  White dwarf (WD) stars may radiate keV-energy axions produced in their
stellar cores. This has been extensively studied as an extra channel by which
WDs may cool, with some analyses even suggesting that axions can help explain
the observed WD luminosity function. We show that the radiated axions may
convert into X-rays in the strong magnetic fields surrounding the WDs, leading
to observable X-ray signatures. We use Suzaku observations of the WD RE
J0317-853 to set the strongest constraints to date on the combination of the
axion-electron ($g_{aee}$) times axion-photon ($g_{a\gamma\gamma}$) couplings,
and we show that dedicated observations of magnetic WDs by telescopes such as
Chandra, XMM-Newton, and NuSTAR could increase the sensitivity to $|g_{aee}
g_{a\gamma\gamma}|$ by over an order of magnitude, allowing for a definitive
test of the axion-like-particle explanation of the stellar cooling anomalies.
