Modeling the pollution of pristine gas in the early universe

Liubin Pan, Evan Scannapieco, Jon Scalo

Research output: Contribution to journalArticle

10 Citations (Scopus)

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 that where n is a measure of the locality of the mixing or PDF convolution events and the convolution timescale τcon 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 τcon 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.

Original languageEnglish (US)
Article number111
JournalAstrophysical Journal
Volume775
Issue number2
DOIs
StatePublished - Oct 1 2013

Fingerprint

pollution
universe
probability distribution functions
convolution integrals
Population III stars
contaminants
gases
gas
modeling
metallicity
pollutant
turbulence
simulation
stars
turbulent mixing
data simulation
turbulent flow
Mach number
closures
star formation

Keywords

  • dark ages, reionization, first stars
  • evolution
  • galaxies: high-redshift
  • ISM: abundances
  • stars: Population III
  • turbulence

ASJC Scopus subject areas

  • Space and Planetary Science
  • Astronomy and Astrophysics

Cite this

Modeling the pollution of pristine gas in the early universe. / Pan, Liubin; Scannapieco, Evan; Scalo, Jon.

In: Astrophysical Journal, Vol. 775, No. 2, 111, 01.10.2013.

Research output: Contribution to journalArticle

@article{4de821b6a16e4bb7a2327748fc9007a3,
title = "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 that where n is a measure of the locality of the mixing or PDF convolution events and the convolution timescale τcon 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 τcon 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.",
keywords = "dark ages, reionization, first stars, evolution, galaxies: high-redshift, ISM: abundances, stars: Population III, turbulence",
author = "Liubin Pan and Evan Scannapieco and Jon Scalo",
year = "2013",
month = "10",
day = "1",
doi = "10.1088/0004-637X/775/2/111",
language = "English (US)",
volume = "775",
journal = "Astrophysical Journal",
issn = "0004-637X",
publisher = "IOP Publishing Ltd.",
number = "2",

}

TY - JOUR

T1 - Modeling the pollution of pristine gas in the early universe

AU - Pan, Liubin

AU - Scannapieco, Evan

AU - Scalo, Jon

PY - 2013/10/1

Y1 - 2013/10/1

N2 - 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 that where n is a measure of the locality of the mixing or PDF convolution events and the convolution timescale τcon 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 τcon 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.

AB - 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 that where n is a measure of the locality of the mixing or PDF convolution events and the convolution timescale τcon 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 τcon 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.

KW - dark ages, reionization, first stars

KW - evolution

KW - galaxies: high-redshift

KW - ISM: abundances

KW - stars: Population III

KW - turbulence

UR - http://www.scopus.com/inward/record.url?scp=84884560519&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884560519&partnerID=8YFLogxK

U2 - 10.1088/0004-637X/775/2/111

DO - 10.1088/0004-637X/775/2/111

M3 - Article

AN - SCOPUS:84884560519

VL - 775

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

M1 - 111

ER -