Models of Jupiterʹs growth incorporating thermal and hydrodynamic constraints

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 planetʹs internal structure using a well tested planetary formation code that is based upon a Henyey-type stellar evolution code. The planetʹs interactions with the protoplanetary disk are calculated using 3-D hydrodynamic simulations. Previous models of Jupiterʹs growth have taken the radius of the planet to be approximately one Hill sphere radius, R H . However, 3-D hydrodynamic simulations show that only gas within ∼ 0.25 R H 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 planetʹs 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 planetʹs 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. Observations suggest that the typical lifetime of massive disks around young stellar objects is ∼ 3   Myr . To account for the dissipation of such disks, we perform some of our simulations of Jupiterʹs growth within a disk whose surface gas density decreases on this timescale. In all of the cases that we simulate, the planetʹs effective radiating temperature rises to well above 1000   K soon after hydrodynamic limits begin to control the rate of gas accretion and the planetʹs distended envelope begins to contract. According to our simulations, proto-Jupiterʹs distended and thermally-supported envelope was too small to capture the planetʹs current retinue of irregular satellites as advocated by Pollack et al. [Pollack, J.B., Burns, J.A., Tauber, M.E., 1979. Icarus 37, 587–611].