  In certain models of a QCD axion, finite density corrections to the axion
potential can result in the axion being sourced by large dense objects. There
are a variety of ways to test this phenomenon, but perhaps the most surprising
effect is that the axion can mediate forces between neutron stars that can be
as strong as gravity. These forces can be attractive or repulsive and their
presence can be detected by Advanced LIGO observations of neutron star
inspirals. By a numerical coincidence, axion forces between neutron stars with
gravitational strength naturally have an associated length scale of tens of
kilometers or longer, similar to that of a neutron star. Future observations of
neutron star mergers in Advanced LIGO can probe many orders of magnitude of
axion parameter space. Because the axion is only sourced by large dense
objects, the axion force evades fifth force constraints. We also outline
several other ways to probe this phenomenon using electromagnetic signals
associated with compact objects.
