Electromagnetic fields in compact binaries: A post-Newtonian approach

Galactic binaries, and notably double white dwarfs systems, will be a prominent source for the future LISA and Einstein Telescope detectors. Contrary to the black holes observed by the current LIGO-Virgo-KAGRA network, such objects bear intense magnetic fields that are naturally expected to leave some imprints on the gravitational wave emission. The purpose of this work is thus to study those imprints within the post-Newtonian (PN) framework, particularly adapted to double white dwarfs systems. To this end, we construct an effective action that takes into account the whole electromagnetic structure of a star, and then specify it to dipolar order. With this action at hand, we compute the acceleration and Noetherian quantities for generic electric and magnetic dipoles, at a relative 2PN order. Finally, focusing on physically relevant systems, we show that the magnetic effects on the orbital frequency, energy, and angular momentum is significant, confirming the conclusions of previous works.