(a) and (b) Evolution timescale t _ev = | dln  r _b / dt| ⁻¹ of SMBH binaries as a function of orbital period P _orb or semi-major axis r _b (upper axis; use to read off the initial semi-major axis r _b (0)). Starting points for each evolutionary track are marked by either triangles (for ) or hexagons (for ). Solid (black) and dotted (red) curves are used for the q = 1 and q = 10 ⁻² binary tracks, respectively. Straight portions of these tracks at low P _orb correspond to the epoch when the orbital evolution of the binary is dominated by GW emission. Note that prior to these epochs, tracks starting at different r _b (0) do not overlap, illustrating the hysteresis of the binary evolution caused by the non-local nature of the self-consistent disk–binary coupling. (c and d) Ratio of the local disk mass M _d to the secondary mass M _s for a sub-sample of evolutionary tracks displayed in Figure  6, showing that M _d / M _s 1 in our calculations. Different tracks are labeled as . See the text for details.