DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Fully coupled simulation of cosmic reionization. I. numerical methods and tests

Abstract

Here, we describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large similar to(100 Mpc)(3) cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. But, we employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling propertiesmore » of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. Finally, we illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200(3) Eulerian grid cells and dark matter particles.« less

Authors:
 [1];  [2];  [1];  [3];  [4]
  1. Univ. of California, San Diego, CA (United States)
  2. Southern Methodist Univ., Dallas, TX (United States)
  3. Univ. of California, San Diego, CA (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  4. Georgia Inst. of Technology, Atlanta, GA (United States)
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF)
OSTI Identifier:
1286996
Grant/Contract Number:  
AC05-00OR22725; AST-0808184; AST-1109243
Resource Type:
Accepted Manuscript
Journal Name:
The Astrophysical Journal. Supplement Series (Online)
Additional Journal Information:
Journal Name: The Astrophysical Journal. Supplement Series (Online); Journal Volume: 216; Journal Issue: 1; Journal ID: ISSN 1538-4365
Publisher:
American Astronomical Society/IOP
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; cosmology: theory; methods: numerical; radiative transfer; ADAPTIVE MESH REFINEMENT; COSMOLOGICAL RADIATIVE-TRANSFER; PROBE WMAP OBSERVATIONS; FLUX-LIMITED DIFFUSION; PIECEWISE PARABOLIC METHOD; POPULATION-III STARS; HYDROGEN REIONIZATION; INTERGALACTIC ME

Citation Formats

Norman, Michael L., Reynolds, Daniel R., So, Geoffrey C., Harkness, Robert P., and Wise, John H.. Fully coupled simulation of cosmic reionization. I. numerical methods and tests. United States: N. p., 2015. Web. doi:10.1088/0067-0049/216/1/16.
Norman, Michael L., Reynolds, Daniel R., So, Geoffrey C., Harkness, Robert P., & Wise, John H.. Fully coupled simulation of cosmic reionization. I. numerical methods and tests. United States. https://doi.org/10.1088/0067-0049/216/1/16
Norman, Michael L., Reynolds, Daniel R., So, Geoffrey C., Harkness, Robert P., and Wise, John H.. Fri . "Fully coupled simulation of cosmic reionization. I. numerical methods and tests". United States. https://doi.org/10.1088/0067-0049/216/1/16. https://www.osti.gov/servlets/purl/1286996.
@article{osti_1286996,
title = {Fully coupled simulation of cosmic reionization. I. numerical methods and tests},
author = {Norman, Michael L. and Reynolds, Daniel R. and So, Geoffrey C. and Harkness, Robert P. and Wise, John H.},
abstractNote = {Here, we describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large similar to(100 Mpc)(3) cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. But, we employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. Finally, we illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200(3) Eulerian grid cells and dark matter particles.},
doi = {10.1088/0067-0049/216/1/16},
journal = {The Astrophysical Journal. Supplement Series (Online)},
number = 1,
volume = 216,
place = {United States},
year = {Fri Jan 09 00:00:00 EST 2015},
month = {Fri Jan 09 00:00:00 EST 2015}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 30 works
Citation information provided by
Web of Science

Figures / Tables:

TABLE 1 TABLE 1: Parameters used in the hypre linear solver

Save / Share:

Works referenced in this record:

Modeling primordial gas in numerical cosmology
journal, August 1997


The Formation of the First Star in the Universe
journal, November 2001


Radiative Transfer Effects during Photoheating of the Intergalactic Medium
journal, July 1999

  • Abel, Tom; Haehnelt, Martin G.
  • The Astrophysical Journal, Vol. 520, Issue 1
  • DOI: 10.1086/312136

Photon‐conserving Radiative Transfer around Point Sources in Multidimensional Numerical Cosmology
journal, September 1999

  • Abel, Tom; Norman, Michael L.; Madau, Piero
  • The Astrophysical Journal, Vol. 523, Issue 1
  • DOI: 10.1086/307739

Adaptive ray tracing for radiative transfer around point sources
journal, March 2002


Cosmological hydrodynamics with multi-species chemistry and nonequilibrium ionization and cooling
journal, August 1997


A radiative transfer scheme for cosmological reionization based on a local Eddington tensor
journal, June 2008


