ON THE RELAXATION OF SUPERSTRING AXIONS

The theoretical existence of oscillating boson stars consisting of a real scalar field, stable to radial perturbations, has been proven by Seidel and Suen. For the QCD axion of the heterotic superstring theory, this implies a mini-star of mass , where λ≡ f_a′/f_a is the ratio of the decay constants of the second and model-independent axions, which, for a suitable value in the range 1≲λ≲10, can explain the astronomical microlensing observations towards the Galactic centre and the Large and Small Magellanic Clouds. Here, we apply the non-linear relaxation theory developed by Tkachev to show that the condition τ_f<τ_r<τ₀ for the formation of such an object, where τ_f, τ_r and τ₀ are the free-fall and relaxation times and the age of the Universe, respectively, leads to the condition , where is the strong-interaction coupling parameter and C is a dimensionless constant defined below. From this, we argue, considering the approximations involved, that the star does condense.