Abstract
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.