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Stella Offner edited subsubsection_Bispectrum_Bicoherence_SSRO_no__.tex
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\subsubsection{Bispectrum/Bicoherence}
%SSRO no capital on bispectrum; note Fourier is a name, hence the capitalization.
The bispectrum measures both the magnitude and phase correlation between Fourier
signals, which signals. This gives it a distinct advantage over two-point correlation methods such as VCA and VCS, which do not preserve phase information. Consequently,
this statistic the bispectrum is useful to quantify nonlinear wave-wave interactions, which may be prevalent in turbulent magnetized gas \citep{burkhart2009}.
The bispectrum is obtained by computing the Fourier transform of the three-point correlation function. In our analysis, we use the bispectrum to calculate the bicoherence, a real-valued, normalized equivalent. (Explain why this is more efficient? Eric discuss why in his paper). %SSRO Yes, will need more elaboration. We also need comparison to past literature on this topic - I'll add it.
Following the analysis of Koch et al. (2015), we generate sets of randomly sampled spatial frequencies that are sampled up to half of the image size (i.e., 127 pixels). %SSRO or do you mean 2.5pc (or the equivalent half size in ''?
For each run, we compute the bicoherence of our integrated intensity maps using the randomly samples sets. Figure 8 depicts the bicoherence matrices for
runs outputs W1T2t0.2 and
W2T2t0. Run W1T2t0.2's matrix contains multiple Bicoherences near zero, while run W2T2t0's T2t0. The bicoherence matrix
of W1T2t0.2 exhibits a clear signal on the diagonal, but exhibits little correlation elsewhere. In contrast, the bicoherence maxtrix of T2t0 contains
multiple Bicoherences grater than 0.5. We a significant fraction of pixels above 0.5, i.e., there is fairly widespread correlation. If magnetic waves enhance correlation across scales, the wind shells may break up the volume and, thus, reduce correlation. Although shell expansion may perturb the magnetic field and excite magnetosonic waves, it is difficult to see any impact against the background turbulence (OA14). This statistic in fact seems to suggest that the shells reduce correlation perhaps by disrupting the propagation of MHD waves.
%We find that the
% run with feedback generates more random phases between signals than that of our run without feedback. SSRO there actually seems to be less correlation in the feedback case -- much higher fraction of blue.
{\bf what does the stronger signal in the diagonal mean in the case with feedback?}