The Phase Coherence of Interstellar Density Fluctuations

Studies of MHD turbulence often investigate the Fourier power spectrum to provide information on the nature of the turbulence cascade. However, the Fourier power spectrum only contains the Fourier amplitudes and rejects all information regarding the Fourier phases. Here we investigate the utility of two statistical diagnostics for recovering information on Fourier phases in ISM density data: the averaged amplitudes of the bispectrum and the phase coherence index (PCI), a new phase technique for the ISM. We create 3D density and 2D column density maps using a set of simulations of isothermal ideal MHD turbulence with a wide range of sonic and Alfv\'enic Mach numbers. We find that the bispectrum averaged along different angles with respect to either the $k_1$ or $k_2$ axis is primarily sensitive to the sonic Mach number while averaging the bispectral amplitudes over different annuli is sensitive to both the sonic and Alfv\'enic Mach numbers. The PCI of density suggests that the most correlated phases occur in supersonic sub-Alfv\'enic turbulence and also near the numerical dissipation regime. This suggests that non-linear interactions with correlated phases are strongest in shock dominated regions, in agreement with findings from the solar wind. Additionally, our results are particularly encouraging as they suggests the phase information contained in the bispectrum and PCI can be used to find parameters of turbulence in column density maps.