Kazuhiro D. Kanagawa1,2, Hidekazu Tanaka3, and Ewa Szuszkiewicz1
The Astrophysical Journal 861, 140 Link to Article [https://doi.org/10.3847/1538-4357/aac8d9]
1Institute of Physics and CASA*, Faculty of Mathematics and Physics, University of Szezecin, Wielkopolska 15, PL-70-451 Szczecin, Poland
2Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
3Astronomical Institute, Tohoku University, Sendai, Miyagi 980-8578, Japan
A large planet orbiting a star in a protoplanetary disk opens a density gap along its orbit due to the strong disk–planet interaction and migrates with the gap in the disk. It is expected that in the ideal case, a gap-opening planet migrates at the viscous drift speed, which is referred to as type II migration. However, recent hydrodynamic simulations have shown that, in general, the gap-opening planet is not locked to the viscous disk evolution. A new physical model is required to explain the migration speed of such a planet. For this reason, we re-examined the migration of a planet in the disk, by carrying out the two-dimensional hydrodynamic simulations in a wide parameter range. We have found that the torque exerted on the gap-opening planet depends on the surface density at the bottom of the gap. The planet migration slows down as the surface density of the bottom of the gap decreases. Using the gap model developed in our previous studies, we have constructed an empirical formula of the migration speed of the gap-opening planets, which is consistent with the results given by the hydrodynamic simulations performed by us and other researchers. Our model easily explains why the migration speed of the gap-opening planets can be faster than the viscous gas drift speed. It can also predict the planet mass at which the type I migration is no longer adequate due to the gap development in the disk, providing a gap formation criterion based on planetary migration.
for the initial mass function high-mass slope and
for the SN Ia normalization, which are broadly consistent across tested yield tables. Additionally, we demonstrate how Chempy can be used to dramatically improve elemental abundance predictions of hydrodynamical simulations by plugging tailored best-fit SSP parameters into a Milky Way analog from Gutcke & Springel. Our code, including a comprehensive tutorial, is freely available and can additionally provide SSP enrichment tables for any combination of parameters and yield tables.
up to
without self-gravity. The study covers domain sizes of
,
, and
in terms of the gas-disk scale height
using the P
and 0.1 mark the upper end of the expected dust growth. SI activity is found up to very high dust-to-gas ratios, providing fluctuations in the local dust-to-gas ratios and turbulent particle diffusion δ. We find an SI-like instability that operates in r–
only to be two orders of magnitude lower than at
, suggesting a
relation that is shallow around
. The (a)SI ability to concentrate particles is found to be uncorrelated with its strength in particle turbulence. Finally, we performed a resolution study to test our findings of the aSI. This paper stresses the importance of properly resolving the (a)SI at high dust-to-gas ratios and planetesimal collapse simulations, leading otherwise to potentially incomplete results.