Models of Jupiter's Growth Incorporating Thermal and Hydrodynamic Constraints

TL;DR

This study models Jupiter's formation considering hydrodynamic and thermal constraints, revealing that gas flow boundaries and disk properties significantly influence growth timescales and final planetary characteristics.

Contribution

It introduces a new boundary condition based on 3-D hydrodynamic simulations, refining Jupiter's growth model by incorporating realistic gas flow limits and disk dissipation effects.

Findings

Growth time increases by ~5% with smaller planetary radius.

Thermal pressure limits gas accretion for smaller planets.

Hydrodynamics regulate accretion rates for larger planets.

Abstract

[Abridged] We model the growth of Jupiter via core nucleated accretion, applying constraints from hydrodynamical processes that result from the disk-planet interaction. We compute the planet's internal structure using a Henyey-type stellar evolution code. The planet's interactions with the protoplanetary disk are calculated using 3-D hydrodynamic simulations. Previous models of Jupiter's growth have taken the radius of the planet to be approximately one Hill sphere radius, Rhill. However, 3-D hydrodynamic simulations show that only gas within 0.25Rhill remains bound to the planet, with the more distant gas eventually participating in the shear flow of the protoplanetary disk. Therefore in our new simulations, the planet's outer boundary is placed at the location where gas has the thermal energy to reach the portion of the flow not bound to the planet. We find that the smaller radius increases the time required for planetary growth by ~5%. Thermal pressure limits the rate at which a planet less than a few dozen times as massive as Earth can accumulate gas from the protoplanetary disk, whereas hydrodynamics regulates the growth rate for more massive planets. Within a moderately viscous disk, the accretion rate peaks when the planet's mass is about equal to the mass of Saturn. In a less viscous disk hydrodynamical limits to accretion are smaller, and the accretion rate peaks at lower mass. To account for disk dissipation, we perform some of our simulations of Jupiter's growth within a disk whose surface gas density decreases on a timescale of 3Myr. According to our simulations, proto-Jupiter's distended and thermally-supported envelope was too small to capture the planet's current retinue of irregular satellites as advocated by Pollack et al. (1979).