Emission signatures from sub-parsec post-Newtonian binaries embedded in circumbinary discs

We studied the dynamical evolution of quasi-circular, equal-mass massive black hole binaries embedded in circumbinary discs from separations of ∼100 Rg down to the merger, following the post merger evolution. The binary orbit evolves owing to the presence of the gaseous disc and the addition of post-Newtonian (PN) corrections up to the 2.5 PN order, therefore including the dissipative gravitational wave back reaction. We investigated two cases of relatively cold and warm circumbinary discs, with aspect ratios of H/R = 0.03, 0.1, respectively, employing 3D hyper-Lagrangian resolution simulations with the GIZMO-MFM code. We extracted spectral energy distributions and light curves in different frequency bands (i.e. X-ray, optical, and UV) from the simulations. We find a clear two orders of magnitude drop in the X-ray flux right before merger if the disc is warm, while we identify a significant increase in the UV flux regardless of the disc temperature. The optical flux shows clear distinctive modulations on the binary orbital period and on the cavity edge period, regardless of the disc temperature. We find that the presence of a cold disc can accelerate the coalescence of the binary by up to 130 s over the last five days of inspiral, implying a phase shift accumulation of about 0.14 radians compared to the binary evolution in vacuum. These differences are triggered by the presence of the gaseous disc and might have implications on the waveforms that can be detected in principle. We discuss the implications that these distinctive signatures might have for existing and upcoming time domain surveys and for multi-messenger astronomy.