Numerical simulation code for self-gravitating Bose–Einstein condensates

Abstract

We completed the development of simulation code that is designed to study the behavior of a conjectured dark matter galactic halo that is in the form of a Bose–Einstein Condensate (BEC). The BEC is described by the Gross–Pitaevskii equation, which can be solved numerically using the Crank–Nicholson method. The gravitational potential, in turn, is described by Poisson’s equation, that can be solved using the relaxation method. Our code combines these two methods to study the time evolution of a self-gravitating BEC. The inefficiency of the relaxation method is balanced by the fact that in subsequent time iterations, previously computed values of the gravitational field serve as very good initial estimates. The code is robust (as evidenced by its stability on coarse grids) and efficient enough to simulate the evolution of a system over the course of 109 years using a finer (100×100×100) spatial grid, in less than a day of processor time on a contemporary desktop computer. Program summaryProgram title: bec3pCatalogue identifier: AEOR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 5248No. of bytes in distributed program, including test data, etc.: 715402Distribution format: tar.gzProgramming language: C++ or FORTRAN.Computer: PCs or workstations.Operating system: Linux or Windows.Classification: 1.5.Nature of problem:Simulation of a self-gravitating Bose–Einstein condensate by simultaneous solution of the Gross–Pitaevskii and Poisson equations in three dimensions.Solution method:The Gross–Pitaevskii equation is solved numerically using the Crank–Nicholson method; Poisson’s equation is solved using the relaxation method. The time evolution of the system is governed by the Gross–Pitaevskii equation; the solution of Poisson’s equation at each time step is used as an initial estimate for the next time step, which dramatically increases the efficiency of the relaxation method.Running time:Depends on the chosen size of the problem. On a typical personal computer, a 100×100×100 grid can be solved with a time span of 10 Gyr in approx. a day of running time.