Consequences of tidal interaction between disks and orbiting protoplanets for the evolution of multi-planet systems with architecture resembling that of Kepler 444

Abstract

We study orbital evolution of multi-planet systems with masses in the terrestrial planet regime induced through tidal interaction with a protoplanetary disk assuming that this is the dominant mechanism for producing orbital migration and circularization. We develop a simple analytic model for a system that maintains consecutive pairs in resonance while undergoing orbital circularization and migration. Migration times for each planet may be estimated once planet masses, circularization times and the migration time for the innermost planet are given. We applied it to a model system with the current architecture of Kepler 444 interacting with a protoplanetary disk, the evolution time for the system as a whole being comparable to current protoplanetary disk lifetimes. In addition we performed numerical simulations with input data obtained from this model. These indicate that although the analytic model is inexact, relatively small corrections to estimated migration rates yield systems for which period ratios vary by a minimal extent. Because of relatively large deviations from exact resonance in the observed system of up to $2\%,$ the migration times obtained in this way indicate only weak convergent migration such that a system for which the planets did not interact would contract by only $\sim 1\%$ although undergoing significant inward migration as a whole. We performed additional simulations to investigate how the system could undergo significant convergent migration before reaching its final state. These indicate migration times have to be significantly shorter and resonances significantly closer. Relative migration rates would then have to decrease allowing period ratios to increase to become more distant from resonances as the system approached its final state in the inner regions of the protoplanetary disk (abridged).

Accepted for publication in Celestial Mechanics and Dynamical Astronomy

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Cited by in corpus (12)

• Convergent Migration Renders TRAPPIST-1 Long-lived
• The TRAPPIST-1 system: Orbital evolution, tidal dissipation, formation and habitability
• Analytical model of multi-planetary resonant chains and constraints on migration scenarios
• Mass, Density, and Formation Constraints in the Compact, Sub-Earth Kepler-444 System including Two Mars-Mass Planets
• TOI-216: Resonant Constraints on Planet Migration
• Resonant Chains of Exoplanets: Libration Centers for Three-body Angles
• Revisiting Kepler-444. II. Rotational, orbital and high-energy fluxes evolution of the system
• Global dynamics and architecture of the Kepler-444 system
• The dynamics of the de Sitter resonance
• The orbital evolution of resonant chains of exoplanets incorporating circularisation produced by tidal interaction with the central star with application to the HD 158259 and EPIC 245950175 systems
• On the Ordering of Exoplanet Systems
• How to measure tidal dissipation in long resonant chains