Core Scouring Dynamics and Gravitational Wave Consequences: Constraints on Supermassive Black Hole Binary Hardening

Abstract We present a multimessenger investigation of supermassive black hole binary (SBHB) hardening by jointly comparing models to the observed stellar mass deficits of nearby core galaxies and to nanohertz gravitational-wave background measurements. Using merger trees from the IllustrisTNG cosmological simulations, we construct a synthetic population of core galaxies and predict their stellar mass deficits under binary evolution driven by dynamical friction, stellar scattering, and gravitational-wave emission, assuming circular orbits. We calibrate the efficiency of stellar scattering by matching the observed relation between stellar mass deficit and galaxy stellar mass. The inferred hardening rates reproduce the observed core population when stellar scattering is more efficient than in our baseline prescription, consistent with additional environmental or dynamical effects. However, these rates do not produce the level of low-frequency attenuation required to match the apparent turnover in the nanohertz gravitational-wave background. This tension suggests that either additional physics—such as eccentricity evolution, gas dynamics, recoils, triple interactions, or changes in the black hole–galaxy scaling relation—or contributions from galaxy populations not represented by local core galaxies (e.g., massive power-law ellipticals) may be important. A comprehensive treatment of these effects is required before identifying the dominant mechanisms shaping the gravitational-wave spectrum.