Accretion of the gaseous envelope of Jupiter around a 5–10 Earth-mass core

Abstract

New numerical simulations of the formation and evolution of Jupiter are presented. The formation model assumes that first a solid core of several M ⊕ accretes from the planetesimals in the protoplanetary disk, and then the core captures a massive gaseous envelope from the protoplanetary disk. Earlier studies of the core accretion–gas capture model [Pollack, J.B., Hubickyj, O., Bodenheimer, P., Lissauer, J.J., Podolak, M., Greenzweig, Y., 1996. Icarus 124, 62–85] demonstrated that it was possible for Jupiter to accrete with a solid core of 10–30 M ⊕ in a total formation time comparable to the observed lifetime of protoplanetary disks. Recent interior models of Jupiter and Saturn that agree with all observational constraints suggest that Jupiter's core mass is 0–11 M ⊕ and Saturn's is 9–22 M ⊕ [Saumon, G., Guillot, T., 2004. Astrophys. J. 609, 1170–1180]. We have computed simulations of the growth of Jupiter using various values for the opacity produced by grains in the protoplanet's atmosphere and for the initial planetesimal surface density, σ init , Z , in the protoplanetary disk. We also explore the implications of halting the solid accretion at selected core mass values during the protoplanet's growth. Halting planetesimal accretion at low core mass simulates the presence of a competing embryo, and decreasing the atmospheric opacity due to grains emulates the settling and coagulation of grains within the protoplanet's atmosphere. We examine the effects of adjusting these parameters to determine whether or not gas runaway can occur for small mass cores on a reasonable timescale. We compute four series of simulations with the latest version of our code, which contains updated equation of state and opacity tables as well as other improvements. Each series consists of a run without a cutoff in planetesimal accretion, plus up to three runs with a cutoff at a particular core mass. The first series of runs is computed with an atmospheric opacity due to grains (hereafter referred to as ‘grain opacity’) that is 2% of the interstellar value and σ init , Z = 10 g / cm 2 . Cutoff runs are computed for core masses of 10, 5, and 3 M ⊕ . The second series of Jupiter models is computed with the grain opacity at the full interstellar value and σ init , Z = 10 g / cm 2 . Cutoff runs are computed for core masses of 10 and 5 M ⊕ . The third series of runs is computed with the grain opacity at 2% of the interstellar value and σ init , Z = 6 g / cm 2 . One cutoff run is computed with a core mass of 5 M ⊕ . The final series consists of one run, without a cutoff, which is computed with a temperature dependent grain opacity (i.e., 2% of the interstellar value for T < 350 K ramping up to the full interstellar value for T > 500 K ) and σ init , Z = 10 g / cm 2 . Our results demonstrate that reducing grain opacities results in formation times less than half of those for models computed with full interstellar grain opacity values. The reduction of opacity due to grains in the upper portion of the envelope with T ⩽ 500 K has the largest effect on the lowering of the formation time. If the accretion of planetesimals is not cut off prior to the accretion of gas, then decreasing the surface density of planetesimals lowers the final core mass of the protoplanet, but increases the formation timescale considerably. Finally, a core mass cutoff results in a reduction of the time needed for a protoplanet to evolve to the stage of runaway gas accretion, provided the cutoff mass is sufficiently large. The overall results indicate that, with reasonable parameters, it is possible that Jupiter formed at 5 AU via the core accretion process in 1 Myr with a core of 10 M ⊕ or in 5 Myr with a core of 5 M ⊕ .