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 δ = (f a / M P ) 2 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 satisfies1, where E a and m a are the energy and mass of the axion. The simultaneous expansion of the equations of motion in δ and ∆ leads to a simplified set of equations, depending only on the parameter, λ = √ δ / ∆ in leading order of the expansions. Keeping leading order in ∆ 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 λ. Numerical solutions are found in a wide range of λ. At small λ the mass and radius of the axion star rise linearly with λ. While at larger λ the radius of the star continues to rise, the mass of the star, M , attains a maximum at λ max 0.58. All stars are unstable for λ > λ max . We discuss the relationship of our results to current observational constraints on dark matter and the phenomenology of Fast Radio Bursts.

Collapse of axion stars

“…(2.7) as a function of the condensate size, in order to estimate the positions of any energy minima. Using the result of [24], we know how the macroscopic parameters of a weakly bound axion star, the radius R and the axion number N , scale with the dimensionful parameters of the theory; we thus define the dimensionless quantities ρ and n by…”

“…It has been pointed out that there exists a maximum particle number N = N c above which no stable energy minimum exists. This critical value corresponds to a radius of R 99 ∼ 500 km for QCD axions [24], and is approximated to the correct order of magnitude by the Gaussian ansatz, which gives a radius R 99 ∼ 200 km. In our notation, this critical particle number occurs at n c = 2π √ 3 and at a radius ρ * = 3/32π, for the Gaussian ansatz.…”

“…We thus submit that when considering dense configurations of axions or collapse of axion stars, it is important to truncate the series on a repulsive term to preserve the global minimum. The leading-order interaction term is contained in e 0 (ρ), and has been considered in great detail previously [24][25][26]29]. It has been pointed out that there exists a maximum particle number N = N c above which no stable energy minimum exists.…”

“…The leading-order expansion in ∆ 1 is equivalent to the infrared limit of the theory, where only the marginal φ 4 term appears in the interaction potential [24]. For weakly bound stars, the leading process A N → A N −3 + a p has a rate which, as a function of ∆, is dominated by an exponential factor,…”

“…The masses of weakly bound axion stars have been computed previously [23,24], and they are bounded above by gravitational stability [24][25][26]. Axion stars which exceed this maximum mass M c have a fate which remains an open question.…”