  It is a well-known fact that compact gravitating objects admit bound state
configurations for massive bosonic fields. In this work we describe a new class
of superradiant instabilities of axion bound states in neutron star
magnetospheres. The instability arises from the mixing of axion and photon
modes in the magnetic field of the neutron star which extract energy from the
rotating magnetosphere. Unlike for black holes, where the dissipation required
for superradiance is provided by an absorbative horizon, the non-hermitian
dynamics in this paper come from the resistivity in the stellar magnetosphere
arising from a finite bulk conductivity. The axion field mixes with photon
modes which superradiantly scatter off the magnetosphere, extracting rotational
energy which is then deposited back into the axion sector leading to an
instability. We derive the superradiant eigenfrequencies for the axion-photon
system using quantum mechanical perturbation theory on the axion boundstate,
drawing an analogy with atomic selection rules. We then compare the
characteristic time scale of the instability to the spin-down measurements of
pulsars which limit the allowed rate of angular momentum extraction from
neutron stars.
