Axion Stars and Repeating Fast Radio Bursts with Finite Bandwidths

We have proposed a model of non repeating fast radio bursts ( FRBs ); the collisions between axion stars and neutron stars generate the bursts. In this paper, we propose a model of repeating FRBs which shows that they arise from the several collisions between magnetized accretion disk of a black hole and an axion star orbiting the black hole. There would be many axions stars condensing as dark matter in an early stage galaxy so that such collisions arises repeatedly. The radiations are emitted by coherent oscillations of electrons in the accretion disk. The oscillations are caused by oscillating electric fields, which are induced by axion stars under strong magnetic field $\sim O(10^{11})$G. The emissions are terminated by the thermal fluctuations of the electrons which result from the thermalization of the oscillation energies. Although the radiations are monochromatic, the thermal Doppler effects broaden the spectral lines; their spectra $S(\nu)$ are given by $S(\nu) \propto \exp(-(\nu-\nu_c)^2/2(\delta\nu)^2)$ with the center frequency $\nu_c$. The bandwidth $\delta\nu=\nu_c\sqrt{T_c/m_e}$ with electron mass $m_e$ is determined by the critical temperature $T_c$ at which the thermal fluctuations terminate the coherent emissions. The observed bandwidths $(3\sim5)\times10^2$MHz are originated from the strong magnetic fields $\sim O(10^{11})$G. With such strong magnetic fields, large amount of the burst energies are produced. Various center frequencies $\nu_c$ of the bursts in the repeating FRB 121102 come from the various rotation speeds in the disk which make an intrinsic frequency of the bursts being Doppler shifted. The recent observation showing an extreme magneto-ionic environment around the source of FRB 121102 supports our model.