New measurements of the ionizing ultraviolet background over 2 < z < 5 and implications for hydrogen reionization
journal, October 2013

  • Becker, George D.; Bolton, James S.
  • Monthly Notices of the Royal Astronomical Society, Vol. 436, Issue 2
  • DOI: 10.1093/mnras/stt1610

The observed ionization rate of the intergalactic medium and the ionizing emissivity at z >= 5: evidence for a photon-starved and extended epoch of reionization
journal, November 2007


A candidate redshift z ≈ 10 galaxy and rapid changes in that population at an age of 500 Myr
journal, January 2011

  • Bouwens, R. J.; Illingworth, G. D.; Labbe, I.
  • Nature, Vol. 469, Issue 7331
  • DOI: 10.1038/nature09717

The First Stars
journal, September 2004


Enzo: an Adaptive mesh Refinement code for Astrophysics
journal, March 2014

  • Bryan, Greg L.; Norman, Michael L.; O'Shea, Brian W.
  • The Astrophysical Journal Supplement Series, Vol. 211, Issue 2
  • DOI: 10.1088/0067-0049/211/2/19

Galaxy formation and physical bias
journal, November 1992

  • Cen, Renyue; Ostriker, Jeremiah P.
  • The Astrophysical Journal, Vol. 399
  • DOI: 10.1086/186620

Cosmological reionization around the first stars: Monte Carlo radiative transfer
journal, June 2001


Halo models of large scale structure
journal, December 2002


Power Spectra for Cold Dark Matter and Its Variants
journal, January 1999

  • Eisenstein, Daniel J.; Hu, Wayne
  • The Astrophysical Journal, Vol. 511, Issue 1
  • DOI: 10.1086/306640

Observational Constraints on Cosmic Reionization
journal, September 2006


Gas clumping in self-consistent reionization models: Gas clumping at z ≥ 5
journal, November 2012


A new moment method for continuum radiative transfer in cosmological re-ionization
journal, March 2009


Characteristic scales during reionization
journal, January 2006

  • Furlanetto, Steven R.; McQuinn, Matthew; Hernquist, Lars
  • Monthly Notices of the Royal Astronomical Society, Vol. 365, Issue 1
  • DOI: 10.1111/j.1365-2966.2005.09687.x

The Growth of H ii Regions During Reionization
journal, September 2004

  • Furlanetto, Steven R.; Zaldarriaga, Matias; Hernquist, Lars
  • The Astrophysical Journal, Vol. 613, Issue 1
  • DOI: 10.1086/423025

Cosmological Reionization by Stellar Sources
journal, June 2000

  • Gnedin, Nickolay Y.
  • The Astrophysical Journal, Vol. 535, Issue 2
  • DOI: 10.1086/308876

Effect of Reionization on Structure Formation in the Universe
journal, October 2000

  • Gnedin, Nickolay Y.
  • The Astrophysical Journal, Vol. 542, Issue 2
  • DOI: 10.1086/317042

Cosmic Reionization on Computers. i. Design and Calibration of Simulations
journal, September 2014


Multi-dimensional cosmological radiative transfer with a Variable Eddington Tensor formalism
journal, October 2001


Cosmic Reionization on Computers. ii. Reionization History and its Back-Reaction on Early Galaxies
journal, September 2014


Radiative Transfer in a Clumpy Universe. iv. new Synthesis Models of the Cosmic Uv/X-Ray Background
journal, February 2012


Beyond Flux‐limited Diffusion: Parallel Algorithms for Multidimensional Radiation Hydrodynamics
journal, July 2003

  • Hayes, John C.; Norman, Michael L.
  • The Astrophysical Journal Supplement Series, Vol. 147, Issue 1
  • DOI: 10.1086/374658

Simulating Radiating and Magnetized Flows in Multiple Dimensions with ZEUS‐MP
journal, July 2006

  • Hayes, John C.; Norman, Michael L.; Fiedler, Robert A.
  • The Astrophysical Journal Supplement Series, Vol. 165, Issue 1
  • DOI: 10.1086/504594

Equation of state of the photoionized intergalactic medium
journal, November 1997

  • Hui, L.; Gnedin, N. Y.
  • Monthly Notices of the Royal Astronomical Society, Vol. 292, Issue 1
  • DOI: 10.1093/mnras/292.1.27

