Rotation of the polarization plane in axion fields: application to neutron star polar cap regions

Abstract

Recent investigations by Noordhuis et al. [1, 2] and others have demonstrated the occurrence of strong local inhomogeneous axion regions in the polar cap regions of neutron stars. These regions are characterized by static magnetic fields $B_0 \sim 10^8\,$T ($=10^{12}\,$G) directed normally outwards from the polar surface (magnetic dipole), together with static electric fields $E_0 \sim 10^{-6}cB_0$ in the same direction (electric dipole). An enormous increase of axion production, up to order $10^{50}$, is predicted in the polar regions. These features are important for phenomena such as polarization plane rotation under both weak and strong axion field populations. We survey the peculiar antenna property of conductive materials, which shows the need for having very strong magnetic fields to make the detection possible. We present the general form of electromagnetic waves in the axion environment, in both the standard form and in a physically instructive hybrid one, showing the nonreciprocity of axion fluid, and calculate the polarization rotation. The rotation is well defined in the case of weak, but still stronger than average value of axion fields in Universe. For very strong fields such a perturbative theory breaks down, however. A noteworthy general property of the rotation of polarization plane is that it can only occur when the axion cloud is varying in space or time. We limit ourselves only variation in space. Finally, as application we discuss the physical picture of local 'gap' regions proposed by Noordhuis et al. in the polar regions of a neutron star. The reason for occurrence of these gaps is plasma effects. To evaluate the time scales involved, we calculate the filling time for surrounding axions flowing into an initial gap. It turns out that the typical filling time is a moderate number of nanoseconds, within the accuracy of atomic clocks precision to be detectable.