Gravity- and temperature-driven phase transitions in a model for collapsed axionic condensates

We show how to use the cubic-quintic Gross-Pitaevskii-Poisson equation (cq-GPPE) and the cubicquintic stochastic Ginzburg-Landau-Poisson equation (cq-SGLPE) to investigate the gravitational collapse of a tenuous axionic gas into a collapsed axionic condensate for both zero and finite temperature T. At T = 0, we use a Gaussian Ansatz for a spherically symmetric density to obtain parameter regimes in which we might expect to find compact axionic condensates. We then go beyond this Ansatz, by using the cqSGLPE to investigate the dependence of the axionic condensate on the gravitational strength G at T = 0. We demonstrate that, as G increases, the equilibrium configuration goes from a tenuous axionic gas, to flat sheets or Zeldovich pancakes, cylindrical structures, and finally a spherical axionic condensate. By varying G, we show that there are first -order phase transitions, as the system goes from one of these structures to the next one; we find hysteresis loops that are associated with these transitions. We examine these states and the transitions between these states via the Fourier truncated cq-GPPE; and we also obtain the thermalized T > 0 states from the cq-SGLPE; the transitions between these states yield thermally driven first -order phase transitions and their associated hysteresis loops. Finally, we discuss how our cq-GPPE approach can be used to follow the spatiotemporal evolution of a rotating axionic condensate and also a rotating binaryaxionic-condensate system; in particular, we demonstrate, in the former, the emergence of vortices at large angular speeds omega and, in the latter, the rich dynamics of the mergers of the components of this binary system, which can yield vortices in the process of merging.