Characteristic evolution of the torque F _J (labeled on the right axis) experienced by the central binary with M _c = 10 ⁷ M _☉ and q = 1 as a function of time. Two cases are shown: F _J ( t) computed self-consistently accounting for the circumbinary disk evolution (thick black solid line) and assuming a standard constant disk (blue dotted line). In both cases, the mass accretion rate in the disk far from the binary is the same and equal to M _Edd. Note the difference between the values of F _J computed in two ways for t 10 ⁵ yr. Also shown is the orbital evolution of the binary (thin solid line) computed according to the first, self-consistent prescription for F _J ( t). Different regimes in which the disk can be present are labeled on the plot (red dotted lines r ^rad/gas and r ^es/ff show their boundaries) and the gas pressure dominated case with κ = κ _es is shaded. The dashed curve shows the run of r ^infl( t) in different regimes, and is closely related to the behavior of the self-consistent F _J ( t). The Eddington limit becomes important below the dot-dashed line in the lower right corner of the plot; see Section 6.2.6. The black square dot marks the transition from the disk- to GW-dominated orbital evolution of the binary. See the text for more details.