Cosmological radiative transfer codes comparison project ��� I. The static density field tests
journal, September 2006

  • Iliev, Ilian T.; Ciardi, Benedetta; Alvarez, Marcelo A.
  • Monthly Notices of the Royal Astronomical Society, Vol. 371, Issue 3
  • DOI: 10.1111/j.1365-2966.2006.10775.x

Simulating cosmic reionization: how large a volume is large enough?
journal, January 2014

  • Iliev, Ilian T.; Mellema, Garrelt; Ahn, Kyungjin
  • Monthly Notices of the Royal Astronomical Society, Vol. 439, Issue 1
  • DOI: 10.1093/mnras/stt2497

Simulating cosmic reionization at large scales - I. The geometry of reionization: Simulating reionization at large scales
journal, June 2006


Can 21-cm observations discriminate between high-mass and low-mass galaxies as reionization sources?
journal, May 2012

  • Iliev, Ilian T.; Mellema, Garrelt; Shapiro, Paul R.
  • Monthly Notices of the Royal Astronomical Society, Vol. 423, Issue 3
  • DOI: 10.1111/j.1365-2966.2012.21032.x

Cosmological radiative transfer comparison project – II. The radiation-hydrodynamic tests
journal, December 2009


SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE ( WMAP ) OBSERVATIONS: SKY MAPS, SYSTEMATIC ERRORS, AND BASIC RESULTS
journal, January 2011

  • Jarosik, N.; Bennett, C. L.; Dunkley, J.
  • The Astrophysical Journal Supplement Series, Vol. 192, Issue 2
  • DOI: 10.1088/0067-0049/192/2/14

A concordance model of the Lyman a forest at z= 1.95
journal, July 2005


Dark Matter Halos in the Standard Cosmological Model: Results from the Bolshoi Simulation
journal, October 2011

  • Klypin, Anatoly A.; Trujillo-Gomez, Sebastian; Primack, Joel
  • The Astrophysical Journal, Vol. 740, Issue 2
  • DOI: 10.1088/0004-637X/740/2/102

FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: COSMOLOGICAL INTERPRETATION
journal, February 2009

  • Komatsu, E.; Dunkley, J.; Nolta, M. R.
  • The Astrophysical Journal Supplement Series, Vol. 180, Issue 2
  • DOI: 10.1088/0067-0049/180/2/330

SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE ( WMAP ) OBSERVATIONS: COSMOLOGICAL INTERPRETATION
journal, January 2011

  • Komatsu, E.; Smith, K. M.; Dunkley, J.
  • The Astrophysical Journal Supplement Series, Vol. 192, Issue 2
  • DOI: 10.1088/0067-0049/192/2/18

Relating Eddington factors to flux limiters
journal, February 1984


A flux-limited diffusion theory
journal, August 1981

  • Levermore, C. D.; Pomraning, G. C.
  • The Astrophysical Journal, Vol. 248
  • DOI: 10.1086/159157

Radiative Transfer in a Clumpy Universe. III. The Nature of Cosmological Ionizing Sources
journal, April 1999

  • Madau, Piero; Haardt, Francesco; Rees, Martin J.
  • The Astrophysical Journal, Vol. 514, Issue 2
  • DOI: 10.1086/306975

crash: a radiative transfer scheme
journal, October 2003


C2-ray: A new method for photon-conserving transport of ionizing radiation
journal, March 2006


Optimized Multi-Frequency Spectra for Applications in Radiative Feedback and Cosmological Reionization
journal, August 2012


Diffusion-limit asymptotics of the transport equation, the P1/3 equations, and two flux-limited diffusion theories
journal, June 2000


The effects of radiative transfer on the reionization of an inhomogeneous universe
journal, March 2001


Numerical Astrophysics
book, January 1999


traphic- radiative transfer for smoothed particle hydrodynamics simulations
journal, September 2008


Multifrequency, thermally coupled radiative transfer with traphic: method and tests: traphic- multifrequency and thermal coupling
journal, January 2011


An implementation of radiative transfer in the cosmological simulation code gadget
journal, July 2009


Simulations of galaxy formation with radiative transfer: hydrogen reionization and radiative feedback: Simulations of galaxy formation with RT
journal, December 2010


