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We present an analytical and numerical study of a system composed of astellar binary pair and a massless, locally isothermal viscous accretion diskthat is coplanar to the binary orbital plane. Analytically, we study the effectof the binary's gravitational potential over short timescales through the studyof stability for epicyclic orbits, and over long timescales by revisiting theconcept of resonant torques. Numerically, we perform two-dimensional Newtoniannumerical simulations of the disk-binary system over a range of binary massratios. We find that the results of our simulations are consistent withprevious numerical studies. We additionally show, by comparison of theanalytical and numerical results, that the circumbinary gap is maintained onthe orbital timescale through the driving of epicyclic instabilities, and doesnot depend on resonant torquing, contrary to standard lore. While our resultsare applicable to any disk-binary system, we highlight the importance of thisresult in the search for electromagnetic and gravitational-wave signatures fromsupermassive black-hole binaries.

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