Gas pile-up, gap overflow and Type 1.5 migration in circumbinary discs: Application to supermassive black hole binaries

We study the interaction of a supermassive black hole (SMBH) binary and a standard radiatively efficient thin accretion disk. We examine steady-state configurations of the disk and migrating SMBH system, self-consistently accounting for tidal and viscous torques and heating, radiative diffusion limited cooling, gas and radiation pressure, and the decay of the binary's orbit. We obtain a "phase diagram" of the system as a function of binary parameters, showing regimes in which both the disk structure and migration have a different character. Although massive binaries can create a central gap in the disk at large radii, the tidal barrier of the secondary causes a significant pile-up of gas outside of its orbit, which can lead to the closing of the gap. We find that this spillover occurs at an orbital separation as large as ~200 M_7^{-1/2} gravitational radii, where M = 10^7 M_7 Msun is the total binary mass. If the secondary is less massive than ~10^6 Msun, then the gap is closed before gravitational waves (GWs) start dominating the orbital decay. In this regime, the disk is still strongly perturbed, but the piled-up gas continuously overflows as in a porous dam, and crosses inside the secondary's orbit. The corresponding migration rate, which we label Type 1.5, is slower than the usual limiting cases known as Type I and II migration. Compared to an unperturbed disk, the steady-state disk in the overflowing regime is up to several hundred times brighter in the optical bands. Surveys such as PanSTARRS or LSST may discover the periodic variability of this population of binaries. Our results imply that the circumbinary disks around SMBHs can extend to small radii during the last stages of their merger, when they are detectable by LISA, and may produce coincident electromagnetic (EM) emission similar to active galactic nuclei (AGN).