Developing the 3-point Correlation Function for the Turbulent Interstellar Medium

We present the first application of the angle-dependent 3-point Correlation Function (3PCF) to the density field 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 Alfvénic 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 to these parameters. We exploit a fast, order N g log N g (Ng is 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 Alfvénic Mach numbers over a range from subsonic to supersonic and sub-Alfvénic to super-Alfvénic. The 3PCF algorithm's speed for the first time enables full quantification of the time-variation of our signal: we study nine timeslices for each condition, demonstrating that the 3PCF is sufficiently time-stable to be used as an ISM diagnostic. In the future, applying this framework to 3D dust maps will enable better treatment of dust as a cosmological foreground, as well as reveal the conditions in the ISM that shape star formation.