---
author:
- 'Jean-François Fortin$^{\ast,}$ and Kuver Sinha$^{\dagger,}$'
bibliography:
- 'Stokes.bib'
date: July 2018
title: |
    X-Ray Polarization Signals from Magnetars\
    with Axion-Like-Particles
---

Introduction {#SIntro}
============

X-ray polarimetry is a nascent field that can explore different astrophysical sources, ranging from compact objects to pulsar wind nebulas, supernova remnants, and molecular clouds. For a recent review of the astrophysical processes that can lead to polarized X-rays, as well as a description of current and planned missions, we refer to [@fabiani].

The emission from compact objects, which are the focus of this article, can exhibit polarization due to the different opacities of the surface plasma to different components of the photon electric field. However, polarization of X-ray radiation from neutron stars can also arise due to fundamental physics whose origin is distinct from astrophysics, and it is this possibility that we will entertain in our work. It is worthwhile to remember that polarization experiments probe physical anisotropies, and there is an important anisotropy in the photon Lagrangian if axion-like-particles (ALPs) [@Peccei:1977hh; @Peccei:1977ur; @Wilczek:1977pj; @Weinberg:1977ma] exist. Namely, ALPs mix only with the parallel and not the perpendicular component of the electric field in the presence of an external magnetic field. This anisotropy 