4:30 PM - 4:45 PM
[PPS06-25] One-dimensional model of disk heating and gap formation by a giant planet
Keywords:planet formation, protoplanetary disks, shock heating
A giant planet growing by gas accretion in a protoplanetary disk excites density waves in the disk. When the density wave creates a shock and decays, it exerts a torque on the disk. This torque creates a gap in the disk with a low surface density, which reduces the planet's gas accretion rate. At the same time, the density waves heat the disk, which is considered a plausible mechanism for heating the solar system material recorded in primitive meteorites. It is known that there is a close relationship between the torque and the heating rate (Goodman and Rafikov, 2001).
In this study, we focused on the relationship between the torque and the heating rate and calculated the heating rate using a one-dimensional model. Kanagawa et al. (2015,2017) constructed the 1D gap model that reproduces 2D hydrodynamical simulations (Kanagawa et al. 2016) over a wide parameter range. We obtained a torque density distribution with a minor modification in this gap model, and the heating rate distribution was calculated from the equation relating torque and heating rate.
The heating rate derived in this study is particularly high in the region where the surface density gradient is rapid in the gap, and the results well reproduce the hydrodynamical simulations of Ono et al. (2024). Ono et al. (2024) also discussed the dependence of the heating rate on the planetary mass and disk viscosity, and our model successfully reproduces these parameter dependencies in the gap.
Also, the heating rate in this study and the viscous heating rate of the disk without the gap were of similar magnitude in the gap, independent of the planetary mass. This means the disk's viscous heating determines the upper limit of the heating rate.
In the gap, in which the surface density is low, the disk is optically thin and heat retention is weak, this result suggests that shock heating of density waves is not a sufficient heating mechanism for solar system materials.
The heating rates in this study are much smaller than those in the fluid simulations of Ono et al.(2024). This may be due to the use of the local approximation in this study. We should consider the global effect to reproduce the heating rate outside the gap.
In this study, we focused on the relationship between the torque and the heating rate and calculated the heating rate using a one-dimensional model. Kanagawa et al. (2015,2017) constructed the 1D gap model that reproduces 2D hydrodynamical simulations (Kanagawa et al. 2016) over a wide parameter range. We obtained a torque density distribution with a minor modification in this gap model, and the heating rate distribution was calculated from the equation relating torque and heating rate.
The heating rate derived in this study is particularly high in the region where the surface density gradient is rapid in the gap, and the results well reproduce the hydrodynamical simulations of Ono et al. (2024). Ono et al. (2024) also discussed the dependence of the heating rate on the planetary mass and disk viscosity, and our model successfully reproduces these parameter dependencies in the gap.
Also, the heating rate in this study and the viscous heating rate of the disk without the gap were of similar magnitude in the gap, independent of the planetary mass. This means the disk's viscous heating determines the upper limit of the heating rate.
In the gap, in which the surface density is low, the disk is optically thin and heat retention is weak, this result suggests that shock heating of density waves is not a sufficient heating mechanism for solar system materials.
The heating rates in this study are much smaller than those in the fluid simulations of Ono et al.(2024). This may be due to the use of the local approximation in this study. We should consider the global effect to reproduce the heating rate outside the gap.