High Resolution TPM Cosmological Simulations

Cosmological simulation of galaxy formation is a grand challenge problem for both astrophysicists and numerical methodologists. The large dynamic range required to simulate structure formation properly stimulates a search for fast and accurate algorithm which can be fitted into the the front end massively parallel computers. In this thesis, we present our efforts to approach this problem. We proposed and implemented a novel algorithm TPM to perform large cosmological N-body simulations on parallel machines. The TPM method combines the advantages of the fast Particle-Mesh (PM) method and the accurate TREE method. We classify the particles in the simulation box to be PM particles and TREE particles according to their local density. Since structure forms at high density regions, we apply the accurate TREE method to the particles in these regions. The fact that the gravity equation is linear allows us to linearly combine the forces calculated using different methods. Individual objects interact with each other through tidal force, which changes slower than the internal evolution of an object. Thus we can allow individual time steps for each object, which is represented by a group of particles in the same TREE. We parallelize the method by throw each processor a different TREE to process, and several processors can collaborate with each other to evolve the same TREE when necessary. This mechanism gives the code high efficiency on massively parallel computers. With the TPM code, we can easily perform N = 128^ {3} particle simulations with high force resolution (~1/7680 of box size). We have also performed simulations with N = 256^3 particles with the best dynamic range achieved in this field. We put special attention when selecting the parameters of the cosmological models in our simulations. The COBE normalization is taken as a standard to normalize the initial condition, while the results from large scale sky surveys are also taken into consideration. In this thesis we studied several variations of Cold Dark Matter (CDM) type. The standard CDM model, although with many known problems, is treated to compare with the previous simulations. The low density models with and without a cosmological constant are of special interest because they give better fit to the large scale structure and much observational evidence implies that Omega_0 < 1.. With our high resolution simulations, we are specially interested to study the structure of the objects from different cosmological models. The slopes of the dark halo density profiles from different models are only slightly different from each other, with a broad distribution within each model. All the models can successfully produce flat rotation curves for dark halos. We find the biggest difference in the cluster structure among various models is the predicted X-ray core radius. The standard CDM model predicts bigger X-ray core radius than the low density models, but all the models predicts smaller core radius than that from X-ray observations. We find the low density models can produce significant substructures in X-ray clusters to be in agreement with observations, while the X-ray clusters in the standard CDM model are known to have abundant substructures.