  By numerically integrating the compressible Navier-Stokes equations in two
dimensions, we calculate the criterion for gap formation by a very low mass (q
~10^{-4}) protoplanet on a fixed orbit in a thin viscous disk. In contrast with
some previously proposed gap-opening criteria, we find that a planet can open a
gap even if the Hill radius is smaller than the disk scale height. Moreover, in
the low-viscosity limit, we find no minimum mass necessary to open a gap for a
planet held on a fixed orbit. In particular, a Neptune-mass planet will open a
gap in a minimum mass solar nebula with suitably low viscosity (\alpha
<10^{-4}). We find that the mass threshold scales as the square root of
viscosity in the low mass regime. This is because the gap width for critical
planet masses in this regime is a fixed multiple of the scale height, not of
the Hill radius of the planet.
