Dilute and dense axion stars

Abstract: Axion stars are hypothetical objects formed of axions, obtained as localized and coherently oscillating solutions to their classical equation of motion. Depending on the value of the field amplitude at the core $|\theta_0| \equiv |\theta(r=0)|$, the equilibrium of the system arises from the balance of the kinetic pressure and either self-gravity or axion self-interactions. Starting from a general relativistic framework, we obtain the set of equations describing the configuration of the axion star, which we solve as a function of $|\theta_0|$. For small $|\theta_0| \lesssim 1$, we reproduce results previously obtained in the literature, and we provide arguments for the stability of such configurations in terms of first principles. We compare qualitative analytical results with a numerical calculation. For large amplitudes $|\theta_0| \gtrsim 1$, the axion field probes the full non-harmonic QCD chiral potential and the axion star enters the {\it dense} branch. Our numerical solutions show that in this latter regime the axions are relativistic, and that one should not use a single frequency approximation, as previously applied in the literature. We employ a multi-harmonic expansion to solve the relativistic equation for the axion field in the star, and demonstrate that higher modes cannot be neglected in the dense regime. We interpret the solutions in the dense regime as pseudo-breathers, and show that the life-time of such configurations is much smaller than any cosmological time scale.

Dilute and Dense Axion Stars: A Critical Overview

Axion stars, hypothetical compact objects composed of axions, represent intriguing structures within the landscape of particle astrophysics, as explored in this paper. The study delves into the field configurations of axion stars, differentiated between dilute and dense regimes, by examining their stability and dynamics. This paper thoroughly investigates the implications of axion self-interactions and gravity in forming axion stars, utilizing both analytical and numerical methods. The paper also challenges some assumptions frequently encountered in the literature on the subject, particularly regarding the dense regime.

Axion Star Configurations

Axion stars can exist in two distinct configurations, namely dilute and dense, based on the axion field amplitude at the star's core, denoted as $|\theta_0|$. The dilute regime occurs when the axion field explores only the harmonic part of its potential for small core amplitudes $|\theta_0| \lesssim 1$. In this regime, the star is maintained by a balance between the gradient pressure from the Heisenberg uncertainty principle and gravitational attraction. Conversely, in the dense regime for large amplitudes $|\theta_0| \gtrsim 1$, self-interactions take precedence and gravity becomes negligible, requiring a full consideration of the axion field's chiral potential.

Analytical and Numerical Insights

The paper first verifies the stability of dilute axion stars, where it aligns with established mass-radius relations and showcases the gravitational influence's dominance at small field values. It emphasizes how the gravitational pull along with the kinetic pressure governs the equilibrium structure of dilute axion stars. For critical axion stars—intermediate states between dilute and dense regimes—the study identifies them as unstable due to stronger quartic self-interactions overpowering gravitational effects.

In the dense regime, the paper critiques prior interpretations that employed a single-frequency approximation, revealing that a multi-harmonic approach is necessary. The authors utilize the Sine-Gordon model to reveal that dense axion stars exhibit oscillons—a phenomenon where dense configurations dissipate energy via relativistic axion emission rapidly compared to cosmological timescales.

Implications and Future Directions

This study has profound implications for understanding axion dark matter distribution in the universe. Dilute axion star configurations offer plausible, stable dark matter clumps, but dense axion stars exhibit a short-lived nature, thereby complicating their dark matter candidate status. The insights prompt reevaluation of dense axion star formation theories and suggest a need for further computational exploration of axion field dynamics in strong interaction potentials.

This research invites further inquiry into how dense axion stars may form from axion dark matter collapses and persist within cosmological frameworks. It hints at the necessity of novel approaches to incorporate multi-frequency dynamics into axion dark matter models, which could reshape our understanding of non-relativistic solutions in the dense regime. Overall, the paper opens up pathways for deeper theoretical inquiries and potential experimental searches related to axion stars and subsequently the broader axion dark matter realm.