Once the critical temperature of a cosmological boson gas is less than the critical temperature, a Bose-Einstein Condensation process can always take place during the cosmic history of the universe. Zero temperature condensed dark matter can be described as a non-relativistic, Newtonian gravitational condensate, whose density and pressure are related by a barotropic equation of state, with barotropic index equal to one. In the present paper we analyze the effects of the finite dark matter temperature on the properties of the dark matter halos. We formulate the basic equations describing the finite temperature condensate, representing a generalized Gross-Pitaevskii equation that takes into account the presence of the thermal cloud. The static condensate and thermal cloud in thermodynamic equilibrium is analyzed in detail, by using the Hartree-Fock-Bogoliubov and Thomas-Fermi approximations. The condensed dark matter and thermal cloud density and mass profiles at finite temperatures are explicitly obtained. Our results show that when the temperature of the condensate and of the thermal cloud are much smaller than the critical Bose-Einstein transition temperature, the zero temperature density and mass profiles give an excellent description of the dark matter halos. However, finite temperature effects may play an important role in the early stages of the cosmological evolution of the dark matter condensates.

Using recently developed nonrelativistic numerical simulation code, we investigate the stability properties of compact astrophysical objects that may be formed due to the Bose-Einstein condensation of dark matter. Once the temperature of a boson gas is less than the critical temperature, a Bose-Einstein condensation process can always take place during the cosmic history of the Universe. Because of dark matter accretion, a Bose-Einstein condensed core can also be formed inside massive astrophysical objects such as neutron stars or white dwarfs, for example. Numerically solving the Gross-Pitaevskii-Poisson system of coupled differential equations, we demonstrate, with longer simulation runs, that within the computational limits of the simulation the objects we investigate are stable. Physical properties of a self-gravitating Bose-Einstein condensate are examined both in nonrotating and rotating cases.

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 10(9) years using a finer (100 x 100 x 100) spatial grid, in less than a day of processor time on a contemporary desktop computer. Program summary Program title: bec3p Catalogue identifier: AEOR_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEOR_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5248 No. of bytes in distributed program, including test data, etc.: 715402 Distribution format: tar.gz Programming 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 x 100 x 100 grid can be solved with a time span of 10 Gyr in approx. a day of running time.