Upper limit on the axion-photon coupling from magnetic white dwarf polarization

Polarization measurements of thermal radiation from magnetic white dwarf (MWD) stars have been proposed as a probe of axion-photon mixing. The radiation leaving the surface of the MWD is unpolarized, but if low-mass axions exist then photons polarized parallel to the direction of the MWD's magnetic field may convert into axions, which induces a linear polarization dependent on the strength of the axion-photon coupling $g_{a\gamma\gamma}$. We model this process by using the formalism of axion-photon mixing in the presence of strong-field vacuum birefringence to show that of all stellar types MWDs are the most promising targets for axion-induced polarization searches. We then consider linear polarization data from multiple MWDs, including SDSS J135141 and Grw+70$^\circ$8247, to show that after rigorously accounting for astrophysical uncertainties the axion-photon coupling is constrained to $|g_{a\gamma\gamma}| \lesssim 5.4 \times 10^{-12}$ GeV$^{-1}$ at 95% confidence for axion masses $m_a \lesssim 3 \times 10^{-7}$ eV. This upper limit puts in tension the previously-suggested explanation of the anomalous transparency of the Universe to TeV gamma-rays in terms of axions. We identify MWD targets for which future data and modeling efforts could further improve the sensitivity to axions.