Numerical simulation code for self-gravitating Bose-Einstein condensates

TL;DR

This paper presents a numerical simulation code that models the evolution of self-gravitating Bose-Einstein Condensates, relevant for dark matter halos, combining the Gross-Pitaevskii and Poisson equations efficiently.

Contribution

The authors developed a robust and efficient simulation code that integrates the Gross-Pitaevskii and Poisson equations for studying self-gravitating BECs over cosmological timescales.

Findings

Code remains stable on coarse grids

Simulates 1 billion-year evolution in less than a day

Effective combination of Crank-Nicholson and relaxation methods

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 1E9 years using a finer (100x100x100) spatial grid, in less than a day of processor time on a contemporary desktop computer.