Stella Offner edited subsubsection_Delta_Variance_We_or__.tex  over 8 years ago

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\subsubsection{Delta Variance}  We (or whoever) define the Delta Variance as a filtered average over the Fourier power spectrum. Koch et. al (2015) calculates the $\Delta$-Variance using the method introduced in Ossenkopf et al. (2008b,a). We follow a similar method. We generate a series of Mexican Hat Wavelets wavelets  that vary in width (or scale..). We approximate the wavelets as the difference of two Gaussians with a diameter (width) ratio of 1.5. For each run, we weight the integrated intensity map by its inverse variance, convolve it to a Mexican Hat Wavelet, and calculate the Delta Variance in Fourier Space. Figure 9 shows our runs' delta variances the $\Delta$-variances  plotted as a function of wavelet width, denoted as "Lag." Similar to the previously discussed Fourier Statistics, we note a common horizontal offset between our plots. Run W2T2t0's delta-variance curve also drops more at Wavelet widths near 0.1 arcminutes than run W2T2t0's curve does.