4PCF Measurements

These panels show the connected 4-point correlation function (4PCF) for various combinations of angular momentum used in the angular basis in which we measure the correlations, originally developed in Cahn & Slepian 2023. 

The connected 4PCF helps isolate structure beyond the Gaussian field.

This depicts results from simulations with varying Mach and Alfvénic numbers, highlighting how these physical parameters impact higher-order clustering. The signal is shown as a function of binned radial distances b1, b2, and b3, and the angular dependence parameter, ℓ. The ℓ= 0 components primarily capture isotropic clustering, while higher ℓ values reflect the anisotropic features of the density field associated with shocks, filaments, and other structures. The lower triangular region of the plot is excluded because it corresponds to unphysical configurations that violate the triangle inequality for radial distances. The vertical column on the left-hand side is whited out because the analysis requires b2 > b1, ensuring that the ordering of distances is consistent with the convention used in the 4PCF calculation. This plot illustrates how varying physical parameters such as Mach and Alfvénic numbers shape the 4PCF signal, providing insight into the interplay between anisotropy and clustering strength.

These plots illustrate significant excess and deficit correlation in certain regions. Dark red regions correspond to excess tetrahedra relative to a random distribution, while dark blue regions indicate a deficit. The darkest regions, where values approach +8 and -8 on the color bar, correspond to the strongest detections, where non-Gaussian correlations intrinsic to the density field are most likely to be represented. Regions of lighter coloring, closer to 0 on the color bar, reflect minimal to no detection of correlation and are more likely consistent with noise.

Plots are available for different values of the parameter b1 (b1=0,5,10,15), showcasing how changes in b1 influence the connected 4PCF. Explore these additional plots through the links provided below, which give detailed visualizations for specific configurations.

These 1D plots display the coefficients of the 4-point correlation function (4PCF) for a fixed value of b1​, providing a simplified view of the data by comparing unique bin combinations. They highlight the contributions of specific ℓ-combinations to the connected 4PCF, offering insight into how these terms shape the overall structure.

Additional 1D plots for other ℓ-combinations are linked below. Explore these plots to examine the variations in the 4PCF coefficients across different configurations.

This depicts the power spectrum of the simulation density fields. The blue line represents the power spectrum averaged over all time slices, while the orange dot-dashed line represents the respective power law fit. The slope of each power law fit is included. The shaded region to the left of the red dotted line, situated at 1.2 x 10^-1, represent the values outside the inertial range, where the power law no longer follows the power spectrum.