Generating ultracompact boson stars with modified scalar potentials
Sarah Louisa Pitz, Jürgen Schaffner–Bielich
Abstract
The properties of self-interacting boson stars with different scalar potentials going beyond the commonly used ${\ensuremath{\phi}}^{4}$ ansatz are studied. The scalar potential is extended to different values of the exponent $n$ of the form $V\ensuremath{\propto}{\ensuremath{\phi}}^{n}$. 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 ${\ensuremath{\phi}}^{4}$ potential. We demonstrate that the maximal compactness can reach extremely high values going to the limit of causality ${C}_{\mathrm{max}}=0.354$ asymptotically for $n\ensuremath{\rightarrow}\ensuremath{\infty}$. The maximal compactnesses exceed previously calculated values of ${C}_{\mathrm{max}}=0.16$ for the standard ${\ensuremath{\phi}}^{4}$-theory and ${C}_{\mathrm{max}}=0.21$ 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 $V\ensuremath{\propto}{\ensuremath{\phi}}^{n}$ can be ultracompact black hole mimickers where the photon ring is located outside the radius of the star.