Stability and Occurrence Rate Constraints on the Planetary Sculpting Hypothesis for "Transitional" Disks

Abstract

Transitional disks, protoplanetary disks with deep and wide central gaps, may be the result of planetary sculpting. By comparing numerical planet-opening-gap models with observed gaps, we find systems of 3-6 giant planets are needed in order to open gaps with the observed depths and widths. We explore the dynamical stability of such multi-planet systems using N-body simulations that incorporate prescriptions for gas effects. We find they can be stable over a typical disk lifetime, with the help of eccentricity damping from the residual gap gas that facilitates planets locking into mean motion resonances. However, in order to account for the occurrence rate of transitional disks, the planet sculpting scenario demands gap-opening-friendly disk conditions, in particular, a disk viscosity $\alpha\lesssim0.001$. In addition, the demography of giant planets at $\sim 3-30$ AU separations, poorly constrained by current data, has to largely follow occurrence rates extrapolated outward from radial velocity surveys, not the lower occurrence rates extrapolated inward from direct imaging surveys. Even with the most optimistic occurrence rates, transitional disks cannot be a common phase that most gas disks experience at the end of their life, as popularly assumed, simply because there are not enough planets to open these gaps. Finally, as consequences of demanding almost all giant planets at large separations participate in transitional disk sculpting, the majority of such planets must form early and end up in a chain of mean motion resonances at the end of disk lifetime.