Axion Stars in the Infrared Limit

Abstract

Following Ruffini and Bonazzola, we use a quantized boson field to describe condensates of axions forming compact objects. Without substantial modifications, the method can only be applied to axions with decay constant, $f_a$, satisfying $\delta =(f_a/M_P{)}^2\ll 1$, where $M_P$ is the Planck mass. Similarly, the applicability of the Ruffini-Bonazzola method to axion stars also requires that the relative binding energy of axions satisfies $\Delta =\sqrt{1-(E_a/m_a{)}^2}\ll 1$, where $E_a$ and $m_a$ are the energy and mass of the axion. The simultaneous expansion of the equations of motion in $\delta$ and $\Delta$ leads to a simplified set of equations, depending only on the parameter, $\lambda =\sqrt{\delta }/\Delta$ in leading order of the expansions. Keeping leading order in $\Delta$ is equivalent to the infrared limit, in which only relevant and marginal terms contribute to the equations of motion. The number of axions in the star is uniquely determined by $\lambda$. Numerical solutions are found in a wide range of $\lambda$. At small $\lambda$ the mass and radius of the axion star rise linearly with $\lambda$. While at larger $\lambda$ the radius of the star continues to rise, the mass of the star, $M$, attains a maximum at ${\lambda }_{\max }\simeq 0.58$. All stars are unstable for $\lambda >{\lambda }_{\max }$ . We discuss the relationship of our results to current observational constraints on dark matter and the phenomenology of Fast Radio Bursts.

14 pages, 2 figures

References in corpus (3)

• A bright millisecond radio burst of extragalactic origin
• Fast Radio Burst Discovered in the Arecibo Pulsar ALFA Survey
• Axion Stars and Fast Radio Bursts

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