Scaling laws of passive-scalar diffusion in the interstellar medium

Abstract

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.

Simulating diverse instabilities of dust in magnetized gas

“…For example, the δB PDFs in almost all cases have this form, as do the δug PDFs in Corona and WIM S/M and HII-far S/M. PDFs with exponential or stretched-exponential tails are common in certain types of gas turbulence, velocity distributions of granular gases, and pas-sive scalar concentrations in sub-sonic incompressible turbulence (Ruiz-Chavarria et al 1996;Yakhot 1997;Ben-Naim & Krapivsky 2000;Antal et al 2002;Ernst & Brito 2002;Kohlstedt et al 2005;Aranson & Tsimring 2006;Monchaux et al 2010;Hopkins 2013;Colbrook et al 2017). This generically arises from a competition between driving and dissipation.…”

FIRE-2 simulations: physics versus numerics in galaxy formation

“…assuming the mixing time scales with the eddy turnover time, based on the local spatial resolution and velocity field). This is tested directly in GIZMO with our same MFM solver in idealized, converged "turbulent box" simulations in Colbrook et al (2017) and Rennehan et al (in prep.). An upper limit to the mixing between cells is enforced, equal to what would be obtained by the GIZMO MFV solver for the same cells and same timestep -in other words, the maximum possible diffusivity of the added term in MFM is simply the un-avoidable diffusivity inherent to the MFV method (itself very similar to that in moving-mesh codes).…”

“…Wadsley et al 2008). In Colbrook et al (2017), we have performed our own study of the turbulent mixing, using 3D, highresolution supersonic turbulent box simulations (with and without magnetic fields and/or shear), and verify that this prescription, with C ≈ 0.05, is reasonable specifically in our identical MFM code with the definitions of h and S here (although such simple prescriptions do fail to capture some potentially important non-Gaussian features which emerge from real, resolved turbulent mixing). An independent, more extensive study (including a range of more complex problem setups) will be presented in Rennehan et al (in prep.…”

Metal Mixing and Ejection in Dwarf Galaxies Are Dependent on Nucleosynthetic Source

“…Previous work on the evolution of metals in the ISM varies from studies concerning the advection of passive scalars in idealized turbulent boxes (e.g. Pope 1991;Pan & Scannapieco 2010;Pan et al 2012;Pan et al 2013;Yang & Krumholz 2012;Sur et al 2014;Colbrook et al 2017) to global galaxy models studying generalized advection and mixing of passive scalars (e.g. de Avillez & Mac Low 2002;Petit et al 2015;Goldbaum et al 2016) to models with more detailed self-consistent metal enrichment (e.g.…”