  Compact objects such as neutron stars and white dwarfs can source axion-like
particles and QCD axions due to CP-violating axion-fermion couplings. The
magnitude of the axion field depends on the stellar density and on the strength
of the axion-fermion couplings. We show that even CP-violating couplings one
order of magnitude smaller than existing constraints source extended axion
field configurations. For axion-like particles, the axion energy is comparable
to the magnetic energy in neutron stars with inferred magnetic fields of the
order of $10^{13}$ G, and exceeds by more than one order of magnitude the
magnetic energy content of white dwarfs with inferred fields of the order of
$10^{4}$ G. On the other hand, the energy stored in the QCD axion field is
orders of magnitude lower due to the smallness of the predicted CP-violating
couplings. It is shown that the sourced axion field can polarize the photons
emitted from the stellar surface, and stimulate the production of photons with
energies in the radio band.
