Axion stars in the infrared limit

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) << 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 = root 1 - (E-a / m(a))(2) << 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 = root 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) similar or equal to 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.