Generating ultracompact boson stars with modified scalar potentials

The properties of self-interacting boson stars with different scalar potentials going beyond the commonly used 04 ansatz are studied. The scalar potential is extended to different values of the exponent n of the form V cc 0n. Two stability mechanism for boson stars are introduced, the first being a mass term and the second one a vacuum term. We present analytic scale-invariant expressions for these two classes of equations of state. The resulting properties of the boson star configurations differ considerably from previous calculations. We find three different categories of mass-radius relation: the first category resembles the mass-radius curve of self-bound stars, the second one those of neutron stars and the third one is the well-known constant radius case from the standard 04 potential. We demonstrate that the maximal compactness can reach extremely high values going to the limit of causality Cmax = 0.354 asymptotically for n -> co. The maximal compactnesses exceed previously calculated values of Cmax = 0.16 for the standard 04-theory and Cmax = 0.21 for vectorlike interactions and is in line with previous results for solitonic boson stars. Hence, boson stars even described by a simple modified scalar potential in the form of V cc 0n can be ultracompact black hole mimickers where the photon ring is located outside the radius of the star.