Modeling the Pollution of Pristine Gas in the Early Universe

Abstract

We conduct a comprehensive theoretical and numerical investigation of the pollution of pristine gas in turbulent flows, designed to provide useful new tools for modeling the evolution of the first generation of stars. The properties of such Population III (Pop III) stars are thought to be very different than those of later stellar generations, because cooling is dramatically different in gas with a metallicity below a critical value Z c , which lies between ∼10 −6 and ∼10 −3 Z . The critical value is much smaller than the typical overall average metallicity, Z , and therefore the mixing efficiency of the pristine gas in the interstellar medium plays a crucial role in determining the transition from Pop III to normal star formation. The small critical value, Z c , corresponds to the far left tail of the probability distribution function (PDF) of the metal abundance. Based on closure models for the PDF formulation of turbulent mixing, we derive evolution equations for the fraction of gas, P, lying below Z c , in statistically homogeneous compressible turbulence. Our simulation data show that the evolution of the pristine fraction P can be well approximated by a generalized "self-convolution" model, which predicts thatṖ = −(n/τ con )P (1 − P 1/n ), where n is a measure of the locality of the mixing or PDF convolution events and the convolution timescale τ con is determined by the rate at which turbulence stretches the pollutants. Carrying out a suite of numerical simulations with turbulent Mach numbers ranging from M = 0.9 to 6.2, we are able to provide accurate fits to n and τ con as a function of M, Z c / Z , and the length scale, L p , at which pollutants are added to the flow. For pristine fractions above P = 0.9, mixing occurs only in the regions surrounding blobs of pollutants, such that n = 1. For smaller values of P , n is larger as the mixing process becomes more global. We show how these results can be used to construct one-zone models for the evolution of Pop III stars in a single high-redshift galaxy, as well as subgrid models for tracking the evolution of the first stars in large cosmological numerical simulations.

Simulating Metal Mixing of Both Common and Rare Enrichment Sources in a Low-mass Dwarf Galaxy

“…Our simulated galaxy lies in the regime where the turbulent driving is generated almost exclusively by supernova explosions (as opposed to gravitational driving from the inflow of gas, for example). Following the discussion in Pan et al (2013), mixing over the whole galaxy (L G ) must therefore occur slowly, as a random walk process of enrichment between individual, independent polluted regions in the galaxy on the transport timescale τ trans = L 2 G /(L turb v rms ), where L turb is the turbulent driving scale, comparable here to the typical size of a supernova remnant. Roughly, L G ∼ 1 kpc, L turb ∼ 100 pc, and v rms ∼ 10 km s −1 for our galaxy, giving a mixing / transport timescale of ∼ 1 Gyr.…”

“…In particular, Côté et al (2018) compares high-resolution hydrodynamics simulations directly with one-zone models, finding the importance of non-uniform mixing in driving abundance spreads in these galaxies, and characterize multiple hydrodynamics effects that are challenging to parameterize in current one-zone models. Additional works have conducted more direct investigations into what drives the enrichment process for individual sources using both hydrodynamics simulations (Pan et al 2013;Ritter et al 2015;Safarzadeh & Scannapieco 2017;Hirai et al 2015;Hirai & Saitoh 2017;Emerick et al 2018;Haynes & Kobayashi 2019) and semianalytic models (e.g. Krumholz & Ting 2018).…”

“…Software: YT (Turk et al 2011), ENZO (Bryan et al 2014), GRACKLE (Smith et al 2017), PYTHON (Van Rossum & Drake Jr 1995), IPYTHON (Pérez & Granger 2007), NUMPY (Oliphant 2006), SCIPY (Jones et al 2001), MAT-PLOTLIB (Hunter 2007), HDF5 (Fortner 1998;Koranne 2011), H5PY (Collette et al 2017), ASTROPY (Astropy Collaboration et al 2013;Price-Whelan et al 2018), CLOUDY (Ferland et al 2013), and DEEPDISH…”

Following the Cosmic Evolution of Pristine Gas. I. Implications for Milky Way Halo Stars

“…By this time big bang nucleosynthesis had produced helium efficiently, but it had been halted by the expansion of the universe before it could go much further, leaving stars and supernovae (SNe) to form and disseminate the heavier elements (Walker et al 1991). These early SNe first enriched the gas in and around protogalaxies which, in turn, led to a gradual, spatially inhomogeneous transition from metal-free Population III (Pop III) star formation to metal-enriched Population II (Pop II) star formation (Scannapieco et al 2003(Scannapieco et al , 2006Brook et al 2007;Tornatore et al 2007;O'Shea & Norman 2007;Trenti & Shull 2010;Maio et al 2010;Crosby et al 2013;Johnson et al 2013;Pan et al 2013;Pallottini et al 2014).…”

On Neutron Star Mergers as the Source of r-process-enhanced Metal-poor Stars in the Milky Way

“…III stars in areas of the simulation that would normally be considered polluted above Z crit ; in effect increasing the chemical resolution of the simulation. Our model for the pristine fraction is based on accepted theoretical models (Pan & Scannapieco 2010) and has been calibrated against numerical simulations that model the dynamical time required to mix pollutants, due to SN stirring, in an astrophysical context (Pan et al 2013).…”