Dynamics of core accretion

Andrew F. Nelson, Maximilian Ruffert

Research output: Contribution to journalArticlepeer-review


We perform three-dimensional hydrodynamic simulations of gas flowing around a planetary core of mass Mpl = 10M⊕ embedded in a near Keplerian background flow, using a modified shearing box approximation. We assume an ideal gas behaviour following an equation of state with a fixed ratio of the specific heats, γ = 1.42, consistent with the conditions of a moderate-temperature background disc with solar composition. No radiative heating or cooling is included in the models. We employ a nested grid hydrodynamic code implementing the `Piecewise Parabolic Method' with as many as six fixed nested grids, providing spatial resolution on the finest grid comparable to the present-day diameters of Neptune and Uranus. We find that a strongly dynamically active flow develops such that no static envelope can form. The activity is not sensitive to plausible variations in the rotation curve of the underlying disc. It is sensitive to the thermodynamic treatment of the gas, as modelled by prescribed equations of state (either `locally isothermal' or `locally isentropic') and the temperature of the background disc material. The activity is also sensitive to the shape and depth of the core's gravitational potential, through its mass and gravitational softening coefficient. Each of these factors influences the magnitude and character of hydrodynamic feedback of the small-scale flow on the background, and we conclude that accurate modelling of such feedback is critical to a complete understanding of the core accretion process. The varying flow pattern gives rise to large, irregular eruptions of matter from the region around the core which return matter to the background flow: mass in the envelope at one time may not be found in the envelope at any later time. No net mass accretion into the envelope is observed over the course of the simulation and none is expected, due to our neglect of cooling. Except in cases of very rapid cooling however, as defined by locally isothermal or isentropic treatments, any cooling that does affect the envelope material will have limited consequences for the dynamics, since the flow quickly carries cooled material out of the core's environment entirely. The angular momentum of material in the envelope, relative to the core, varies both in magnitude and in sign on time-scales of days to months near the core and on time-scales a few years at distances comparable to the Hill radius. The dynamical activity contrasts with the largely static behaviour typically assumed within the framework of the core accretion model for Jovian planet formation. We show that material entering the dynamically active environment may suffer intense heating and cooling events the durations of which are as short as a few hours to a few days. Shorter durations are not observable in our work due to the limits of our resolution. Peak temperatures in these events range from T ˜ 1000 K to as high as T ˜ 3-4000 K, with densities ρ ˜ 10-9 to 10-8 g cm-3. These time-scales, densities and temperatures span a range consistent with those required for chondrule formation in the nebular shock model. We therefore propose that dynamical activity in the Jovian planet formation environment could be responsible for the production of chondrules and other annealed silicates in the solar nebula.
Original languageEnglish
Pages (from-to)1791-1826
JournalMonthly Notices of the Royal Astronomical Society
Issue number2
Publication statusPublished - 1 Feb 2013


  • hydrodynamics
  • meteorites, meteors, meteoroids
  • planets and satellites: formation
  • planet-disc interactions
  • planetary systems


Dive into the research topics of 'Dynamics of core accretion'. Together they form a unique fingerprint.

Cite this