Electromagnetic fields in compact binaries: a post-Newtonian approach

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.

arXiv comment23 pages, no figure, supplementary material attached. v2: references and acknowledgments updated. v3: post-referee version (Eq. (3.3b) and typos corrected, discussions added)

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• Generalized Perturbed Kepler Problem: Gravitational Wave Imprints from Eccentric Compact Binaries
• Post-Newtonian Dynamics of Radiating Charges: Canonical Formulation and Binary Inspiral Laws
• Graviton Photoproduction by a Kerr-Newman Black Hole with Worldline EFT
• Hamiltonian normal forms for the post-Newtonian binary problem