  The recently measured 3.5 keV line in a number of galaxy clusters, the
Andromeda galaxy (M31) and the Milky Way (MW) center can be well accounted for
by a scenario in which dark matter decays to axion-like particles (ALPs) and
subsequently convert to 3.5 keV photons in magnetic fields of galaxy clusters
or galaxies. We propose to test this hypothesis by performing X-ray
polarization measurements. Since ALPs can only couple to photons with
polarization orientation parallel to magnetic field, we can confirm or reject
this model by measuring the polarization of 3.5 keV line and comparing it to
the orientation of magnetic field. We discuss luminosity and polarization
measurements for both galaxy cluster and spiral galaxy, and provide a general
relation between polarization and galaxy inclination angle. This effect is
marginally detectable with X-ray polarimetry detectors currently under
development, such as the enhanced X-ray Timing and Polarization (eXTP), the
Imaging X-ray Polarimetry Explorer (IXPE) and the X-ray Imaging Polarimetry
Explorer (XIPE). The sensitivity can be further improved in the future with
detectors of larger effective area or better energy resolutions.
