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 |θ0|≡|θ(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 |θ0|. For small |θ0|≲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 |θ0|≳1, the axion field probes the full non-harmonic QCD chiral potential and the axion star enters the 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.
Highlights
The QCD axion [1,2,3,4,5,6,7,8,9] arising within the Peccei–Quinn solution of the strong CP-problem [10,11] is one of the best motivated dark matter candidates
We study the stability of axion stars as a function of the amplitude of the axion field at the core of the star |θ0| ≡ |θ (r = 0)|
Kolb and Tkachev [26] discovered the so called “axitons” when studying the cosmological evolution of the axion field in the dark matter context. They followed the evolution of the Sine–Gordon equation in an expanding Universe in which the axion mass strongly depends on the cosmic time, and identified an instability condition that leads to small clumps of the axion field with large values θ ∼ π to disappear in bursts of relativistic axions
Summary
The QCD axion [1,2,3,4,5,6,7,8,9] arising within the Peccei–Quinn solution of the strong CP-problem [10,11] is one of the best motivated dark matter candidates. For small field values |θ0| 10−6 10−5 eV/m with m the axion mass, the axion field only probes the harmonic part of the potential, and it can be treated as a free field In this regime, self-gravity is balanced by the kinetic pressure arising from the uncertainty principle. For amplitudes |θ0| 10−6(10−5 eV/m), the attractive quartic selfinteraction is stronger than gravity, which is negligible in this regime In this critical branch, we find solutions when the quartic self-interaction balance the kinetic pressure with mass-radius relation R ∝ M. If configurations are perturbed to radii smaller than the equilibrium value, the quartic interaction is too strong to be balanced by the pressure and the star collapses to even higher densities It has recently been pointed out, that new stable configurations, called dense axion stars, are obtained when the amplitude of the axion field in the core reaches |θ0| = O(1) [27].
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