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Cosmic Reionization of the Early Universe

(Multi-scale, Multi-physics Modeling and Petascale Scientific Computing)

We have recently been actively collaborating with researchers from the Laboratory for Computational Astrophysics at the University of California at San Diego, addressing fundamental questions regarding reionization of the early universe following the Big Bang. Modern observational astronomy has offered some glimpses into the earliest precursors of galactic formation, giving rise to debate as to the underlying physical processes that formed our universe. Through this collaboration, we aim to address the core components of this debate, through developing new models for cosmic reionization in an attempt to match computational simulation to telescope observation.

For these studies, we are developing coupled radiation-hydrodynamic-chemical kinetics simulations that will attempt to test some of these modern theories against experimental observation. As with our research efforts in fusion energy and core-collapse supernovae, these models involve the coupling of a large number of physical processes, including the compressible Euler equations for gas motion, nonlinear radiation diffusion equations for multi-frequency radiation transport, chemical kinetics models for tracking the ionization state of primordial elemental species, as well as a model for gravitational acceleration due to star clustering and galactic formation. This problem therefore combines all challenges facing modern scientific computation: consistent modeling of the relevant physical processes, analysis of the well-posedness of the resulting PDE modeling system, the derivation and development of high-fidelity numerical methods for accurately approximating processes at large (cosmic) and ``small'' (solar) scales, and the invention of solution strategies for efficiently solving the resulting PDE model system on some of the largest NSF supercomputers available.

Figure 1:  Numerical Simulations of Cosmic Reionization (left) and Cluster Formation (right). Images courtesy of collaborators at the LCA.


In this effort we have been working on nearly all of these fronts: deriving a coupled PDE modeling system that will both capture the dominant physical processes while lending itself to efficient numerical solution; deriving an accurate time-evolution technique for the coupled radiation transport and chemical kinetics processes occurring on multiple time and space scales, and implementing computational algorithms based on these approaches designed to utilize next-generation petascale computing hardware [1, 2].

Figure 2:  Density field (left) and Neutral Fraction (right) in cosmological reionization simulations using new scalable algorithms (256^3 grid).


We show results from simulations of the early universe. The results in Figure 1 are from simulations by collaborators prior to the development of our new self-consistent radiation transport module. The results in Figures 2-4 are from simulations using the new fully implicit solver for radiation transport, chemical ionization and gas energy feedback.

Figure 3:  Density field (top-left), star sources (top right), ionized fraction (bottom left) at redshift z=6, for an early universe simulation at 512^3 spatial resolution. Bottom right: weak scaling of the radiation solver on a test cosmology run, showing ideal O(n log(n)) growth in wall-clock time as the problem size is increased.



Figure 4:  Density, Radiation Energy, and Temperature fields (left to right) at redshifts 20, 15, 12, 11, 10 and 9 (top to bottom), for an early universe simulation at 1024^3 spatial resolution (using 4096 cores on Kraken).








    HPCWire news release (Jan 7, 2010): Mathematical Model Aids Simulations of Early Universe.

    InsideHPC news release (Nov 30, 2011): Video: Birth of the Universe -- Direct Numerical Simulations of Cosmological Reionization.

    Videos from InsideHPC news release (Nov 30, 2011):


    Current Enzo release: Google code site.

    Earlier Enzo releases, documentation, automated regression testing results, etc: LCA site.


[1] M.L. Norman, G.L.Bryan, R. Harkness, J. Bordner, D. Reynolds, B. O'Shea, and R. Wagner. Petascale Computing: Algorithms and Applications, chapter "Simulating cosmological evolution with Enzo." CRC Press, 2007.
[2] D.R. Reynolds, J.C. Hayes, P. Paschos, and M.L. Norman. "Self-Consistent Solution of Cosmological Radiation-Hydrodynamics and Chemical Ionization." Journal of Computational Physics, 228:6833-6854, 2009.
[3] M.L. Norman, D.R. Reynolds, and G.C. So. "Cosmological Radiation Hydrodynamics with Enzo," Recent Directions in Astrophysical Quantitative Spectroscopy and Radiation Hydrodynamics, AIP, 2009.
[4] I.T. Iliev, D. Whalen, K. Ahn, S. Baek, N.Y. Gnedin, A.V. Kravtsov, G. Mellema, M. Norman, M. Raicevic, D.R. Reynolds, D. Sato, P.R. Shapiro, B. Semelin, J. Smidt, H. Susa, T. Theuns, and M. Umemura. "Cosmological Radiative Transfer Codes Comparison Project II: The Radiation-Hydrodynamic Tests," MNRAS, 400:1283-1316, 2009.
[5] M.L. Norman, D.R. Reynolds, G.C. So, R.P. Harkness and J.H. Wise, "Fully-coupled simulation of cosmic reionization I: numerical methods and tests," The Astrophysical Journal, 216:16, 2014.
[6] G.L. Bryan, M.L. Norman, B.W. O'Shea, T. Abel, J.W. Wise, M.J. Turk, D.R. Reynolds, D.C. Collins, P. Wang, S.W. Skillman, B. Smith, R.P. Harkness, J. Bordner, J.-H. Kim, M. Kuhlen, H. Xu, N. Goldbaum, C. Hummels, A.G. Kritsuk, E. Tasker, S. Skory, C.M. Simpson, O. Hahn, J.S. Oishi, G.C. So, F. Zhao, R. Cen and Y. Li, "Enzo: an adaptive mesh refinement code for astrophysics," The Astrophysical Journal Supplement, 211:19, 2014.
[7] G.C. So, M.L. Norman, D.R. Reynolds and J.H. Wise, "Fully-Coupled Simulation of Cosmic Reionization II: Recombinations, Clumping Factors, and the Photon Budget for Reionization," The Astrophysical Journal, 789:149, 2014.

Funding Support

    NSF AST Grant 1109008 (co-PI; with M. Norman), 2011-2014.

    DOE INCITE Awards "How High Redshift Galaxies Reionized the Universe" (co-PI; with M. Norman & R. Harkness), 2011-2012, 2012-2013.

    NSF AAG Grant 0808184 (co-PI; with M. Norman), 2008-2011.

    NSF OCI Grant 0832662 (supporting; with B. O'Shea), 2009-2011.


Maintained by reynolds [at] smu [dot] edu

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