Figure 1: A Cosmological Structure Formation Simulation

An example of a production run using the parallel TVD code. The gas mesh has a total of 512 cubed (134 million) points and 256 cubed (17 million) particles represent dark matter. The computation was done on 64 and 128 nodes of the IBM SP2 at the Cornell Theory Center; the total running time was four and a half days and turnaround time was a week. The simulation volume is a cube with each side 32 megaparsecs in length (1 parsec = 3.3 light-years). The pictures below show the projected density of a slab 8 megaparsec deep taken from the center of the cube; a large cluster containing X-ray emitting gas forms in the center as gravity causes dense regions to collapse. The colors show increasing density in the order black (least dense), blue, green, yellow, red, white (most dense); the scale is logarithmic. 90 percent of the mass is in dark matter and the remaining 10 percent is baryonic (H and He gas); the Hubble constant is 50 km/sec/Mpc and space is flat.

Figure 1a: Dark matter

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The initial dark matter density (redshift z=40). The simulation begins in the linear regime, when perturbations from the mean density are small; thus the density is near average everywhere.

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Dark matter density at z=0 (today). Black regions are empty voids (density is less than a tenth of the mean density); white regions are over 250 times denser than the mean. Thus the particle distribution is highly anisotropic: many grid points are completely empty and others contain many thousands of particles.

Movie 1: Dark Matter Density Evolution

This movie shows how the dark matter density evolves in this small patch of the universe. The overall comsological expansion is shown; the movie begins when the universe is 1/41 as large as it is today. Regions of higher density expand slower and regions of low density expand faster (creating empty voids); high density regions eventually collapse under their own gravitational attraction. Periodic boundary conditions are assumed.

Figure 1b: Gas

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The gas density at z=0 (today). The original small perturbations are the same as those for the dark matter shown above.

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Temperature of the gas at z=0; black regions are less than 100,000 degrees Kelvin, white regions are over 50 million degrees; a logarithmic scale is used. It can be seen that the gas is strongly shocked.

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What the gas would appear like in the X-ray today. The observed properties of X-ray clusters are a useful means of constraining cosmological theories.

Movie 2: Gas Density Evolution

This movie shows how the gas density evolves with time. This is shown in co-moving coordinates; the overall expansion of the universe is taken into account as part of the coordinate system.


Figure 2: Timing on the SP2

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The wallclock time consumed per step as a function of the number of processors used. To compare runs with differently sized grids the times are divided by a factor NX*NY*NZ/128, i.e. the 256 cubed mesh run times (shown in red) are divided by 8 and the 512 cubed run times (shown in blue) are divided by 64, and so on (the number of particles is NX*NY*NZ/8 in all cases). Purple and green represent 768 and 792 cubed meshes. Circles: total time. Triangles: purely computational portion of the hydrodynamical code. Squares: time required for message passing in solving the TVD equations. Crosses: the PM portion of the code. The dashed lines are proportional to 1/NCPU.