Binary-disk interaction: Gap-Opening criteria
  We study the interaction of an equal mass binary with an isothermal
circumbinary disk motivated by the theoretical and observational evidence of
the formation of massive black holes 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 formation of
a gap 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
gravitational interaction we derive an analytic criterion for the formation of
a gap in the disk that can be expressed on the structural parameters h/a and
M(< r)/M_{bin}. Using SPH 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 in two well separate regions. Our analytic gap-opening
criterion predicts a shape of the threshold between this 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 (binaries with extreme mass ratios), 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).
