A Magnetic Unification of Merging Supermassive Black Hole Binaries

The detection of an electromagnetic (EM) transient from a supermassive black hole binary (SMBHB) merging within a gaseous environment will constitute a multi-messenger milestone. Numerical simulations of these systems have mostly been performed in 2D with a constant viscosity parameter representing turbulent and magnetic stresses. These simulations predict a steep drop in accretion rate and X-ray luminosity at merger, followed by a slow recovery. However, 3D-GRMHD and 3D-MHD simulations have shown only a modest reduction in accretion rate and a fast post-merger recovery. We present a new 2D pseudo-Newtonian framework with physically motivated prescriptions for stochastic viscosity, relativistic apsidal precession, and large-scale magnetic fields. When suitably calibrated, this 2D framework accurately captures key 3D-GRMHD behavior, demonstrating that it can be used to explore binary accretion without the high computational cost of 3D-GRMHD simulations. We find that the merger signatures are most sensitive to the strength of the magnetic field, with a drop in the accretion rate at merger progressively less pronounced for stronger fields. Post-merger evolution is determined by both magnetization and relativistic precession of orbiting gas, yielding rapid recovery of accretion. For low-magnetization disks, recovery is driven by self-intersection shocks, and the dip at merger is followed by a distinct second dimming. Large-scale magnetic fields of increasing magnitude lead to magnetically arrested disk (MAD) behavior which disturbs the merging system progressively earlier before merger, and longer after. Our results unify the EM signatures of the merger of embedded coplanar SMBHBs, and provide novel observational constraints on their intrinsic magnetization.