Effects of dark dipole radiation on eccentric supermassive black hole binary inspirals

The final-parsec problem has long posed a central challenge in understanding the merger of supermassive black hole binaries. In this paper, we investigate a scenario in which a dark scalar or vector field is sourced by eccentric binaries, leading to accelerated mergers through additional dipole radiation, and thereby extending the range of masses for which the binary can merge within a Hubble time. The Newtonian-order radiation fluxes from an eccentric charged Keplerian binary are derived using general results for localized periodic sources in flat spacetime. We find that dipole radiation, although insufficient to fully resolve the final-parsec problem, can alter the low-frequency spectrum of the stochastic gravitational-wave background from supermassive black hole binary inspirals. We construct a simplified model for the spectrum and perform a Bayesian analysis using the current pulsar timing array data.