Hydrodynamics of giant planet formation: II: model equations and critical mass

Abstract

The aim of this series of articles is to investigate the physical nature and development of the nucleated instability (also called the core instability) using a spherically symmetric protoplanetary model consisting of a growing rigid core and a solar-composition gaseous envelope. In this article the model equations are formulated and the static evolution of a proto-giant planet at Jupiter's distance from the Sun in the “Kyoto” solar nebula is followed up to the critical core mass. The alleged hydrodynamical evolution beyond that point is discussed in G. Wuchterl (1991, Icarus 91, 53–64). The equations of radiation hydrodynamics describing core-envelope structures are formulated on a moving, self-adaptive grid. Convective energy transfer is newly formulated to be included in implicit radiation hydrodynamical calculations. To prepare the physics for the following hydrodynamical calculations of the nucleated instability, the static evolution is described and the concept of the critical mass is discussed. It is shown that a collapse does not necessarily occur at the critical mass. The value of the critical core mass is 13.1 Earth masses, in good agreement with earlier investigations.