  Axions are one of the most promising candidates of dark matter. The axions
have been shown to form miniclusters with masses $\sim 10^{-12}M_{\odot}$ and
to become dominant component of dark matter. Some of the axion miniclusters
condense to form axion stars. We have recently shown a possible origin of fast
radio bursts ( FRBs ) by assuming that the axion stars are main component of
halos: FRBs arise from the collisions between the axion stars and neutron
stars. It is remarkable that the masses of the axion stars obtained by the
comparison of the theoretical and observational event rates are coincident with
the mass $\sim 10^{-12}M_{\odot}$. In this paper, we describe our model of FRBs
in detail. We derive the approximate solutions of the axion stars with large
radii and constraint their masses for the approximation to be valid. The FRBs
are emitted by electrons in atmospheres of neutron stars. By calculating the
optical depth of the atmospheres, we show that they are transparent for the
radiations with the frequency given by the axion mass $m_a$ such as
$m_a/2\pi\simeq 2.4$GHz$(m_a/10^{-5}\rm eV)$. Although the radiations are
linearly polarized when they are emitted, they are shown to be circularly
polarized after they pass magnetospheres of neutron stars. We also show that
the FRBs are not broadband and their frequencies have finite bandwidths owing
to the thermal fluctuations of the electrons in the atmospheres of the neutron
stars. The presence of the finite bandwidths is a distinctive feature of our
model and can be tested observationally. Furthermore, we show that similar FRBs
may arise when the axion stars collide with magnetic white dwarfs $B\sim
10^9$G. The distinctive feature is that the durations of the bursts are of the
order of $0.1$second.
