The erratic path to coalescence of LISA massive black hole binaries in
  sub-pc resolution simulations of smooth circumnuclear gas disks
  We report on high-resolution simulations that explore the orbital decay of
massive black hole (MBH) pairs with masses between $10^5$ and $10^7 M_{\odot}$
embedded in a circumnuclear gas disk (CND). An adiabatic equation of state is
adopted, with a range of adiabatic indices, which maintains a smooth flow.
Mergers between MBHs in this mass range would be detectable by the upcoming
Laser Inteferometer Space Antenna (LISA). The orbital evolution is followed
from the CND scale ($100$~pc) down to separations of $0.1$--$0.01$~pc at which
a circumbinary disk (CBD) could form. The decay is erratic and strongly
dependent on the gas flow within the disk, that ultimately determines the net
torques experienced by the sinking MBH. Overall, we can identify three
different evolutionary stages: (i) an initially slow decay that leads to no
significant change in the orbital angular momentum, resulting in some
circularization; (ii) a fast migration phase in which the orbital angular
momentum decreases rapidly; and (iii) a final, very slow decay phase, in which
orbital angular momentum can even increase, and a CBD can form. The fast
migration phase owes to disk-driven torques originating primarily from the
co-orbital region of the secondary MBH, at a distance of 1--3 Hill radii. We
find strong analogies with fast Type III migration for massive planets in
protoplanetary disks. The CBD forms only when the decay rate becomes small
enough to allow it enough time to carve a cavity around the primary MBH, at
scales $\lesssim 1$~pc; when this happens, the MBH separation nearly stalls in
our higher-resolution run. We suggest an empirically modified gap-opening
criterion that takes into account such timescale effects as well as other
deviations from standard assumptions made in the literature. [Abriged]
