Electromagnetic fields in compact binaries: post-Newtonian wave generation and application to double white dwarfs systems

TL;DR

This paper develops a formalism for gravitational wave generation in Einstein-Maxwell theory for compact sources, applying it to binary white dwarf systems with magnetic dipoles to compute energy fluxes, orbital evolution, and gravitational wave signals.

Contribution

It introduces a wave-generation formalism for Einstein-Maxwell systems and applies it to magnetic white dwarf binaries, including next-to-leading order flux calculations.

Findings

Derived orbital evolution for eccentric binaries.

Computed gravitational wave modes and phase for quasi-circular orbits.

Estimated magnetic dipole contributions for realistic white dwarf systems.

Abstract

The aim of this work is twofold: (i) to properly define a wave-generation formalism for compact-supported sources embedded in Einstein-Maxwell theory, relying on matched post-Newtonian and multipolar-post-Minkowskian expansions; (ii) to apply this formalism (which is valid for any type of post-Newtonian sources) to the case of two stars with constant and aligned magnetic dipoles, by computing the fluxes of energy and angular momentum to the next-to-leading order, as well as the gravitational amplitude modes. Assuming eccentric orbits, we derive the evolution of orbital parameters, as well as the observables of the system, notably the gravitational phase for quasi-circular orbits. Finally, we give some numerical estimates for the contribution of the magnetic dipoles for some realistic systems.