  Axion stars could form binaries with neutron stars. Given the extremely
strong external magnetic field exhibited by individual neutron stars, there can
be a substantial conversion of axions to photons in these binaries. The photon
emission is doubly modulated due to the neutron star spinning and the axion
star orbiting, yielding a unique discovery signal. Similar features are also
generated in binaries between a neutron star and an axion-clouded black hole.
Encouragingly, such binaries are found to be within the reach of ongoing and
upcoming experiments (e.g., the Five hundred meter Aperture Spherical Telescope
and the future Square Kilometer Array) for certain parameter regions. They thus
provide a promising astronomical laboratory for detecting axions and axion dark
matter.
