Mass flow in the circumbinary disk with gap around supermassive binary black holes

In this paper, we study the interaction between the supermassive binary black holes in elliptical orbit and their surrounding disk with a gap. The gap in the disk is a low density region formed due to the tidal effects of the less massive black hole. The binary we have investigated has a sub-parsec separation and is coplanar with the disk. We find that the maximum variation of the surface density in the gap reaches 50% during an orbital period. However, in other regions of the disk, the density variation is much less than 1%. Furthermore, we calculate the corresponding variation of spectral energy distribution within a period, but little variation is found. The reason for these results is that the viscosity timescale of the disk at the binary radius is much longer than the orbital period of the binary.