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According to the canonical planet formation theory, planets form "in-situ" within a planetesimal disk via runaway and oligarchic growth. This theory, however, cannot naturally account for the formation timescale of ice giants or the…

Earth and Planetary Astrophysics · Physics 2026-01-29 Tenri Jinno , Takayuki R. Saitoh , Yoko Funato , Junichiro Makino

Context. Planet formation with pebbles has been proposed to solve a couple of long-standing issues in the classical formation model. Some sophisticated simulations have been done to confirm the efficiency of pebble accretion. However, there…

Earth and Planetary Astrophysics · Physics 2017-11-29 Soko Matsumura , Ramon Brasser , Shigeru Ida

Prevailing $N$-body planet formation models typically start with lunar-mass embryos and show a general trend of rapid migration of massive planetary cores to the inner Solar System in the absence of a migration trap. This setup cannot…

Earth and Planetary Astrophysics · Physics 2024-03-27 Tommy Chi Ho Lau , Man Hoi Lee , Ramon Brasser , Soko Matsumura

It is widely held that the first step in forming the gas giant planets, such as Jupiter and Saturn, is to form solid `cores' of roughly 10 M$_\oplus$. Getting the cores to form before the solar nebula dissipates ($\sim\!1-10\,$Myr) has been…

Earth and Planetary Astrophysics · Physics 2015-10-09 Harold F. Levison , Katherine A. Kretke , Martin J. Duncan

We present N-body simulations of planetary accretion beginning with 1 km radius planetesimals in orbit about a 1 solar mass star at 0.4 AU. The initial disk of planetesimals contains too many bodies for any current N-body code to integrate;…

Earth and Planetary Astrophysics · Physics 2015-05-13 Rory Barnes , Thomas R. Quinn , Jack J. Lissauer , Derek C. Richardson

We present Particle-Particle-Particle-Mesh (PPPM) and Tree Particle-Mesh (TreePM) implementations on GRAPE-5 and GRAPE-6A systems, special-purpose hardware accelerators for gravitational many-body simulations. In our PPPM and TreePM…

Astrophysics · Physics 2015-06-24 Kohji Yoshikawa , Toshiyuki Fukushige

Planetary bodies form by accretion of smaller bodies. It has been suggested that a very efficient way to grow protoplanets is by accreting particles of size <<km (e.g., chondrules, boulders, or fragments of larger bodies) as they can be…

Earth and Planetary Astrophysics · Physics 2015-05-19 C. W. Ormel , H. H. Klahr

This paper presents a fast, economical particle-multiple-mesh N-body code optimized for large-N modelling of collisionless dynamical processes, such as black-hole wandering or bar-halo interactions, occurring within isolated galaxies. The…

Astrophysics · Physics 2007-11-07 John Magorrian

State-of-the-art planet formation models are now capable of accounting for the full spectrum of known planet types. This comes at the cost of increasing complexity of the models, which calls into question whether established links between…

Earth and Planetary Astrophysics · Physics 2021-12-08 M. Schlecker , D. Pham , R. Burn , Y. Alibert , C. Mordasini , A. Emsenhuber , H. Klahr , Th. Henning , L. Mishra

Accumulation of dust and ice particles into planetesimals is an important step in the planet formation process. Planetesimals are the seeds of both terrestrial planets and the solid cores of gas and ice giants forming by core accretion.…

Earth and Planetary Astrophysics · Physics 2015-06-18 Anders Johansen , Jürgen Blum , Hidekazu Tanaka , Chris Ormel , Martin Bizzarro , Hans Rickman

Pebble accretion refers to the assembly of rocky planet cores from particles whose velocity dispersions are damped by drag from circumstellar disc gas. Accretion cross-sections can approach maximal Hill-sphere scales for particles whose…

Earth and Planetary Astrophysics · Physics 2018-08-15 Jonathan W. Lin , Eve J. Lee , Eugene Chiang

In this chapter, we summarize the underlying numerical methods needed for efficient $N$-body integration of planetary systems. We discuss how symplectic integrators have been developed to tackle the complementary problems of long-term…

Earth and Planetary Astrophysics · Physics 2026-04-13 Simon L. Grimm , Joachim G. Stadel

We have developed a parallel Particle-Particle, Particle-Mesh (P3M) simulation code for the Cray T3E parallel supercomputer that is well suited to studying the time evolution of systems of particles interacting via gravity and gas forces in…

Astrophysics · Physics 2009-10-30 Tom MacFarland , H. M. P. Couchman , F. R. Pearce , Jakob Pichlmeier

Though ~10 Earth mass rocky/icy cores are commonly held as a prerequisite for the formation of gas giants, theoretical models still struggle to explain how these embryos can form within the lifetimes of gaseous circumstellar disks. In…

Earth and Planetary Astrophysics · Physics 2015-06-22 K. A. Kretke , H. F. Levison

The formation of planetary cores must proceed rapidly in order for the giant planets to accrete their gaseous envelopes before the dissipation of the protoplanetary gas disc (<3 Myr). In orbits beyond 10 AU, direct accumulation of…

Earth and Planetary Astrophysics · Physics 2016-04-05 Michiel Lambrechts , Anders Johansen

An unsolved issue in the standard core accretion model for gaseous planet formation is how kilometre-sized planetesimals form from, initially, micron-sized dust grains. Solid growth beyond metre sizes can be difficult both because the…

Astrophysics · Physics 2009-11-11 W. K. M. Rice , G. Lodato , J. E. Pringle , P. J. Armitage , I. A. Bonnell

We performed N-body simulations of a dust layer without a gas component and examined the formation process of planetesimals. We found that the formation process of planetesimals can be divided into three stages: the formation of…

Astrophysics · Physics 2008-11-26 Shugo Michikoshi , Shu-ichiro Inutsuka , Eiichiro Kokubo , Izumi Furuya

We developed a Keplerian-based Hamiltonian splitting for solving the gravitational $N$-body problem. This splitting allows us to approximate the solution of a general $N$-body problem by a composition of multiple, independently evolved…

Cosmology and Nongalactic Astrophysics · Physics 2015-06-18 G. Gonçalves Ferrari , T. Boekholt , S. F. Portegies Zwart

We describe a new implementation of a parallel Tree-SPH code with the aim to simulate Galaxy Formation and Evolution. The code has been parallelized using SHMEM, a Cray proprietary library to handle communications between the 256 processors…

Astrophysics · Physics 2009-10-31 Cesario Lia , Giovanni Carraro

Planetesimal formation models often invoke the gravitational collapse of pebble clouds to overcome various barriers to grain growth and propose processes to concentrate particles sufficiently to trigger this collapse. On the other hand, the…

Earth and Planetary Astrophysics · Physics 2024-12-11 P. Segretain , H. Méheut , M. Moreira , G. Lesur , C. Robert , J. Mauxion