Gas-induced Perturbations on the Gravitational Wave Inspiral of Live Post-Newtonian LISA Massive Black Hole Binaries

We investigate the effect of dynamically coupling gas torques with gravitational wave (GW) emission during the orbital evolution of an equal-mass massive black hole binary (MBHB). We perform hydrodynamical simulations of eccentric MBHBs with total mass M = 106 M circle dot embedded in a prograde locally isothermal circumbinary disk (CBD). We evolve the binary from 55 to 49 Schwarzschild radii separations using up to 2.5 post-Newtonian corrections to the binary dynamics, which allow us to follow the GW-driven inspiral. For the first time, we report the measurement of gas torques onto a live binary a few years before the merger, with and without concurrent GW radiation. We also report the gas-induced orbital dephasing delta phi orb similar to -0.007 rad over 278 orbital cycles that is likely driven mainly by disk-induced precession, and LISA should be able to detect it at redshift z = 1. Our results show how GWs alone can be used to probe the astrophysical properties of CBDs and have important implications for multimessenger strategies aimed at studying the environments of MBHBs.