FIRSTORDER RESONANCE OVERLAP AND THE STABILITY OF CLOSE TWOPLANET SYSTEMS
Abstract
Motivated by the population of observed multiplanet systems with orbital period ratios 1 < P{sub 2}/P{sub 1} {approx}< 2, we study the longterm stability of packed twoplanet systems. The Hamiltonian for two massive planets on nearly circular and nearly coplanar orbits near a firstorder mean motion resonance can be reduced to a onedegreeoffreedom problem. Using this analytically tractable Hamiltonian, we apply the resonance overlap criterion to predict the onset of largescale chaotic motion in close twoplanet systems. The reduced Hamiltonian has only a weak dependence on the planetary mass ratio m{sub 1}/m{sub 2}, and hence the overlap criterion is independent of the planetary mass ratio at lowest order. Numerical integrations confirm that the planetary mass ratio has little effect on the structure of the chaotic phase space for close orbits in the loweccentricity (e {approx}< 0.1) regime. We show numerically that orbits in the chaotic web produced primarily by firstorder resonance overlap eventually experience largescale erratic variation in semimajor axes and are therefore Lagrange unstable. This is also true of the orbits in this overlap region which satisfy the Hill criterion. As a result, we can use the firstorder resonance overlap criterion as an effective stability criterion for pairs ofmore »
 Authors:
 Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States)
 HarvardSmithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
 Publication Date:
 OSTI Identifier:
 22133888
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Astrophysical Journal; Journal Volume: 774; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CHAOS THEORY; DEGREES OF FREEDOM; HAMILTONIANS; ORBITS; PHASE SPACE; PLANETS; RESONANCE; TWOBODY PROBLEM
Citation Formats
Deck, Katherine M., Payne, Matthew, and Holman, Matthew J., Email: kdeck@mit.edu. FIRSTORDER RESONANCE OVERLAP AND THE STABILITY OF CLOSE TWOPLANET SYSTEMS. United States: N. p., 2013.
Web. doi:10.1088/0004637X/774/2/129.
Deck, Katherine M., Payne, Matthew, & Holman, Matthew J., Email: kdeck@mit.edu. FIRSTORDER RESONANCE OVERLAP AND THE STABILITY OF CLOSE TWOPLANET SYSTEMS. United States. doi:10.1088/0004637X/774/2/129.
Deck, Katherine M., Payne, Matthew, and Holman, Matthew J., Email: kdeck@mit.edu. Tue .
"FIRSTORDER RESONANCE OVERLAP AND THE STABILITY OF CLOSE TWOPLANET SYSTEMS". United States.
doi:10.1088/0004637X/774/2/129.
@article{osti_22133888,
title = {FIRSTORDER RESONANCE OVERLAP AND THE STABILITY OF CLOSE TWOPLANET SYSTEMS},
author = {Deck, Katherine M. and Payne, Matthew and Holman, Matthew J., Email: kdeck@mit.edu},
abstractNote = {Motivated by the population of observed multiplanet systems with orbital period ratios 1 < P{sub 2}/P{sub 1} {approx}< 2, we study the longterm stability of packed twoplanet systems. The Hamiltonian for two massive planets on nearly circular and nearly coplanar orbits near a firstorder mean motion resonance can be reduced to a onedegreeoffreedom problem. Using this analytically tractable Hamiltonian, we apply the resonance overlap criterion to predict the onset of largescale chaotic motion in close twoplanet systems. The reduced Hamiltonian has only a weak dependence on the planetary mass ratio m{sub 1}/m{sub 2}, and hence the overlap criterion is independent of the planetary mass ratio at lowest order. Numerical integrations confirm that the planetary mass ratio has little effect on the structure of the chaotic phase space for close orbits in the loweccentricity (e {approx}< 0.1) regime. We show numerically that orbits in the chaotic web produced primarily by firstorder resonance overlap eventually experience largescale erratic variation in semimajor axes and are therefore Lagrange unstable. This is also true of the orbits in this overlap region which satisfy the Hill criterion. As a result, we can use the firstorder resonance overlap criterion as an effective stability criterion for pairs of observed planets. We show that for lowmass ({approx}< 10 M{sub CircledPlus }) planetary systems with initially circular orbits the period ratio at which complete overlap occurs and widespread chaos results lies in a region of parameter space which is Hill stable. Our work indicates that a resonance overlap criterion which would apply for initially eccentric orbits likely needs to take into account secondorder resonances. Finally, we address the connection found in previous work between the Hill stability criterion and numerically determined Lagrange instability boundaries in the context of resonance overlap.},
doi = {10.1088/0004637X/774/2/129},
journal = {Astrophysical Journal},
number = 2,
volume = 774,
place = {United States},
year = {Tue Sep 10 00:00:00 EDT 2013},
month = {Tue Sep 10 00:00:00 EDT 2013}
}

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