Search for TeV Gamma-ray Emission from GRB 100621A, an extremely bright GRB in X-rays, with H.E.S.S.
journal, April 2014


Fully threaded transport engine: new method for multi-scale radiative transfer: Fully threaded transport engine
journal, August 2005


Cosmological Hydrogen Reionization with Three‐dimensional Radiative Transfer
journal, June 2002

  • Razoumov, Alexei O.; Norman, Michael L.; Abel, Tom
  • The Astrophysical Journal, Vol. 572, Issue 2
  • DOI: 10.1086/340451

The Fate of the First Galaxies. I. Self‐consistent Cosmological Simulations with Radiative Transfer
journal, August 2002

  • Ricotti, Massimo; Gnedin, Nickolay Y.; Shull, J. Michael
  • The Astrophysical Journal, Vol. 575, Issue 1
  • DOI: 10.1086/341255

Hybrid characteristics: 3D radiative transfer for parallel adaptive mesh refinement hydrodynamics
journal, June 2006


Early star-forming galaxies and the reionization of the Universe
journal, November 2010

  • Robertson, Brant E.; Ellis, Richard S.; Dunlop, James S.
  • Nature, Vol. 468, Issue 7320
  • DOI: 10.1038/nature09527

ramses-rt: radiation hydrodynamics in the cosmological context
journal, October 2013

  • Rosdahl, J.; Blaizot, J.; Aubert, D.
  • Monthly Notices of the Royal Astronomical Society, Vol. 436, Issue 3
  • DOI: 10.1093/mnras/stt1722

Cosmological H II regions and the photoionization of the intergalactic medium
journal, October 1987

  • Shapiro, Paul R.; Giroux, Mark L.
  • The Astrophysical Journal, Vol. 321
  • DOI: 10.1086/185015

Photoevaporation of cosmological minihaloes during reionization
journal, March 2004

  • Shapiro, Paul R.; Iliev, Ilian T.; Raga, Alejandro C.
  • Monthly Notices of the Royal Astronomical Society, Vol. 348, Issue 3
  • DOI: 10.1111/j.1365-2966.2004.07364.x

Cosmological H ii Bubble Growth during Reionization
journal, July 2008

  • Shin, Min‐Su; Trac, Hy; Cen, Renyue
  • The Astrophysical Journal, Vol. 681, Issue 2
  • DOI: 10.1086/588247

Fully Coupled Simulation of Cosmic Reionization. ii. Recombinations, Clumping Factors, and the Photon Budget for Reionization
journal, June 2014

  • So, Geoffrey C.; Norman, Michael L.; Reynolds, Daniel R.
  • The Astrophysical Journal, Vol. 789, Issue 2
  • DOI: 10.1088/0004-637X/789/2/149

Simulating reionization in numerical cosmology
journal, September 2001


Cosmic reionization by stellar sources: Population II stars
journal, September 2003


Cosmic reionization by stellar sources: population III stars
journal, May 2004


First‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Determination of Cosmological Parameters
journal, September 2003

  • Spergel, D. N.; Verde, L.; Peiris, H. V.
  • The Astrophysical Journal Supplement Series, Vol. 148, Issue 1
  • DOI: 10.1086/377226

Simulations of the formation, evolution and clustering of galaxies and quasars
journal, June 2005

  • Springel, Volker; White, Simon D. M.; Jenkins, Adrian
  • Nature, Vol. 435, Issue 7042
  • DOI: 10.1038/nature03597

ZEUS-2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. III - The radiation hydrodynamic algorithms and tests
journal, May 1992

  • Stone, James M.; Mihalas, Dimitri; Norman, Michael L.
  • The Astrophysical Journal Supplement Series, Vol. 80
  • DOI: 10.1086/191682

Radiative Transfer Simulations of Cosmic Reionization. I. Methodology and Initial Results
journal, December 2007

  • Trac, Hy; Cen, Renyue
  • The Astrophysical Journal, Vol. 671, Issue 1
  • DOI: 10.1086/522566

Imprint of Inhomogeneous Hydrogen Reionization on the Temperature Distribution of the Intergalactic Medium
journal, November 2008

  • Trac, Hy; Cen, Renyue; Loeb, Abraham
  • The Astrophysical Journal, Vol. 689, Issue 2
  • DOI: 10.1086/595678

