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 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.
