Constraining the axion-photon coupling using radio data of the Bullet
  Cluster
  Axion is one of the most popular candidates of the cosmological dark matter.
Recent studies considering the misalignment production of axions suggest some
benchmark axion mass ranges near $m_a \sim 20$ $\mu$eV. For such axion mass,
the spontaneous decay of axions can give photons in radio band frequency $\nu
\sim 1-3$ GHz, which can be detected by radio telescopes. In this article, we
show that using radio data of galaxy clusters would be excellent to constrain
axion dark matter. Specifically, by using radio data of the Bullet cluster (1E
0657-55.8), we find that the upper limit of the axion-photon coupling constant
can be constrained to $g_{a \gamma \gamma} \sim 10^{-12}-10^{-11}$ GeV$^{-1}$
for $m_a \sim 20$ $\mu$eV, which is tighter than the limit obtained by the CERN
Axion Solar Telescope (CAST).
