Direct Large-Scale N-Body Simulations of Planetesimal Dynamics

Abstract We describe a new direct numerical method for simulating planetesimal dynamics in which N ∼10 6 or more bodies can be evolved simultaneously in three spatial dimensions over hundreds of dynamical times. This represents several orders of magnitude improvement in resolution over previous studies. The advance is made possible through modification of a stable and tested cosmological code optimized for massively parallel computers. However, owing to the excellent scalability and portability of the code, modest clusters of workstations can treat problems with N ∼10 5 particles in a practical fashion. The code features algorithms for detection and resolution of collisions and takes into account the strong central force field and flattened Keplerian disk geometry of planetesimal systems. We demonstrate the range of problems that can be addressed by presenting simulations that illustrate oligarchic growth of protoplanets, planet formation in the presence of giant planet perturbations, the formation of the jovian moons, and orbital migration via planetesimal scattering. We also describe methods under development for increasing the timescale of the simulations by several orders of magnitude.

[1]  Junichiro Makino,et al.  N-Body simulation of gravitational interaction between planetesimals and a protoplanet. I : velocity distribution of planetesimals , 1992 .

[2]  V. Safronov,et al.  Evolution of the protoplanetary cloud and formation of the earth and the planets , 1972 .

[3]  Thomas R. Quinn,et al.  A Three Million Year Integration of the Earth's Orbit , 1991 .

[4]  G. Wetherill,et al.  Formation of planetary embryos: effects of fragmentation, low relative velocity, and independent variation of eccentricity and inclination. , 1993, Icarus.

[5]  G. Lake,et al.  Time stepping N body simulations , 1997, astro-ph/9710043.

[6]  P. Bodenheimer,et al.  Orbital migration of the planetary companion of 51 Pegasi to its present location , 1996, Nature.

[7]  V. S. Safronov,et al.  The random component of planetary rotation , 1991 .

[8]  J. Makino,et al.  Scattering of Planetesimals by a Protoplanet: Slowing Down of Runaway Growth , 1993 .

[9]  Jack Wisdom,et al.  The resonance overlap criterion and the onset of stochastic behavior in the restricted three-body problem , 1980 .

[10]  George W. Wetherill,et al.  Evolution of planetesimal velocities , 1988 .

[11]  Eiichiro Kokubo,et al.  Oligarchic growth of protoplanets , 1996 .

[12]  Gerald Jay Sussman,et al.  The outer solar system for 200 million years , 1986 .

[13]  H. Salo.  Gravitational wakes in Saturn's rings , 1992, Nature.

[14]  S. Tremaine,et al.  Symplectic integrators for solar system dynamics , 1992 .

[15]  J. Makino,et al.  N-body simulation of gravitational interaction between planetesimals and a protoplanet II. Dynamical friction , 1992 .

[16]  A Planetary Companion to a Nearby M4 Dwarf, Gliese 876* , 1998, astro-ph/9807307.

[17]  Hansen,et al.  Migrating planets , 1998, Science.

[18]  S. Ida,et al.  Distribution of Planetesimals around a Protoplanet in the Nebula Gas , 1996 .

[19]  Jack J. Lissauer,et al.  Formation of the Giant Planets by Concurrent Accretion of Solids and Gas , 1995 .

[20]  Evolutionary time scales for circumstellar disks associated with intermediate- and solar-type stars , 1993 .

[21]  S. Ida,et al.  Lunar accretion from an impact-generated disk , 1997, Nature.

[22]  D. Richardson,et al.  A Self-Consistent Numerical Treatment of Fractal Aggregate Dynamics , 1995 .

[23]  E. Kokubo,et al.  ON RUNAWAY GROWTH OF PLANETESIMALS , 1996 .

[24]  Martin J. Duncan,et al.  The long-term evolution of orbits in the solar system: A mapping approach , 1989 .

[25]  DYNAMICS OF ’ THE TRANS-NEPTUNE REGION : APSIDAL WAVES IN THE KUIPER BELT , 1999 .

[26]  S. Ida,et al.  Distribution of planetesimals around a protoplanet in the nebular gas. II. Numerical simulations , 1997 .

