Large Scale Structure of Galaxy Distribution

Objective

Our scientific objective is to compare the predicted large-scale structure of matter, under the assumption of various cosmological models, to the observed structure from redshift surveys. The computational objectives are to implement a fully scalable technique for applying observational constraints to the largest scales and to improve the accuracy and efficiency of the N-body code.

Approach

Dynamics are modeled initially using an MPI-based, momentum-conserving, particle-mesh scheme, with 134 million particles (268 million for models with 2 different dark matter types) to model the density field. Unconstrained initial conditions are generated using a standard parallelized Zeldovich approximation (i.e., a perturbative mapping from an Eulerian to a Lagrangian representation of the density field). They are then constrained with a Fourier-space implementation of the "Hoffman-Ribak" method—the density field is forced to conform to observed density data from the IRAS 1.2 Jansky (Jy) survey, on a very widely spaced grid, using a maximum-likelihood formalism.

Accomplishments

We have ported the particle-mesh code to the CRAY T3E and demonstrated acceptable performance, and all parts, including the constraining procedure, are tested. Scaling behavior is nearly perfectly linear for initial conditions and the constraining procedure, but the N-body dynamics are starting to become communication-intensive on 512 processors. Data extraction, in the form of a "halo finder" is much more expensive than we would like, due to a load imbalance, particularly when clustering becomes very heavy at late times in the simulation.

The code is presently in production mode. So far, a mixed dark matter model and a low-density model with a cosmological constant have been run, with separate realizations of the northern and southern galactic hemispheres.

Significance

Unconstrained simulations depend upon a realization of a Gaussian random field in Fourier space. Since there are only a few long-wavelength waves, the variance from run to run is substantial, and nonlinear feedback mechanisms such as biased galaxy formation cause the excess or deficient amplitude of these waves to couple with much smaller wavelengths that participate in the formation of individual objects. Thus, excess variance can dramatically alter the number density of objects, and any statistic sensitive to that number density can be artificially skewed.

Unlike a laboratory experiment, there is only one universe, so we don't need to create a statistically fair representation of the universe. So, we draw our realization from a smaller population—one which represents the maximum likelihood for consistency with observed data at the largest scales, with observational errors taken into account. Thus, our realizations reproduce the "Great Wall" of galaxies in a very coarse sense, to within observational errors, but the fine details that are not resolved by our sampling of the survey are filled in by the assumed model.

Making our simulations reproduce observations on the largest scales makes small -scale comparisons to data more fair.

Four Panel Visualization Series

Visualizations of test runs with constraints taken from the smoothed IRAS 1.2 Jy survey. Shown is the constrained portion of the simulation, and the same volume in the IRAS data. Our position corresponds to the green sphere at the center of the bottom face of the cube. The top row shows the IRAS data smoothed to the same scale it was when initial conditions were drawn, and the simulation data at zero redshift smoothed to the same scale. The bottom row shows the same data sets, undersmoothed by a factor of two. These figures show that the simulation reproduces the data very well on the largest scales, but differs strongly even on scales only slightly smaller.

Status/Plans

Some other models need running: a low density model without a cosmological constant, and a mixed dark matter model with a cosmological constant. The latter represents our attempt to simultaneously match high-redshift supernova observations (which require a significant cosmological constant) with the autocorrelation function of galaxies in the local universe.

An alternative to constraining simulations from data is to use a larger simulation volume, because the mean-field fluctuation amplitude peaks at wavelengths of 100-150 h^-1 Mpc. On a uniform grid, the consequences of that are unacceptable, because memory limits the size of a grid cell to be much larger than a galaxy or even a group of galaxies. For our long-range plans, we will abandon the use of a uniform grid and place more grid cells where "interesting" things, like the formation of a stable object, are happening. Since initial conditions are best described on a uniform grid (and the density of the universe is nearly uniform at these very early times), the mesh must be fully adaptive. A project to implement a particle-mesh algorithm on top of the PARAMESH adaptive mesh refinement toolkit is currently underway.

The largest uncertainty in N-body simulation analysis is how to map density to observational variables. We plan to follow the baryonic component of the universe using a coupled gas dynamics code, also built upon PARAMESH.

Points of Contact

Michael A. K. Gross<
Earth & Space Data Computing Division
Code 931
NASA Goddard Space Flight Center
Greenbelt, MD 20771
gross@fozzie.gsfc.nasa.gov
301-286-9096

Joel R. Primack
Physics Department
University of California
Santa Cruz, CA 95064
joel@ucolick.org
831-459-2580