Multimessenger window into galactic magnetic fields and black-hole mergers with LISA

Large-scale (i.e., $\ensuremath{\gtrsim}\mathrm{kpc}$) and micro-Gauss-scale magnetic fields have been observed throughout the Milky Way and nearby galaxies. These fields depend on the geometry and matter-energy composition, can display complicated behavior such as direction reversals, and are intimately related to the evolution of the source galaxy. Simultaneously, gravitational-wave astronomy offers a new probe into astrophysical systems; for example, the Laser Interferometer Space Antenna (LISA) will observe the mergers of massive (i.e., $M>{10}^{6}{M}_{\ensuremath{\bigodot}}$) black-hole binaries and provide extraordinary constraints on the evolution of their galactic hosts. In this work, we show how galactic, large-scale magnetic fields and their electromagnetic signatures are connected with LISA gravitational-wave observations via their common dependence on the massive black-hole binary formation scenario of hierarchical galaxy mergers. Combining existing codes, we astrophysically evolve a population of massive binaries from formation to merger and find that they are detectable by LISA with signal-to-noise ratio $\ensuremath{\sim}{10}^{3}$ which is correlated with quantities from the progenitors' phase of circumbinary disk migration such as the maximum magnetic field magnitude $|\mathbf{B}|\ensuremath{\approx}7\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{G}$, polarized intensity, and Faraday rotation measure. Interesting correlations result between these observables arising from their dependencies on the black-hole binary total mass, suggesting a need for further analyses of the full parameter space. We conclude with a discussion on this new multimessenger window into galactic magnetic fields.