Stability of Self-Gravitating Bosonic Configurations

We investigate the equilibrium and stability properties of self-gravitating bosonic congurations in the nonrelativistic regime by numerically solving the nonlinear Gross-Pitaevskii-Poisson (GPP) system of equations. By adopting a suitable coordinate transformation and a specic gauge choice for the gravitational potential, the GPP equations are cast into a dimensionless form independent of the physical parameters of the model. In this formulation, equilibrium congurations are uniquely characterized by the central value of the dimensionless wave function, which determines the central density once physical units are restored. We compute sequences of stationary solutions including both ground-state and radially excited congurations and identify bifurcation points at which transitions between these states occur. The virial relation is employed as a diagnostic criterion for equilibrium, allowing us to determine a critical central density above which stationary congurations cease to exist. Excited-state solutions satisfying the virial relation are probably metastable and are expected to decay toward the ground state through gravitational cooling. The critical central density is associated with a maximum allowed particle number, leading to an estimate of the maximum stable mass of the conguration. For axion-like bosons with masses of order 10?5 eV, the resulting maximum mass is of the order of tens of Earth mass, while the characteristic size of the conguration is of order one meter. The compactness of these objects places them close to the limit of validity of the Newtonian approximation.