On the Evolution and Survival of Protoplanets Embedded in a Protoplanetary Disk

We model the evolution of a Jupiter-mass protoplanet formed by the disk instability mechanism at various radial distances accounting for the presence of the disk. Using three different disk models, it is found that a newly-formed Jupiter-mass protoplanet at radial distance of $\lesssim$ 5-10 AU cannot undergo a dynamical collapse and evolve further to become a gravitational bound planet. We therefore conclude that {\it giant planets, if formed by the gravitational instability mechanism, must form and remain at large radial distances during the first $\sim$ 10$^5-10^6$ years of their evolution}. The minimum radial distances in which protoplanets of 1 Saturn-mass, 3 and 5 Jupiter-mass protoplanets can evolve using a disk model with $\dot{M}=10^{-6} M_{Sun}/yr$ and $\alpha=10^{-2}$ are found to be 12, 9, and 7 AU, respectively. The effect of gas accretion on the planetary evolution of a Jupiter-mass protoplanet is also investigated. It is shown that gas accretion can shorten the pre-collapse timescale substantially. Our study suggests that the timescale of the pre-collapse stage does not only depend on the planetary mass, but is greatly affected by the presence of the disk and efficient gas accretion.