Can the dark matter halo be a collisionless ensemble of axion stars?

If dark matter is mainly composed of axions, the density distribution can be nonuniformly distributed, being clumpy instead. By solving the Einstein-Klein-Gordon system of a scalar field with the potential energy density of an axionlike particle, we obtain the maximum mass of the self-gravitating system made of axions, called axion stars. The collision of axion stars with neutron stars may release the energy of axions due to the conversion of axions into photons in the presence of the neutron stars magnetic field. We estimate the energy release and show that it should be much less than previous estimates.Future data from femtolensing should strongly constrain this scenario.