Distinct photon-ALP propagation modes

Measurement of cosmic photons may reveal their propagation in the interstellar environment, thereby offering a promising way to probe axions and axion-like particles (ALPs). Numerical methods are usually used to compute the propagation of the photon-ALP beam due to the complexity of both the interstellar magnetic field and the evolution equation. However, under certain conditions, the evolution equation can be greatly simplified so that the photon-ALP propagation can be analytically solved. By using analytic methods, we find two distinct photon-ALP propagation modes, determined by the relative magnitude of the photon-ALP mixing term in comparison to the photon attenuation term. In one mode, the intensity of photons decreases with the increasing distance; in the other mode, it also exhibits oscillatory behavior. To distinguish the two propagation modes, we compute the observable quantities such as the photon survival probability and the degree of polarization. We also determine through analytic methods the conditions under which maximum polarization can be observed and the corresponding upper bound of the survival probability.