Axion sourcing in dense stellar matter via $CP$-violating couplings

Compact objects such as neutron stars and white dwarfs can source axionlike 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 axionlike 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.