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 sixth term in the axion potential expansion. We found that axion stars would have masses of the order of asteroids and radius of the order of few centimeters.
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