Formation of a Bose star in a rotating cloud

In this paper, we study the evolutions of a self-gravitating cloud of bosonic dark matter with finite angular momentum and self-interaction. This is achieved by using the sixth-order pseudospectral operator splitting method to solve the system of nonlinear Schrödinger and Poisson equations. The initial cloud is assumed to have mass density randomly distributed throughout three-dimensional space. The dark matter particles in the initial cloud are in the kinetic regime, i.e., their de Broglie wavelength is much smaller than the halo size. It is shown that Bose stars are indeed formed in the numerical simulation presented here. The presence of angular momentum and self-interaction in the initial cloud can significantly influence the star formation time in a non-trivial fashion. For the cases when the self-interaction is negligible or attractive, our analysis indicates that the stars formed in such scenarios may not have any intrinsic angular momentum. Conversely, if the self-interaction is repulsive, it is possible to have an angular momentum transfer from the cloud to the star. The presented numerical results agree with the expectation based on analytical calculations related to the instability of a rotating boson star with self-interaction. Furthermore, it is shown that the average mass and radius diagrams of the star are strongly influenced by the presence of angular momentum in the initial cloud.