Developing the 3-Point Correlation Function For the Turbulent Interstellar Medium

TL;DR

This paper introduces an angle-dependent 3-Point Correlation Function (3PCF) for analyzing MHD turbulence simulations of the interstellar medium, providing enhanced diagnostic power over previous methods.

Contribution

It presents the first application of angle-dependent 3PCF to MHD turbulence simulations, demonstrating its ability to discriminate turbulence parameters with high computational efficiency.

Findings

3PCF offers additional discriminatory power for turbulence parameters.

The algorithm is fast enough for time-series analysis of turbulence.

3PCF is stable over time, suitable for ISM diagnostics.

Abstract

We present the first application of the angle-dependent 3-Point Correlation Function (3PCF) to the density fields magnetohydrodynamic (MHD) turbulence simulations intended to model interstellar (ISM) turbulence. Previous work has demonstrated that the angle-averaged bispectrum, the 3PCF's Fourier-space analog, is sensitive to the sonic and Alfv\'enic Mach numbers of turbulence. Here we show that introducing angular information via multipole moments with respect to the triangle opening angle offers considerable additional discriminatory power on these parameters. We exploit a fast, order $N_{\rm g} \log N_{\rm g}$ ($N_{\rm g}$ the number of grid cells used for a Fourier Transform) 3PCF algorithm to study a suite of MHD turbulence simulations with 10 different combinations of sonic and Alfv\'enic Mach numbers over a range from sub to super-sonic and sub to super-Alfv\'{e}nic. The 3PCF algorithm's speed for the first time enables full quantification of the time-variation of our signal: we study 9 timeslices for each condition, demonstrating that the 3PCF is sufficiently time-stable to be used as an ISM diagnostic. In future, applying this framework to 3-D dust maps will enable better treatment of dust as a cosmological foreground as well as reveal conditions in the ISM that shape star formation.