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.Comment: 11 pages, 4 figures. v2: added references, matches published versio

Moduli stars

“…In this section we will show that the same solutions already obtained in [19,48,49,51,52,54] imply that string moduli potentials support star-like solutions in the dilute regime. We will explore the properties and possible phenomenological features of these objects.…”

“…ϕ n (with n ≥ 3) of the field are negligible. The system can be studied in the weak gravity approximation, in which case the metric components can be assumed to be static and can be expanded as A 2 (r) ∼ 1 + 2 φ(r) and B 2 (r) ∼ 1 − 2 φ(r) where φ(r) is the Newtonian potential [49,54]. The equations of motion are then the Klein-Gordon equation for a massive real scalar field in the weak gravity regime coupled to the Poisson equation for φ(r).…”

“…Oscillatons include the important case in which the real scalar is an axion-like particle giving rise to axion stars (see [54] and references therein for the state of the art). The Lagrangian is…”

“…1, called the critical regime [54]. In the critical regime the amplitude of the background field is still small but large enough such that the leading order selfinteraction is stronger than gravity and balance the kinetic pressure from the uncertainty principle.…”

“…Following [54], after using the ansatz in eq. (3.10) it is easier to solve the system by taking an average of the previous equations integrating over a period 2π/ω.…”