Observable signature of magnetic tidal coupling in hierarchical triple systems

Abstract

We study hierarchical triple systems formed by a compact binary orbiting a supermassive black hole (SMBH), focusing on the role of relativistic magnetic tidal interactions. Extending previous analyses of precession resonances to 0.5 post-Newtonian order, we incorporate quadrupolar magnetic tidal moments, which have no Newtonian counterpart. We find that magnetic tides introduce new resonances absent at lower order, leading to additional eccentricity excitations and significantly modifying the binary's long-term evolution. Numerical solutions of the Lagrange Planetary Equations confirm these analytical predictions and reveal how resonance strength depends on orbital eccentricity and inclination. The resulting dynamics accelerates the binary merger and imprints distinctive signatures on gravitational waves, potentially observable by LISA. Our findings identify magnetic tidal coupling as a novel strong-gravity effect and establish its importance for the resonant dynamics of compact-object binaries near SMBHs.