Analytical and Numerical Analysis of Circumbinary Disk Dynamics -- I: Coplanar Systems

Abstract: We present an analytical and numerical study of a system composed of a stellar binary pair and a massless, locally isothermal viscous accretion disk that is coplanar to the binary orbital plane. Analytically, we study the effect of the binary's gravitational potential over short timescales through the study of stability for epicyclic orbits, and over long timescales by revisiting the concept of resonant torques. Numerically, we perform two-dimensional Newtonian numerical simulations of the disk-binary system over a range of binary mass ratios. We find that the results of our simulations are consistent with previous numerical studies. We additionally show, by comparison of the analytical and numerical results, that the circumbinary gap is maintained on the orbital timescale through the driving of epicyclic instabilities, and does not depend on resonant torquing, contrary to standard lore. While our results are applicable to any disk-binary system, we highlight the importance of this result in the search for electromagnetic and gravitational-wave signatures from supermassive black-hole binaries.