Mathematics
Scientific paper
Oct 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991ipesprept.....m&link_type=abstract
M.S. Thesis Instituto de Pesquisas Espaciais, Sao Jose dos Campos (Brazil).
Mathematics
Computer Programs, Computerized Simulation, Data Structures, Error Analysis, Galactic Evolution, Many Body Problem, Markov Processes, Stellar Models, Stellar Systems, Trees (Mathematics), Dynamic Models, Elliptical Galaxies, Integrators, Stellar Luminosity, Truncation Errors
Scientific paper
An implementation of a tree code for the force calculation in gravitational N-body systems simulations is presented. The technique consists of virtualizing the entire system in a tree data-structure, which reduces the computational effort to theta(N log N) instead of the theta(N exp 2), typical of direct summation. The adopted time integrator is the simple leap-frog with second-order accuracy. A brief discussion about the truncation-error effects on the morphology of the system shows them to be essentially negligible. However, these errors do propagate in a Markovian way if a potential-adaptive time-step is used in order to maintain the expected truncation-error approximately constant in the entire system. The tests show that, even with totally arbitrary distributions, the total computation time obeys theta(N log N). As an application of the code, we evolved an initially cold and homogeneous sphere of point masses to simulate a primordial process of galaxy formation. The evolution of the global entropy of the system suggests that a quasi-equilibrium configuration is achieved after approximately 2 x 10 exp 9 years. It is shown that the final configuration displays a close resemblance to the well observed giant elliptical galaxies, in both kinematical and luminosity distribution properties. A discussion is given on the evolution of the important dynamic quantities characterizing the model. During all the computations, the energy is conserved to better than 0.1 percent.
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