Abstract. As yet undiscovered light bosons may constitute all or part of the dark matter (DM) of our Universe, and are expected to have (weak) self-interactions. We show that quartic self-interactions generically induce the capture of dark matter from the surrounding halo by external gravitational potentials such as those of stars, including the Sun. This leads to the subsequent formation of dark matter bound states supported by such external potentials, resembling gravitational atoms (e.g. a solar halo around our own Sun). Their growth is governed by the ratio ξfoc = λdB/R⋆ between the de Broglie wavelength of the incoming DM waves, λdB, and the radius of the ground state R⋆. For ξfoc ≲ 1, the gravitational atom grows to a steady state that balances the capture of particles and the inverse, stripping, process. For ξfoc ≳ 1, a significant gravitational-focusing effect leads to exponential accumulation of mass from the galactic DM halo into the atom. For instance, a dark matter axion with mass of the order of 10^{−14} eV and decay constant between 10^7 and 10^8 GeV would lead to formation of a dense halo, with local DM density at the position of the Earth O(10^4) times larger than that predicted by the standard halo model. For attractive self-interactions, after the formation, the gravitational atom is destabilized at a large density, leading to collapse accompanied by emission of relativistic bosons (‘Bosenova’) on a timescale that can be comparable to the lifetime of the Solar System. Based on 2306.12477.