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A general model of resonance capture in planetary systems: first- and second-order resonances

Mustill, Alexander LU and Wyatt, Mark C (2011) In Monthly Notices of the Royal Astronomical Society 413(1). p.554-572
Abstract
Mean motion resonances are a common feature of both our own Solar system and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semimajor axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first- and second-order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a massive planet. We quantify how the probability of capture into a resonance depends on the relative migration rate of the planet and particle, and the... (More)
Mean motion resonances are a common feature of both our own Solar system and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semimajor axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first- and second-order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a massive planet. We quantify how the probability of capture into a resonance depends on the relative migration rate of the planet and particle, and the particle's eccentricity. Resonant capture fails for high migration rates, and has decreasing probability for higher eccentricities, although for certain migration rates, capture probability peaks at a finite eccentricity. More massive planets can capture particles at higher eccentricities and migration rates. We also calculate libration amplitudes and the offset of the libration centres for captured particles, and the change in eccentricity if capture does not occur. Libration amplitudes are higher for larger initial eccentricity. The model allows for a complete description of a particle's behaviour as it successively encounters several resonances. Data files containing the integration grid output will be available online. We discuss implications for several scenarios: (i) Planet migration through gas discs trapping other planets or planetesimals in resonances: we find that, with classical prescriptions for Type I migration, capture into second-order resonances is not possible, and lower mass planets or those further from the star should trap objects in first-order resonances closer to the planet than higher mass planets or those closer to the star. For fast enough migration, a planet can trap no objects into its resonances. We suggest that the present libration amplitude of planets may be a signature of their eccentricities at the epoch of capture, with high libration amplitudes suggesting high eccentricity (e.g. HD 128311). (ii) Planet migration through a debris disc: we find the resulting dynamical structure depends strongly both on migration rate and on planetesimal eccentricity. Translating this to spatial structure, we expect clumpiness to decrease from a significant level at e ≲ 0.01 to non-existent at e ≳ 0.1. (iii) Dust migration through Poynting-Robertson (PR) drag: we predict that Mars should have its own resonant ring of particles captured from the zodiacal cloud, and that the capture probability is ≲25 per cent that of the Earth, consistent with published upper limits for its resonant ring. To summarize, the Hamiltonian model will allow quick interpretation of the resonant properties of extrasolar planets and Kuiper Belt Objects, and will allow synthetic images of debris disc structures to be quickly generated, which will be useful for predicting and interpreting disc images made with Atacama Large Millimeter Array (ALMA), Darwin/Terrestrial Planet Finder (TPF) or similar missions. (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Astrophysics - Earth and Planetary Astrophysics, celestial mechanics, disc interactions, planet, planets and satellites: dynamical evolution and stability, protoplanetary discs, zodiacal dust
in
Monthly Notices of the Royal Astronomical Society
volume
413
issue
1
pages
554 - 572
publisher
Wiley-Blackwell
external identifiers
  • Scopus:79959277956
ISSN
1365-2966
DOI
10.1111/j.1365-2966.2011.18201.x
language
English
LU publication?
no
id
8711a5be-16d8-4514-937e-acfa1aee5e24 (old id 4500295)
date added to LUP
2014-06-25 15:08:32
date last changed
2016-10-27 13:02:21
@misc{8711a5be-16d8-4514-937e-acfa1aee5e24,
  abstract     = {Mean motion resonances are a common feature of both our own Solar system and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semimajor axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first- and second-order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a massive planet. We quantify how the probability of capture into a resonance depends on the relative migration rate of the planet and particle, and the particle's eccentricity. Resonant capture fails for high migration rates, and has decreasing probability for higher eccentricities, although for certain migration rates, capture probability peaks at a finite eccentricity. More massive planets can capture particles at higher eccentricities and migration rates. We also calculate libration amplitudes and the offset of the libration centres for captured particles, and the change in eccentricity if capture does not occur. Libration amplitudes are higher for larger initial eccentricity. The model allows for a complete description of a particle's behaviour as it successively encounters several resonances. Data files containing the integration grid output will be available online. We discuss implications for several scenarios: (i) Planet migration through gas discs trapping other planets or planetesimals in resonances: we find that, with classical prescriptions for Type I migration, capture into second-order resonances is not possible, and lower mass planets or those further from the star should trap objects in first-order resonances closer to the planet than higher mass planets or those closer to the star. For fast enough migration, a planet can trap no objects into its resonances. We suggest that the present libration amplitude of planets may be a signature of their eccentricities at the epoch of capture, with high libration amplitudes suggesting high eccentricity (e.g. HD 128311). (ii) Planet migration through a debris disc: we find the resulting dynamical structure depends strongly both on migration rate and on planetesimal eccentricity. Translating this to spatial structure, we expect clumpiness to decrease from a significant level at e ≲ 0.01 to non-existent at e ≳ 0.1. (iii) Dust migration through Poynting-Robertson (PR) drag: we predict that Mars should have its own resonant ring of particles captured from the zodiacal cloud, and that the capture probability is ≲25 per cent that of the Earth, consistent with published upper limits for its resonant ring. To summarize, the Hamiltonian model will allow quick interpretation of the resonant properties of extrasolar planets and Kuiper Belt Objects, and will allow synthetic images of debris disc structures to be quickly generated, which will be useful for predicting and interpreting disc images made with Atacama Large Millimeter Array (ALMA), Darwin/Terrestrial Planet Finder (TPF) or similar missions.},
  author       = {Mustill, Alexander and Wyatt, Mark C},
  issn         = {1365-2966},
  keyword      = {Astrophysics - Earth and Planetary Astrophysics,celestial mechanics,disc interactions,planet,planets and satellites: dynamical evolution and stability,protoplanetary discs,zodiacal dust},
  language     = {eng},
  number       = {1},
  pages        = {554--572},
  publisher    = {ARRAY(0x9388020)},
  series       = {Monthly Notices of the Royal Astronomical Society},
  title        = {A general model of resonance capture in planetary systems: first- and second-order resonances},
  url          = {http://dx.doi.org/10.1111/j.1365-2966.2011.18201.x},
  volume       = {413},
  year         = {2011},
}