Scaling Laws of Passive-Scalar Diffusion in the Interstellar Medium
This work provides a theoretical framework for understanding metal mixing in astrophysical turbulence, which is critical for models of galaxy formation and star formation.
The authors derived scaling laws for passive-scalar diffusion in supersonic, magnetized, shearing turbulence relevant to the interstellar medium, showing that a fractional diffusion equation with scale-dependent diffusivity matches simulation results and outperforms constant-diffusivity models. The scalings hold across Mach numbers and shear flows, but apply only to ensemble averages, not individual patches.
Passive scalar mixing (metals, molecules, etc.) in the turbulent interstellar medium (ISM) is critical for abundance patterns of stars and clusters, galaxy and star formation, and cooling from the circumgalactic medium. However, the fundamental scaling laws remain poorly understood in the highly supersonic, magnetized, shearing regime relevant for the ISM. We therefore study the full scaling laws governing passive-scalar transport in idealized simulations of supersonic turbulence. Using simple phenomenological arguments for the variation of diffusivity with scale based on Richardson diffusion, we propose a simple fractional diffusion equation to describe the turbulent advection of an initial passive scalar distribution. These predictions agree well with the measurements from simulations, and vary with turbulent Mach number in the expected manner, remaining valid even in the presence of a large-scale shear flow (e.g. rotation in a galactic disk). The evolution of the scalar distribution is not the same as obtained using simple, constant "effective diffusivity" as in Smagorinsky models, because the scale-dependence of turbulent transport means an initially Gaussian distribution quickly develops highly non-Gaussian tails. We also emphasize that these are mean scalings that only apply to ensemble behaviors (assuming many different, random scalar injection sites): individual Lagrangian "patches" remain coherent (poorly-mixed) and simply advect for a large number of turbulent flow-crossing times.