Ionization Front Instabilities in Primordial H ii Regions
journal, February 2008

  • Whalen, Daniel; Norman, Michael L.
  • The Astrophysical Journal, Vol. 673, Issue 2
  • DOI: 10.1086/524400

Three‐Dimensional Dynamical Instabilities in Galactic Ionization Fronts
journal, January 2008

  • Whalen, Daniel J.; Norman, Michael L.
  • The Astrophysical Journal, Vol. 672, Issue 1
  • DOI: 10.1086/522569

Radiation hydrodynamical instabilities in cosmological and galactic ionization fronts
journal, January 2011


enzo+moray: radiation hydrodynamics adaptive mesh refinement simulations with adaptive ray tracing: AMR simulations with adaptive ray tracing
journal, May 2011


The birth of a galaxy – III. Propelling reionization with the faintest galaxies
journal, June 2014

  • Wise, John H.; Demchenko, Vasiliy G.; Halicek, Martin T.
  • Monthly Notices of the Royal Astronomical Society, Vol. 442, Issue 3
  • DOI: 10.1093/mnras/stu979

The Birth of a Galaxy: Primordial Metal Enrichment and Stellar Populations
journal, December 2011

  • Wise, John H.; Turk, Matthew J.; Norman, Michael L.
  • The Astrophysical Journal, Vol. 745, Issue 1
  • DOI: 10.1088/0004-637X/745/1/50

Population iii Stars and Remnants in High-Redshift Galaxies
journal, July 2013


Simulations of Early Structure Formation: Primordial Gas Clouds
journal, August 2003

  • Yoshida, Naoki; Abel, Tom; Hernquist, Lars
  • The Astrophysical Journal, Vol. 592, Issue 2
  • DOI: 10.1086/375810

Simulations and Analytic Calculations of Bubble Growth during Hydrogen Reionization
journal, January 2007

  • Zahn, Oliver; Lidz, Adam; McQuinn, Matthew
  • The Astrophysical Journal, Vol. 654, Issue 1
  • DOI: 10.1086/509597

Comparison of reionization models: radiative transfer simulations and approximate, seminumeric models: Comparison of reionization models
journal, April 2011


Works referencing / citing this record:

Lyman α radiation hydrodynamics of galactic winds before cosmic reionization
journal, October 2016

  • Smith, Aaron; Bromm, Volker; Loeb, Abraham
  • Monthly Notices of the Royal Astronomical Society, Vol. 464, Issue 3
  • DOI: 10.1093/mnras/stw2591

Inhomogeneous reionization models in cosmological hydrodynamical simulations
journal, May 2019

  • Oñorbe, Jose; Davies, F. B.; Lukić, Z.
  • Monthly Notices of the Royal Astronomical Society, Vol. 486, Issue 3
  • DOI: 10.1093/mnras/stz984

Challenges and Techniques for Simulating Line Emission
journal, September 2018


Self-consistent Modeling of Reionization in Cosmological Hydrodynamical Simulations
journal, March 2017

  • Oñorbe, Jose; Hennawi, Joseph F.; Lukić, Zarija
  • The Astrophysical Journal, Vol. 837, Issue 2
  • DOI: 10.3847/1538-4357/aa6031

Magnetohydrodynamical Effects on Nuclear Deflagration Fronts in Type Ia Supernovae
journal, April 2018

  • Hristov, Boyan; Collins, David C.; Hoeflich, Peter
  • The Astrophysical Journal, Vol. 858, Issue 1
  • DOI: 10.3847/1538-4357/aab7f2

Fully Coupled Simulation of Cosmic Reionization. III. Stochastic Early Reionization by the Smallest Galaxies
journal, October 2018

  • Norman, Michael L.; Chen, Pengfei; Wise, John H.
  • The Astrophysical Journal, Vol. 867, Issue 1
  • DOI: 10.3847/1538-4357/aae30b

Self-Consistent Modeling of Reionization in Cosmological Hydrodynamical Simulations
text, January 2016


Lyman-alpha radiation hydrodynamics of galactic winds before cosmic reionization
text, January 2016


Magneto-Hydrodynamical Effects on Nuclear Deflagration Fronts in Type Ia Supernovae
text, January 2017


Inhomogeneous Reionization Models in Cosmological Hydrodynamical Simulations
text, January 2018