Analytical model of multi-planetary resonant chains and constraints on migration scenarios

Abstract

Resonant chains are groups of planets for which each pair is in resonance, with an orbital period ratio locked at a rational value (2/1, 3/2, etc.). Such chains naturally form as a result of convergent migration of the planets in the proto-planetary disk. In this article, I present an analytical model of resonant chains of any number of planets. Using this model, I show that a system captured in a resonant chain can librate around several possible equilibrium configurations. The probability of capture around each equilibrium depends on how the chain formed, and especially on the order in which the planets have been captured in the chain. Therefore, for an observed resonant chain, knowing around which equilibrium the chain is librating allows for constraints to be put on the formation and migration scenario of the system. I apply this reasoning to the four planets orbiting Kepler-223 in a 3:4:6:8 resonant chain. I show that the system is observed around one of the six equilibria predicted by the analytical model. Using N-body integrations, I show that the most favorable scenario to reproduce the observed configuration is to first capture the two intermediate planets, then the outermost, and finally the innermost.

arXiv commentAccepted for publication in A&A

References in corpus (10)

• A resonant chain of four transiting, sub-Neptune planets
• Transit Timing Observations from Kepler: VII. Confirmation of 27 planets in 13 multiplanet systems via Transit Timing Variations and orbital stability
• The Laplace resonance in the Kepler-60 system
• Dissipation in planar resonant planetary systems
• On the dynamics of multiple systems of hot super-Earths and Neptunes: Tidal circularization, resonance and the HD 40307 system
• Resonance breaking due to dissipation in planar planetary systems
• Three body resonances in close orbiting planetary systems: Tidal dissipation and orbital evolution
• Stability of resonant configurations during the migration of planets and constraints on disk-planet interactions
• Trapping in three-planet resonances during gas-driven migration
• Consequences of tidal interaction between disks and orbiting protoplanets for the evolution of multi-planet systems with architecture resembling that of Kepler 444

Cited by in corpus (39)

• Six transiting planets and a chain of Laplace resonances in TOI-178
• Warm terrestrial planet with half the mass of Venus transiting a nearby star
• Planetary system LHS 1140 revisited with ESPRESSO and TESS
• TOI-1136 is a Young, Coplanar, Aligned Planetary System in a Pristine Resonant Chain
• The path to instability in compact multi-planetary systems
• A resonant sextuplet of sub-Neptunes transiting the bright star HD 110067
• The SOPHIE search for northern extrasolar planets. XVI. HD 158259: A compact planetary system in a near-3:2 mean motion resonance chain
• Orbital and dynamical analysis of the system around HR 8799. New astrometric epochs from VLT/SPHERE and LBT/LUCI
• An exact, generalised Laplace resonance in the HR 8799 planetary system
• Resonance Capture and Dynamics of 3-Planet Systems
• Masses for the seven planets in K2-32 and K2-233. Four diverse planets in resonant chain and the first young rocky worlds
• Unbiasing the density of TTV-characterised sub-Neptunes: Update of the mass-radius relationship of 34 Kepler planets
• Three Pathways for Observed Resonant Chains
• Alleviating the transit timing variation bias in transit surveys. I. RIVERS: Method and detection of a pair of resonant super-Earths around Kepler-1705
• Resonant Chains of Exoplanets: Libration Centers for Three-body Angles
• Sequential giant planet formation initiated by disc substructure
• celmech: A Python package for celestial mechanics
• Prospecting for exo-Earths in multiple planet systems with a gas giant
• A Tidal Origin for a 3-body Resonance in Kepler-221
• Predicting multiple planet stability and habitable zone companions in the TESS era
• The Kepler-223 resonance holds information on turbulence during the gas disk phase
• Dynamical Evolution of Closely Packed Multiple Planetary Systems Subject to Atmospheric Mass-Loss
• Forming the Trappist-1 system in two steps during the recession of the disc inner edge
• Stability Constrained Characterization of the 23 Myr-old V1298 Tau System: Do Young Planets Form in Mean Motion Resonance Chains?
• Alleviating the Transit Timing Variations bias in transit surveys. II. RIVERS: Twin resonant Earth-sized planets around Kepler-1972 recovered from Kepler's false positive
• Laplace-like resonances with tidal effects
• Tidal interactions shape period ratios in planetary systems with three-body resonant chains
• Characterization of the HD 108236 system with CHEOPS and TESS. Confirmation of a fifth transiting planet
• WASP-35 and HAT-P-30/WASP-51: re-analysis using TESS and ground-based transit photometry
• Kepler-80 Revisited: Assessing the Participation of a Newly Discovered Planet in the Resonant Chain
• The study on transiting systems HAT-P-13, HAT-P-16 and WASP-32 through combining ground-based and TESS photometry
• Inferred Properties of Planets in Mean-Motion Resonances are Biased by Measurement Noise
• Dynamics of co-orbital exoplanets in a first order resonance chain with tidal dissipation
• Resonant chains in triple-planetary systems
• Transit Timing Variations in HIP 41378: CHEOPS and TESS confirm a non-transiting sixth planet in the system
• The Dynamical History of the Kepler-221 Planet System
• Semi-analytical model for planetary resonances: application to planets around single and binary stars
• How to measure tidal dissipation in long resonant chains
• The Effects of Disk Induced Apsidal Precession on Planets Captured into Mean Motion Resonance