   %and the structure to be correlated with changes in magnetic field strengths. The correlations between weak wind models does not occur in the PCA and SCF, since their distances for W2 are quite small. Thus, they are weakly sensitive to magnetic field strength. Here, we only note blurring in our strong wind models  The Cramer Statistic statistic  is by definition a distance metric, so it we include its discussion and analysis here. As described in Yeremi et. al (2014), this statistic compares the interpoint differences between two data sets with the point differences between each individual data set. Following K16, we compute the Cramer Statistic statistic  using only the top 20\% of the integrated-intensity values. The statistic exhibits a behavior different from that of the other intensity statistics. As figure ??? shows, the Cramer statistic displays very large distances between purely turbulent runs and runs with any degree of feedback. Wind strength appears less important to the statistic than wind presence does, which indicates a binary sensitivity to stellar-mass loss rates. The Cramer statistic is also sensitive to magnetic field strength, because of the different distances between the purely turbulent models. Considering the various degrees of sensitivity, we find the PCA to be strong a candidate for constraining feedback signatures. As Figure 3 shows, this statistic displays sharp, distinct features for a strong wind model, and its color-plot only shows strong sensitivity to changes in stellar-mass loss rate. The other intensity statistics either exhibit less-distinct features, or react to multiple physical changes.%(may have to address the PCA pairs of W1T1 and W2T2's).  Because of this, we recommend using these statistics in concert with the PCA. Of the remaining intensity statistics, the SCF is the second most promising candidate, as its color-plot behaves similarly to the PCA.