Radiations from Oscillating Axionic Boson Stars in an External Magnetic Field

We solve numerically a field equation of axions coupled with gravity and show solutions representing oscillating axionic boson stars with small mass $\sim 10^{-12}M_{\odot}$ and large radius $\sim 10^{8}$ cm. We present explicitly a relation between the mass and the radius of the boson stars with such a small mass. These axionic boson stars are shown to possess oscillating electric currents in an external magnetic field and to radiate electromagnetic fields with a frequency given by mass of the axions. We estimate the luminosity of the radiation in a strong magnetic field $10^{12}$G of neutron stars, typically $\sim 10^{24}$ erg/s with the axion mass being $10^{-5}$eV.