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Abstract

Galactic binaries, and notably double white dwarfs systems, will be a
prominent source for the future LISA and Einstein Telescope detectors.
Contrarily 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 previous works
conclusions.