HOW EMPTY ARE DISK GAPS OPENED BY GIANT PLANETS?
Fung et al
Gap clearing by giant planets has been proposed to explain the optically thin cavities observed in many protoplanetary disks. How much material remains in the gap determines not only how detectable young planets are in their birth environments, but also how strong co-rotation torques are, which impacts how planets can survive fast orbital migration. We determine numerically how the average surface density inside the gap, Σgap, depends on planet-to-star mass ratio q, Shakura-Sunyaev viscosity parameter α, and disk height-to-radius aspect ratio h/r. Our results are derived from our new graphics processing unit accelerated Lagrangian hydrodynamical code PEnGUIn and are verified by independent simulations with ZEUS90. For Jupiter-like planets, we find Σgapvpropq –2.2α1.4(h/r)6.6, and for near brown dwarf masses, Σgapvpropq –1α1.3(h/r)6.1. Surface density contrasts inside and outside gaps can be as large as 104, even when the planet does not accrete. We derive a simple analytic scaling, Σgapvpropq –2α1(h/r)5, that compares reasonably well to empirical results, especially at low Neptune-like masses, and use discrepancies to highlight areas for progress.