Hydrodynamics of giant planet formation III: Jupiter's nucleated instability

Abstract

In this series of articles the formation of giant planets is investigated using a spherically symmetric protoplanetary model consisting of a growing rigid core and a solar composition, gaseous envelope. The protoplanet is located at Jupiter's distance from the Sun in the “Kyoto” solar nebula. In the previous article in this series G. Wuchterl (1991, Icarus 91, 39–52), the model equations were discussed and the evolution of a static envelope was followed up to the “critical core mass,” confirming H. Mizuno's (1980, Prog. Theor. Phys. 64, 544–557) results. In this article, the critical model is used as an initial condition for a radiation hydrodynamical calculation of the nucleated instability and the phases following. After a very short quasi-hydrostatic contraction immediately following the critical mass, nonlinear hydrodynamical waves were excited by a κ mechanism and an outflow was driven. After the ejection of a large part of the envelope mass the activity faded and a new quasi-static state of the protoplanet was found. This remnant object had a pulsating envelope of 1.4 M ⊕ around a core of 13.1 M ⊕, i.e., similar in mass to Uranus and Neptune. No collapse or (rapid) contraction of the envelope and no onset of accretion up to the present mass of Jupiter was found. The integral equations of radiation hydrodynamics, in conservation form, were solved on a self-adaptive grid with an implicit finite difference technique.