Stability of Self-Gravitating Bosonic Configurations

We study equilibrium and stability properties of self-gravitating bosonic configurations in the nonrelativistic regime by numerically solving the nonlinear Gross–Pitaevskii–Poisson (GPP) equations system. Using an appropriate coordinate transformation, the equations are written in a dimensionless form independent of the physical model parameters, so that each configuration is determined only by the central value of the wave function. We compute sequences of stationary solutions including ground and radially excited states and identify bifurcation points between them. The virial relation is used as a diagnostic condition for equilibrium, leading to the determination of a critical central density and a maximum particle number above which no stationary solutions are found. Excited configurations satisfying the virial relation are expected to be metastable since they violate stability conditions resulting from radial perturbation analyses. From the critical particle number, we estimate the maximum stable mass and radius. For axion-like bosons with mass 10−5 eV, the resulting configurations have masses of the order of tens of Earth masses and meter-scale radii.