Scalar field dark matter: Nonspherical collapse and late-time behavior

We show the evolution of nonspherically symmetric balls of a self-gravitating scalar field in the Newtonian regime or equivalently an ideal self-gravitating condensed Bose gas. In order to do so, we use a finite differencing approximation of the Schr\"odinger-Poisson (SP) system of equations with axial symmetry in cylindrical coordinates. Our results indicate: (i) that spherically symmetric ground state equilibrium configurations are stable against nonspherical perturbations and (ii) that such configurations of the SP system are late-time attractors for nonspherically symmetric initial profiles of the scalar field, which is a generalization of such behavior for spherically symmetric initial profiles. Our system and the boundary conditions used, work as a model of scalar field dark matter collapse after the turnaround point. In such case, we have found that the scalar field overdensities tolerate nonspherical contributions to the profile of the initial fluctuation.