  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.
