The Pollution of Pristine Material in Compressible Turbulence

TL;DR

This study investigates how turbulence mixes and pollutes pristine gas in astrophysical environments, using theoretical models and numerical simulations to understand the evolution of unpolluted material in compressible turbulent flows.

Contribution

The paper develops and tests new PDF-based models for the pollution of pristine gas in compressible turbulence, validated through high Mach number simulations.

Findings

The continuous convolution model accurately describes pristine fraction decay at Mach 0.9.

An early nonlinear integral phase occurs for small initial pollutant fractions.

Higher Mach number turbulence slows the decay of pristine material.

Abstract

The first generation of stars had very different properties than later stellar generations, as they formed from a "pristine" gas that was free of heavy elements. Normal star formation took place only after the first stars polluted the surrounding turbulent interstellar gas, increasing its local heavy element concentration, Z, beyond a critical value, Z_c (10^-8 < Z_c <10^-5). Motivated by this astrophysical problem, we investigate the fundamental physics of the pollution of pristine fluid elements in isotropic compressible turbulence. Turbulence stretches the pollutants, produces concentration structures at small scales, and brings the pollutants and the unpolluted flow in closer contact. Our theoretical approach employs the probability distribution function (PDF) method for turbulent mixing. We adopt three PDF closure models and derive evolution equations for the pristine fraction from the models. To test and constrain the theoretical models, we conduct numerical simulations for decaying passive scalars in isothermal turbulent flows with Mach numbers of 0.9 and 6.2, and compute the mass fraction, P(Z_c, t), of the flow with Z < Z_c. In the Mach 0.9 flow, the evolution of P(Z_c, t)$ is well described by a continuous convolution model and dP(Z_c, t)/dt = P(Z_c, t) ln[P(Z_c, t)]/tau_con, if the mass fraction of the polluted flow is larger than ~ 0.1. If the initial pollutant fraction is smaller than ~ 0.1, an early phase exists during which the pristine fraction follows an equation from a nonlinear integral model: dP(Z_c, t)/dt = P(Z_c, t) [P(Z_c, t)-1]/tau_int. The timescales tau_con and tau_int are measured from our simulations. When normalized to the flow dynamical time, the decay of P(Z_ c, t) in the Mach 6.2 flow is slower than at Mach 0.9, and we show that P(Z_c, t) in the Mach 6.2 flow can be well fit using a formula from a generalized version of the self-convolution model.