Computer Simulations of Cosmic Reionization

The cosmic reionization of hydrogen was the last major phase transition in the evolution of the universe, which drastically changed the ionization and thermal conditions in the cosmic gas. To the best of our knowledge today, this process was driven by the ultra-violet radiation from young, star-forming galaxies and from first quasars. We review the current observational constraints on cosmic reionization, as well as the dominant physical effects that control the ionization of intergalactic gas. We then focus on numerical modeling of this process with computer simulations. Over the past decade, significant progress has been made in solving the radiative transfer of ionizing photons from many sources through the highly inhomogeneous distribution of cosmic gas in the expanding universe. With modern simulations, we have finally converged on a general picture for the reionization process, but many unsolved problems still remain in this young and exciting field of numerical cosmology.Comment: Invited Review to appear on Advanced Science Letters (ASL), Special Issue on Computational Astrophysics, edited by Lucio Maye

A Moving Frame Algorithm for High Mach Number Hydrodynamics

We present a new approach to Eulerian computational fluid dynamics that is designed to work at high Mach numbers encountered in astrophysical hydrodynamic simulations. The Eulerian fluid conservation equations are solved in an adaptive frame moving with the fluid where Mach numbers are minimized. The moving frame approach uses a velocity decomposition technique to define local kinetic variables while storing the bulk kinetic components in a smoothed background velocity field that is associated with the grid velocity. Gravitationally induced accelerations are added to the grid, thereby minimizing the spurious heating problem encountered in cold gas flows. Separately tracking local and bulk flow components allows thermodynamic variables to be accurately calculated in both subsonic and supersonic regions. A main feature of the algorithm, that is not possible in previous Eulerian implementations, is the ability to resolve shocks and prevent spurious heating where both the preshock and postshock Mach numbers are high. The hybrid algorithm combines the high resolution shock capturing ability of the second-order accurate Eulerian TVD scheme with a low-diffusion Lagrangian advection scheme. We have implemented a cosmological code where the hydrodynamic evolution of the baryons is captured using the moving frame algorithm while the gravitational evolution of the collisionless dark matter is tracked using a particle-mesh N-body algorithm. The MACH code is highly suited for simulating the evolution of the IGM where accurate thermodynamic evolution is needed for studies of the Lyman alpha forest, the Sunyaev-Zeldovich effect, and the X-ray background. Hydrodynamic and cosmological tests are described and results presented. The current code is fast, memory-friendly, and parallelized for shared-memory machines.Comment: 19 pages, 5 figure

Planar shape manipulation using approximate geometric primitives

We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is \bigo(n\log n+k) for an input of size $n$ with k=\bigo(n^2) consistency violations. The output is as accurate as the geometric primitives. We validate our algorithms in floating point using sequences of six set operations and Euclidean transforms on shapes bounded by curves of algebraic degree~1 to~6. We test generic and degenerate inputs. Keywords: robust computational geometry, plane subdivisions, set operations