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We study self-gravitating bosonic systems, candidates for dark-matter halos,by carrying out a suite of direct numerical simulations (DNSs) designed toinvestigate the formation of finitetemperature, compact objects in thethree-dimensional (3D) Fourier-truncated Gross-Pitaevskii-Poisson equation(GPPE). This truncation allows us to explore the collapse and fluctuations ofcompact objects, which form at both zero temperature and finite temperature. Weshow that the statistically steady state of the GPPE, in the large-time limitand for the system sizes we study, can also be obtained efficiently by tuningthe temperature in an auxiliary stochastic Ginzburg-Landau-Poisson equation(SGLPE). We show that, over a wide range of model parameters, this systemundergoes a thermally driven first-order transition from a collapsed, compact,Bose-Einstein condensate (BEC) to a tenuous Bose gas without condensation. By asuitable choice of initial conditions in the GPPE, we also obtain a binarycondensate that comprises a pair of collapsed objects rotating around theircenter of mass.

The formation of compact objects at finite temperatures in a dark-matter-candidate self-gravitating bosonic system