skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: TRANSIENT CHAOS AND FRACTAL STRUCTURES IN PLANETARY FEEDING ZONES

Abstract

The circular restricted three-body problem is investigated in the context of accretion and scattering processes. In our model, a large number of identical non-interacting mass-less planetesimals are considered in the planar case orbiting a star-planet system. This description allows us to investigate the gravitational scattering and possible capture of the particles by the forming planetary embryo in a dynamical systems approach. Although the problem serves a large variety of complex motions, the results can be easily interpreted because of the low dimensionality of the phase space. We show that initial conditions define isolated regions of the disk, where planetesimals accrete or escape, which have, in fact, a fractal structure. The fractal geometry of these ''basins'' implies that the dynamics is very complex. Based on the calculated escape rates and escape times, it is also demonstrated that the planetary accretion rate is exponential for short times and follows a power law for longer integration. A new numerical calculation of the maximum mass that a planet can reach (described by the expression of the isolation mass) is also derived.

Authors:
 [1];  [2]
  1. Also at University of Applied Sciences, Nagy Lajos kir. útja 1-9, H-1148 Budapest, Hungary. (Hungary)
  2. Konkoly Observatory of the Hungarian Academy of Sciences, P.O. Box 67, H-1525 Budapest (Hungary)
Publication Date:
OSTI Identifier:
22364747
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal Letters; Journal Volume: 798; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCRETION DISKS; CHAOS THEORY; FRACTALS; MASS; PHASE SPACE; PLANETS; SATELLITES; SCATTERING; STAR EVOLUTION; STARS; THREE-BODY PROBLEM; TRANSIENTS

Citation Formats

Kovács, T., and Regály, Zs. TRANSIENT CHAOS AND FRACTAL STRUCTURES IN PLANETARY FEEDING ZONES. United States: N. p., 2015. Web. doi:10.1088/2041-8205/798/1/L9.
Kovács, T., & Regály, Zs. TRANSIENT CHAOS AND FRACTAL STRUCTURES IN PLANETARY FEEDING ZONES. United States. doi:10.1088/2041-8205/798/1/L9.
Kovács, T., and Regály, Zs. Thu . "TRANSIENT CHAOS AND FRACTAL STRUCTURES IN PLANETARY FEEDING ZONES". United States. doi:10.1088/2041-8205/798/1/L9.
@article{osti_22364747,
title = {TRANSIENT CHAOS AND FRACTAL STRUCTURES IN PLANETARY FEEDING ZONES},
author = {Kovács, T. and Regály, Zs.},
abstractNote = {The circular restricted three-body problem is investigated in the context of accretion and scattering processes. In our model, a large number of identical non-interacting mass-less planetesimals are considered in the planar case orbiting a star-planet system. This description allows us to investigate the gravitational scattering and possible capture of the particles by the forming planetary embryo in a dynamical systems approach. Although the problem serves a large variety of complex motions, the results can be easily interpreted because of the low dimensionality of the phase space. We show that initial conditions define isolated regions of the disk, where planetesimals accrete or escape, which have, in fact, a fractal structure. The fractal geometry of these ''basins'' implies that the dynamics is very complex. Based on the calculated escape rates and escape times, it is also demonstrated that the planetary accretion rate is exponential for short times and follows a power law for longer integration. A new numerical calculation of the maximum mass that a planet can reach (described by the expression of the isolation mass) is also derived.},
doi = {10.1088/2041-8205/798/1/L9},
journal = {Astrophysical Journal Letters},
number = 1,
volume = 798,
place = {United States},
year = {Thu Jan 01 00:00:00 EST 2015},
month = {Thu Jan 01 00:00:00 EST 2015}
}