Cubic ratio between the sound speed of the gas and the rotational velocity of the binary–disk system, ( c _s/ v) ³, plotted against the quadratic ratio between the rotational velocity of the isolated binary and the rotational velocity of the binary–disk system, ( v _bin/ v) ². The red circles indicate simulations where the binary has opened a gap in the disk (opened simulations), and the blue circles are simulations where the disk does not have a gap (closed simulations). We plot together all the simulations with different values of the mass ratio q that we explore. The straight line is the linear q-independent threshold between the opened simulations and the closed simulations predicted by our analytic gap-opening criterion. Below the line are the opened simulations and above are the closed simulations. The slope of the interface is the function f.