  We perform two-dimensional hydrodynamical simulations to quantitatively
explore the torque balance criterion for gap-opening (as formulated by Crida et
al. 2006) in a variety of disks when considering a migrating planet. We find
that even when the criterion is satisfied, there are instances when planets
still do not open gaps. We stress that gap-opening is not only dependent on
whether a planet has the ability to open a gap, but whether it can do so
quickly enough. This can be expressed as an additional condition on the
gap-opening timescale versus the crossing time, i.e. the time it takes the
planet to cross the region which it is carving out. While this point has been
briefly made in the previous literature, our results quantify it for a range of
protoplanetary disk properties and planetary masses, demonstrating how crucial
it is for gap-opening. This additional condition has important implications for
the survival of planets formed by core accretion in low mass disks as well as
giant planets or brown dwarfs formed by gravitational instability in massive
disks. It is particularly important for planets with intermediate masses
susceptible to Type III-like migration. For some observed transition disks or
disks with gaps, we expect that estimates on the potential planet masses based
on the torque balance gap-opening criterion alone may not be sufficient. With
consideration of this additional timescale criterion theoretical studies may
find a reduced planet survivability or that planets may migrate further inwards
before opening a gap.
