Towards a realistic axion star

In this work we estimate the radius and the mass of a self-gravitating system made of axions. The quantum axion field satisfies the Klein-Gordon equation in a curved space-time and the metric components of this space-time are solutions to the Einstein equations with a source term given by the vacuum expectation value of the energy-momentum operator constructed from the axion field. As a first step towards an axion star we consider the up to the φ6 term in the axion potential expansion. We found that axion stars would have masses of the order of asteroids (∼ 10−10M⊙) and radius of the order ∼ few centimeters. 1. Boson stars Boson stars (BS) are gravitationally bounded systems made of scalar particles. They were introduced for the very first time in 1968 by Kaup and later by Ruffini and Bonazzola [1]. The inclusion of a self-interacting term was done in [2] and the stability under general perturbations was studied in [3]. BS are fully characterized by the scalar field properties, i.e. the mass m of the scalar field and its potential V (φ) = m2φ 2 + λφ 4/2, where λ is the self-interaction parameter. BS rise as solutions of the EinsteinKlein-Gordon equations Gμν = 8πG < Tμν >, (