A dead star with a magnetic field billions of times stronger than Earth's is a magnetar. Its crust cracks, sending a powerful X-ray burst into space. But some of that light doesn't reach us in its usual form. In an ultra-strong field, photons can turn into gravitational waves — the trembling of space itself.

The authors recalculated this process using Stokes parameters — four numbers describing a wave's polarization. They showed that the usual simplification (slowly changing field) doesn't always hold. For two specific field geometries where the simplification is justified, they obtained analytical estimates. The birth of gravitational waves from a magnetar's own light turns out to be negligible, such a contribution to the cosmic hum would be impossible to detect.

Far more interesting is the reverse process: background gravitational waves, passing through the magnetosphere, convert into X-ray emission. Comparing the calculated extra brightness with the actual luminosity of magnetars, the researchers set an upper limit on the high-frequency background. This is an important step: the frequency range above what ordinary cosmic sources produce remains largely unexplored.