We study the interaction of an equal mass binary with an isothermal circumbinary disk motivated by the evidence of the formation of massive black hole binaries surrounded by gas, after a major merger of gas-rich galaxies. We focus on the torques that the binary produces on the disk and how the exchange of angular momentum can drive the gap formation on it. We propose that the angular momentum exchange between the binary and the disk is through the gravitational interaction of the binary and a (tidally formed) global non-axisymmetric perturbation in the disk. Using this interaction, we derive an analytic criterion for the gap formation in the disk that can be expressed either via the characteristic velocities of the binary-disk system or in terms of the structural parameters h/a and M( r)/M bin. Using numerical simulations we show that the simulations where the binary opens a gap in the disk and the simulations where the disk does not have a gap are distributed into two well separated regions. Our analytic criterion predicts a shape of the threshold between these two regions that is consistent with our simulations and the other ones in the literature. We propose an analogy between the regime without (with) a gap in the disk and the Type I (Type II) migration that is observed in simulations of planet-disk interaction (extreme mass ratio binary), emphasizing that the interaction that drives the formation of a gap on the disk is different in the regime that we analyze (comparable mass binary).
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