  Dark matter may consist of axion-like particles (ALPs). When polarized
electromagnetic radiation passes through the dark-matter media, interaction
with background ALPs affects the polarization of photons. The condensate of
axionic dark matter experiences periodic oscillations, and the period of the
oscillations is of order of years for ultra-light dark matter. This would
result in observable periodic changes in the polarization plane, determined by
the phases of the ALP field at the Earth and at the source. In this paper, we
use recent polarimetric observations of the HL Tauri protoplanetary disk
performed in different years to demonstrate the lack of changes of polarization
angles, and hence to constrain masses and photon couplings of the hypothetical
axion-like ultralight dark matter.
