  In the standard model of gas giant planet formation, a large solid core (~ 10
times the Earth's mass) forms first, then accretes its massive envelope (100 or
more Earth masses) of gas. However, inward planet migration due to
gravitational interaction with the proto-stellar gas disk poses a difficulty in
this model. Core-sized bodies undergo rapid "Type I" migration; for typical
parameters their migration timescale is much shorter than their accretion
timescale. How, then, do growing cores avoid spiraling into the central star
before they ever get the chance to become gas giants? Here, we present a simple
model of core formation in a gas disk which is viscously evolving. As the disk
dissipates, accretion and migration timescales eventually become comparable. If
this happens while there is still enough gas left in the disk to supply a
jovian atmosphere, then a window of opportunity for gas giant formation opens.
We examine under what circumstances this happens, and thus, what predictions
our model makes about the link between proto-stellar disk properties and the
likelihood of forming giant planets.
