A Pseudo-Newtonian Stationary Circumbinary Slim Disk Model

We present a pseudo-Newtonian stationary circumbinary slim disk model. We extend the slim disk formalism by including the binary tidal torque and solve the resulting steady-state equations to determine the circumbinary disk structure. We compare the binary slim disk solutions with corresponding binary thin disk solutions, calculate the disk spectrum, explore the impact of different parameters on the system, and estimate the binary shrinkage timescale. We find that (1) due to the different disk density profiles, the integrated tidal torque exerted on the disk is significantly smaller for the slim disk than for the thin disk; as a result, thin disks onto binary black holes can be significantly more radiatively efficient than slim disks. (2) The presence of the secondary alters the emission of the circumbinary disk, making it different from the spectrum of a single black hole active galactic nucleus. (3) The tidal torque boosts the viscous torque in the outer part of the disk (at radii greater than the binary separation), which is strongly dependent on the disk parameters, including the binary mass ratio q, the orbital separation a, the viscous parameter α, and the accretion rate M. (4) The vertical component of the potential of the secondary slightly decreases the integrated tidal torque. However, both the vertical and radial components of the potential of the secondary have small impacts on the disk radiative flux. (5) Using the integrated disk tidal torque backreacting on the secondary at different orbital separations, we find that the disk provides an efficient way to shrink the binary orbital separation.