Abstract
Equilibrium configurations for a self-gravitating scalar field with self-interaction are constructed. The corresponding Schrödinger-Poisson (SP) system is solved using finite differences, assuming spherical symmetry. It is shown that equilibrium configurations of the SP system are late-time attractor solutions for initially quite arbitrary density profiles, which relax and virialize through the emission of scalar field bursts—a process dubbed gravitational cooling. Among other potential applications, these results indicate that scalar field dark matter models (in their different flavors) tolerate the introduction of a self-interaction term in the SP equations. This study can be useful in exploring models in which dark matter in galaxies is not pointlike.
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