OVERSTABLE LIBRATIONS CAN ACCOUNT FOR THE PAUCITY OF MEAN MOTION RESONANCES AMONG EXOPLANET PAIRS
By Peter Goldreich, H. Schlichting. 2013
171 citations recorded by the source corpus.
We assess the multi-planet systems discovered by the Kepler satellite in terms of current ideas about orbital migration and eccentricity damping due to planet–disk interactions. Our primary focus is on first order mean motion resonances, which we investigate analytically to lowest order in eccentricity. Only a few percent of planet pairs are in close proximity to a resonance. However, predicted migration rates (parameterized by ) imply that during convergent migration most planets would have been captured into first order resonances. Eccentricity damping (parameterized by ) offers a plausible resolution. Estimates suggest τe/τn ∼ (h/a)2 ∼ 10−2, where h/a is the ratio of disk thickness to radius. Together, eccentricity damping and orbital migration give rise to an equilibrium eccentricity, eeq ∼ (τe/τn)1/2. Capture is permanent provided eeq ≲ μ1/3, where μ denotes the planet to star mass ratio. But for eeq ≳ μ1/3, capture is only temporary because librations around equilibrium are overstable and lead to passage through resonance on timescale τe. Most Kepler planet pairs have eeq > μ1/3. Since τn ≫ τe is the timescale for migration between neighboring resonances, only a modest percentage of pairs end up trapped in resonances after the disk disappears. Thus the paucity of resonances among Kepler pairs should not be taken as evidence for in situ planet formation or the disruptive effects of disk turbulence. Planet pairs close to a mean motion resonance typically exhibit period ratios 1%–2% larger than those for exact resonance. The direction of this shift undoubtedly reflects the same asymmetry that requires convergent migration for resonance capture. Permanent resonance capture at these separations from exact resonance would demand μ(τn/τe)1/2 ≳ 0.01, a value that estimates of μ from transit data and (τe/τn)1/2 from theory are insufficient to match. Plausible alternatives involve eccentricity damping during or after disk dispersal. The overstability referred to above has applications beyond those considered in this investigation. It was discovered numerically by Meyer & Wisdom in their study of the tidal evolution of Saturn's satellites.
Subfields: Astronomy and Astrophysics, Instrumentation
View Paper: https://www.semanticscholar.org/paper/74b191aa5afa1cb8f7f410c2cede765ca903962a
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Citations in the corpus
- Breaking the chains: hot super-Earth systems from migration and disruption of compact resonant chains (2017, background): “To summarize, the lack of resonance between planet pairs should not be taken as evidence against inward migration (Goldreich & Schlichting 2014).”
- IN SITU FORMATION AND DYNAMICAL EVOLUTION OF HOT JUPITER SYSTEMS (2015, background): “Possible reasons for the relative lack of resonances include turbulent fluctuations in protoplanetary disks (Adams et al. 2008; Rein and Papaloizou 2009), resonant metastability (Goldreich and Schlichting 2014; Deck and Batygin 2015), as well as small disk 6 eccentricities (Batygin 2015).”
- The Occurrence and Architecture of Exoplanetary Systems (2014, background): “Retrospectively, it has been possible to find ways to avoid this faulty conclusion (Goldreich & Schlichting 2014, Chatterjee & Ford 2014).”
- A STELLAR-MASS-DEPENDENT DROP IN PLANET OCCURRENCE RATES (2014, background): “Trapping migrating planets in meanmotion resonances and subsequent destabilization has also been proposed to explain the presence of Kepler multi-planet systems (Baruteau & Papaloizou 2013; Goldreich & Schlichting 2014).”