  If dark matter is composed of axions, then axion stars form in the cores of
dark matter halos. These stars are unstable above a critical mass, decaying to
radio photons that heat the intergalactic medium, offering a new channel for
axion indirect detection. We recently provided the first accurate calculation
of the axion decay rate due to axion star mergers. In this work we show how
existing data concerning the CMB optical depth leads to strong constraints on
the axion photon coupling in the mass range $10^{-14}\,{\rm eV}\lesssim
m_a\lesssim 10^{-8}\,{\rm eV}$. Axion star decays lead to efficient
reionization of the intergalactic medium during the dark ages. By comparing
this non-standard reionization with Planck legacy measurements of the Thompson
optical width, we show that couplings in the range $10^{-14}\,{\rm GeV}^{-1}
\lesssim g_{a\gamma\gamma} \lesssim 10^{-10}\,{\rm GeV}^{-1}$ are excluded for
our benchmark model of axion star abundance. Future measurements of the 21cm
emission of neutral hydrogen at high redshift could improve this limit by an
order of magnitude or more, providing complementary indirect constraints on
axion dark matter in parameter space also targeted by direct detection
haloscopes.
