QED effects are negligible for neutron-star spin-down

Abstract

The energy loss of a rotationally powered pulsar is primarily carried away as electromagnetic radiation and a particle wind. Considering that the magnetic field strength of pulsars ranges from about $10^8$ to $10^{15}$ G, one could expect quantum electrodynamics (QED) to play a role in their spin-down, especially for strongly magnetized ones (magnetars). In fact several authors have argued that QED corrections will dominate the spin-down for slowly rotating stars. They called this effect quantum vacuum friction (QVF). However, QVF was originally derived using a problematic self-torque technique, which leads to a dramatic overestimation of this spin-down effect. Here, instead of using QVF, we explicitly calculate the energy loss from rotating neutron stars using the Poynting vector and a model for a particle wind, and we include the QED one-loop corrections. We express the excess emission as QED one-loop corrections to the radiative magnetic moment of a neutron star. We do find a small component of the spin-down luminosity that originates from the vacuum polarization. However, it never exceeds one percent of the classical magnetic dipole radiation in neutron stars for all physically interesting field strengths. Therefore, we find that the radiative corrections of QED are irrelevant in the energetics of neutron-star spin-down.