Planet formation by coagulation: A focus on Uranus and Neptune

By Peter Goldreich, Y. Lithwick, R. Sari. 2004

258 citations recorded by the source corpus.

Planets form in the circumstellar disks of young stars. We review the basic physical processes by which solid bodies accrete each other and alter each others' random velocities, and we provide order-of-magnitude derivations for the rates of these processes. We discuss and exercise the two-groups approximation, a simple yet powerful technique for solving the evolution equations for protoplanet growth. We describe orderly, runaway, neutral, and oligarchic growth. We also delineate die conditions under which each occurs. We refute a popular misconception by showing that the outer planets formed quickly by accreting small bodies. Then we address the final stages of planet formation. Oligarchy ends when the surface density of the oligarchs becomes comparable to that of the small bodies. Dynamical friction is no longer able to balance viscous stirring and the oligarchs' random velocities increase. In the inner-planet system, oligarchs collide and coalesce. In the outer-planet system, some of the oligarchs are ejected. In both the inner- and outer-planet systems, this stage ends once the number of big bodies has been reduced to the point that their mutual interactions no longer produce large-scale chaos. Subsequently, dynamical friction by the residual small bodies circularizes and flattens their orbits. The final stage of planet formation involves the clean up of the residual small bodies. Clean up has been poorly explored.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/93a3ba4a18547916e3264c52d0e7e5124f90a0db

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Jon Fortney
2. C. Mordasini
3. N. Madhusudhan
4. Anders Johansen
5. J. Owen
6. M. Perryman
7. B. Bowler
8. A. Morbidelli

Citations in the corpus

• Shaping the Kuiper belt size distribution by shattering large but strengthless bodies (2004, background): “However, other effects may also be responsible for the lightcurve shape (see, for example, Goldreich et al. 2004).”
• SUPER-EARTH ATMOSPHERES: SELF-CONSISTENT GAS ACCRETION AND RETENTION (2015, background): “At close orbits, planetesimal impacts may be ignored, as explained above, but giant impacts of protoplanets (or alternatively, inward migration of rocky cores) may be relevant, since isolation masses are small (see, e.g. Goldreich et al. 2004; Inamdar & Schlichting 2015).”
• The California-Kepler Survey. V. Peas in a Pod: Planets in a Kepler Multi-planet System Are Similar in Size and Regularly Spaced (2017, background): “…and a swarm of planetesimals is sufficiently small that the gravitational force of the protoplanet wins over competing forces on the planetesimals (Lissauer & Stewart 1993; Goldreich et al. 2004) 13 masses (compared to their stars) and sufficiently high eccentricities (Pan & Schlichting 2017).”
• Variations on Debris Disks: Icy Planet Formation at 30-150 AU for 1-3 M☉ Main-Sequence Stars (2008, background): “Goldreich et al. (2004) demonstrate that our numerical results agree with analytic estimates.”
• MAKE SUPER-EARTHS, NOT JUPITERS: ACCRETING NEBULAR GAS ONTO SOLID CORES AT 0.1 AU AND BEYOND (2014, background): “These gravitational focussing factors (a.k.a. Safronov numbers) are uncertain, depending sensitively on the size distribution of planetesimals and the means by which velocity dispersions are damped (see Goldreich et al. 2004 for a pedagogic review).”
• Forming Planetesimals in Solar and Extrasolar Nebulae (2009, background): “Section 8 outlines the nonlinear outcome of GI, describing breakthrough numerical simulations.”
• A COMBINED SUBARU/VLT/MMT 1–5 μm STUDY OF PLANETS ORBITING HR 8799: IMPLICATIONS FOR ATMOSPHERIC PROPERTIES, MASSES, AND FORMATION (2011, background): “However, gas drag and dynamical friction from planetesimals are critically important as they promote orbit circularization and stability (e.g. Goldreich et al. 2004; Ford and Chiang 2007)17.”
• The Orbital Eccentricity of Small Planet Systems (2018, background): “…of planets formed in situ leads to eccentricities limited to the ratio of the escape velocity from the surface of the planet to the Keplerian velocity (e.g., Goldreich et al. 2004; Petrovich et al. 2014; Schlichting 2014), because subsequent close encounters lead to mergers rather than scattering.”
• Extrasolar planet population synthesis I: Method, formation tracks and mass-distance distribution (2009, background): “…to the concurrent growth of many planets, see below), inside the iceline, for disks similar to the MMSN, growth from Miso ∼ 0.01 − 0.1 M⊕ to the final masses occurs through giant impacts on timescales that exceed by roughly one order of magnitude typical gas disk lifetimes (Goldreich et al. 2004a).”
• Final Stages of Planet Formation (2004, background): “This 2 The heating rate given in the literature is proportional to (vH/v) 2 instead of to vH/v. Goldreich et al. (2004) show that the latter is correct.”
• Debris disc stirring by secular perturbations from giant planets (2009, background): “…in the context of debris disc evolution include planet formation proceeding more rapidly when a gap-opening giant planet has formed (Bryden et al. 2000; Thommes 2005), or an outer disc being stirred by planetesimal that have been scattered out from the inner system (Goldreich et al. 2004a).”
• Streaming Instabilities in Protoplanetary Disks (2004, background): “Forming planetesimals via gravitational instabilities would be trivial in a gas-free disk, since collisional damping dominates viscous stirring in the absence of protoplanets (Goldreich et al. 2004a).”
• Rapid growth of gas-giant cores by pebble accretion (2012, background): “At 5 AU, this gives a reduction in the accretion rate of α ≈ 10−3 (r/5 AU)−1, for a standard solid density (Goldreich et al. 2004).”
• THE RUNTS OF THE LITTER: WHY PLANETS FORMED THROUGH GRAVITATIONAL INSTABILITY CAN ONLY BE FAILED BINARY STARS (2009, background): “In contrast, typical core accretion times increase with radius and exceed 10 Myr beyond 20 AU (e.g. Levison & Stewart 2001; Goldreich et al. 2004).”
• Planet formation and migration (2005, background): “Goldreich et al (2004) suggest that a residue of small particles derived from collisions amongst the original planetesimals, such as has been produced in calculations directed towards explaining the distribution of Kuiper belt objects, by Kenyon & Bromley (2004), may remain and damp the velocity…”
• The Size Distribution of Kuiper Belt Objects (2004, background): “As the observations improve, the theoretical challenge is to combine collisional (this paper; Goldreich et al. 2004) and dynamical (e.g., Malhotra 1995; Gomes 2003; Hahn 2003; Levison & Morbidelli 2003; Quillen et al. 2004) calculations to derive robust predictions for the formation and evolution…”
• The effect of gas drag on the growth of protoplanets. Analytical expressions for the accretion of small bodies in laminar disks (2010, background): “The accretion then takes place at low va – the shear-dominated regime – which is very favorable for growth (Goldreich et al. 2004).”