[27]  S. Aarseth,et al.  A numerical simulation of the formation of the terrestrial planets , 1986 .

[28]  W. Ward.  Protoplanet Migration by Nebula Tides , 1997 .

[29]  John E. Chambers,et al.  The Stability of Multi-Planet Systems , 1996 .

[30]  W. Benz,et al.  Density of comet Shoemaker–Levy 9 deduced by modelling breakup of the parent 'rubble pile' , 1994, Nature.

[31]  Jon Louis Bentley,et al.  Data Structures for Range Searching , 1979, CSUR.

[32]  D. Lin,et al.  Evolution of planetesimals. I - Dynamics: Relaxation in a thin disk. II - Numerical simulations , 1993 .

[33]  Alan P. Boss,et al.  Giant Planet Formation by Gravitational Instability , 1997 .

[34]  George W. Wetherill,et al.  Accumulation of a swarm of small planetesimals , 1989 .

[35]  S. Aarseth,et al.  N-body simulations of planetary formation , 1990, Monthly Notices of the Royal Astronomical Society.

[36]  D. Richardson,et al.  Tree code simulations of planetary rings , 1994 .

[37]  Renu Malhotra,et al.  The origin of Pluto's peculiar orbit , 1995, Nature.

[38]  William K. Hartmann,et al.  Planetesimals to planets: Numerical simulation of collisional evolution , 1978 .

[39]  S. Tremaine,et al.  Why Does the Earth Spin Forward? , 1993, Science.

[40]  John E. Chambers,et al.  Making the Terrestrial Planets: N-Body Integrations of Planetary Embryos in Three Dimensions , 1998 .

[41]  Richard J. Anderson.  Tree data structures for N-body simulation , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[42]  D. Lin,et al.  Evolution of Planetesimals. II. Numerical Simulations , 1993 .

[43]  P. Hut,et al.  Building a better leapfrog , 1995 .

[44]  J. Lissauer,et al.  Growth of planets from planetesimals , 1991 .

[45]  J. Wisdom,et al.  Symplectic maps for the N-body problem. , 1991 .

[46]  R. Hutchison.  The formation of the Earth , 1974, Nature.

[47]  Junichiro Makino,et al.  On a Hermite Integrator with Ahmad-Cohen Scheme for Gravitational Many-Body Problems , 1992 .

[48]  Jack J. Lissauer,et al.  Timescales for planetary accretion and the structure of the protoplanetary disk , 1986 .

[49]  Peter Goldreich,et al.  Disk-Satellite Interactions , 1980 .

[50]  S. Love,et al.  Tidal Distortion and Disruption of Earth-Crossing Asteroids , 1997 .

[51]  S. Tremaine,et al.  Dark Matter in the Solar System , 1990 .

[52]  R. Greenberg,et al.  Sources of Planetary Rotation: Mapping Planetesimals' Contributions to Angular Momentum , 1996 .

[53]  D. Richardson.  A new tree code method for simulation of planetesimal dynamics , 1993 .

[54]  W. Ward.  Density waves in the solar nebula: Diffential Lindblad torque , 1986 .

[55]  Piet Hut,et al.  A hierarchical O(N log N) force-calculation algorithm , 1986, Nature.

[56]  S. Weidenschilling.  The distribution of mass in the planetary system and solar nebula , 1977 .

[57]  C. Chapman,et al.  Distribution of taxonomic classes and the compositional structure of the asteroid belt. , 1989 .

[58]  C. Hayashi.  Structure of the Solar Nebula, Growth and Decay of Magnetic Fields and Effects of Magnetic and Turbulent Viscosities on the Nebula , 1981 .

[59]  H. Melosh,et al.  The origin of the moon and the single-impact hypothesis III. , 1991, Icarus.

[60]  Harold F. Levison,et al.  The Long-Term Dynamical Behavior of Short-Period Comets , 1993 .

[61]  E. Kokubo,et al.  Orbital Evolution of Protoplanets Embedded in a Swarm of Planetesimals , 1995 .

[62]  H. Yoshida.  Construction of higher order symplectic integrators , 1990 .