Photon-Axion Conversion, Magnetic Field Configuration, and Polarization
  of Photons
  We study the evolution of photon polarization during the photon-axion
conversion process with focusing on the magnetic field configuration
dependence. Most previous studies have been carried out in a conventional model
where a network of magnetic domains is considered and each domain has a
constant magnetic field. We investigate a more general model where a network of
domains is still assumed, but each domain has a helical magnetic field. We find
that the asymptotic behavior does not depend on the configuration of magnetic
fields. Remarkably, we analytically obtain the asymptotic values of the
variance of polarization in the conventional model. When the helicity is small,
we show that there appears the damped oscillating behavior in the early stage
of evolution. Moreover, we see that the constraints on the axion coupling and
the cosmological magnetic fields using polarization observations are affected
by the magnetic field configuration. This is because the different transient
behavior of polarization dynamics is caused by the different magnetic field
configuration. Recently, [C. Wang and D. Lai, J. Cosmol. Astropart. Phys. 06
(2016) 006.] claimed that the photon-axion conversion in helical model behaves
peculiarly. However, our helical model gives much closer predictions to the
conventional discontinuous magnetic field configuration model.
