Generating ultra compact boson stars with modified scalar potentials

Abstract

The properties of selfinteracting boson stars with different scalar potentials going beyond the commonly used ${\varphi }^4$ ansatz are studied. The scalar potential is extended to different values of the exponent $n$ of the form $V\propto {\varphi }^n$. 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 selfbound stars, the second one those of neutron stars and the third one is the well known constant radius case from the standard ${\varphi }^4$ potential. We demonstrate that the maximal compactness can reach extremely high values going to the limit of causality $C_{\text{max}}=0.354$ asymptotically for $n\to \infty$. The maximal compactnesses exceed previously calculated values of $C_{\text{max}}=0.16$ for the standard ${\varphi }^4$-theory and $C_{\text{max}}=0.21$ for vector-like 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 $V\propto {\varphi }^n$ can be ultra compact black hole mimickers where the photon ring is located outside the radius of the star.

arXiv comment18 pages, 5 figures, data files

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• Observational Probes of the Neutron Star Equation of State with Hyperons, Bosonic Dark Matter, and Quark Matter
• Superfluid dark stars
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