Chandrajit Bajaj

Simulations of Structure Formation in the Universe

Overview

The formation of galaxies and large scale structure in the universe is thought to proceed by the gravitational amplification of initially small-amplitude primordial density fluctuations present in the early universe. Current cosmological models have a mass density dominated by two components: a gaseous component of mostly Hydrogen and Helium of which all luminous matter (stars, galaxies, etc.) is composed, and a "dark" collisionless component which has thus far only been detected by its gravitational influence on the luminous matter.

The visualizations presented here are of simulations which attempt to follow these two mass components of the universe from their nearly smooth distribution in the early universe to their present highly inhomogeneous, clustered state. This is accomplished by evolving the system according to the equations of hydrodynamics and gravity. The numerical method used to solve the equations of hydrodynamics is Adaptive Smoothed Particle Hydrodynamics (ASPH), while that for the gravity is the Particle-Particle Particle-Mesh (P3M) method. Both methods discretize the domain by representing the continuum by a set of interacting particles that can then be used to give function values (density, temperature, etc.) at locations other than the particle positions. Presented here are three simulations performed to address three different problems:

The feedback effect of explosions during galaxy formation
The distribution of "minihalos" and their effect on cosmological reionization
The formation of a typical Cluster of galaxies as simulated with different codes

Figure 1: (left) Hydro+N-body simulation of explosive energy release on galaxy formation. Gas temperature volume rendered from green to red, gas density from blue to green. (center) Hydro+N-body simulation of the formation of a massive galaxy cluster. Spheres are a sampling of the gas particles used; the larger and bluer the particles, the lower the gas density at that point. Translucent isosurfaces show the filamentary substructure in which the central galaxy cluster is embedded, which could contain as many as 1000 galaxies. (right) N-body simulation using about 2 million simulation particles of the universe at a redshift of 9, about 500 million years after the big bang. The structure that existed at that epoch is important to the study of cosmological reionization, in which some of the first objects to form in the universe (i.e. stars and quasars) emmitted radiation that eventually ionized the entire universe.

Explosions During Galaxy Formation

When density fluctuations collapse gravitationally out of the expanding cosmological background universe to form galaxies, the secondary energy release which results can affect their subsequent evolution profoundly. Focused upon here are the effects of one form of such energy release - explosions, such as might result from the supernovae which end the lives of the first generation of massive stars to form inside protogalaxies. As an idealized model which serves to illustrate and quantify the importance of these effects, the effect of explosions on the quasi-spherical objects which form in the plane of a cosmological pancake, as a result of gravitational instability and fragmentation of the pancake, are studied by numerical gas dynamical simulation in 3D coupled to a P3M gravity solver.

Movies:

I. Strongest Explosion

P51_512x384 -- The red surface is of a high temperature iso-contour, the temperature is volume rendered for the full volume using a color table which increases from blue to red, while the cyan surface is a density contour representing the average gas density in the volume. After the explosion happens in the highest density region,multiple shocks can be seen to propogate outward and along the central axis perpendicular to the pancake where some meet the shocks propogating from the neighbor box, illustrating the effect of periodic boundary conditions in the simulation.

P52_512x384 -- This visualization is the same as the first, but from a different perspective. The effect of the explosion on the cosmological pancake in which the halo is embedded can clearly be seen.

P53_512x384 -- Here the full volume of density and temperature are viewed together, with the density increasing from blue to green, and the temperature increasing from green to red.

P54_512x384 -- Fly-through of the simulation, temperature isosurface in red, with density in blue.

II. Intermediate Explosion

P41 -- A straight-on view of the explosion happening in a central volume which is 1/20 the volume of the full computational domain. The blue surface is of a density which is 200 times the average density, while temperature is displayed using both the red isosurface and volume rendering, where areas of higher opacity represent greater temperature.

P42 -- Similar to previous animation but frome a different angle and with density and then temperature shown with surfaces of progressively lower values at the end.

Minihalos and Cosmological Reionization

Cosmological reionization occured when the first star and quasar light propagated into the intergalactic medium and ionized the neutral gas comprised mostly of hydrogen and helium. The study of cosmological reionization is intimately related to the fundamental problems of galaxy and star formation. Astronomers have recently detected light from galaxies and quasars emitted almost 13 billion years ago, cosmologically redshifted by the fractional amount z = 6, which means it left those sources less than a billion years after the Big Bang. It is not yet known when the first of these sources of light formed to end the "dark ages" of cosmic history, completing reionization. The currently-favored Cold Dark Matter (CDM) model predicts that galaxies formed when dark-matter dominated "halos" collapsed out of the background universe, with small halos forming first and then merging to form larger ones later, in a continuous hierarchy of clustering, starting from Gaussian-random-noise initial density fluctuations. The first galaxies to form stars are believed to have done so within the first few hundred million years after the Big Bang, at redshifts greater than those yet observed directly.

Minihalos -- Shown in this animation is an illustrative cubic volume which comoves with the general expansion and which today would be 1 Mpc (or 3.26 million light years) on a side, as seen at a much earlier time corresponding to redshift z = 9. These simulations traced the evolving dark matter distribution in space by solving the Poisson equation and the collisionless Boltzmann equation with periodic boundary conditions using the P3M method with 2 million particles on a grid of 16 million cells. Translucent isosurfaces indicate the geometry of the regions containing more than twice the average mass density (with higher, more opaque surfaces embedded within), while opaque spheres show the size and location of dark matter halos whose mass is indicated by their color (red = 100 million solar masses, blue = 400,000 solar masses), the sites of the first galaxy formation.

Galaxy Cluster Formation

The simulation visualized here is embedded in a cube 64 megaparsecs (209 million light years) on a side at present, and models dark matter and gaseous components. The large structure in the center is a massive central galaxy cluster (the "Santa Barbara Cluster"), which could contain on the order of 1,000 galaxies.

SB1_512x384 -- Shown here is a volume rendering of the evolution of the density field increasing in density and becoming more opaque from blue-green-red-white.

SB2_512x384 -- The same simulation, but showing the actual ASPH simulation particles colored according to density, increasing from purple to white. The evolution is first shown, illustrating the hierarchical nature of the collapse, then a short fly-through.

SB4_512x384 -- Fly-through of the final time step in the simulation. A sampling of the ASPH particles are shown, colored according to their density from blue to red with a size indicative of their density (smaller = higher density), along with several translucent isocontours embedded within each other of increasing opacity with density.

Simulations performed on the CRAY SV1 at the Texas Advanced Computing Center (TACC) by:
  Paul Shapiro & Hugo Martel 
  Galaxy Formation and Intergalactic Research Group
  Department of Astronomy

Visualizations created by Marcelo Alvarez using VisTools developed at
  The Computational Visualization Center(CVC)