Axion boson stars

We study novel solitonic solutions to Einstein-Klein-Gordon theory in the presence of a periodic scalar potential arising in models of axion-like particles. The potential depends on two parameters: the mass of the scalar field ma and the decay constant fa; the standard case of the QCD axion is recovered when ma 1/fa. When fa the solutions reduce to the standard case of "mini" boson stars supported by a massive free scalar field. As the energy scale fa of the scalar self-interactions decreases we unveil several novel features of the solution: new stability branches emerge at high density, giving rise to very compact, radially stable, boson stars. Some of the most compact configurations acquire a photon sphere. When fa is at the GUT scale, a boson star made of QCD axions can have a mass up to ten solar masses and would be more compact than a neutron star. Gravitational-wave searches for these exotic compact objects might provide indirect evidence for ultralight axion-like particles in a region not excluded by the black-hole superradiant instability.