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

TL;DR

This study models how tidal interactions with a protoplanetary disk influence the orbital evolution of multi-planet systems like Kepler 444, highlighting weak convergent migration and the potential for significant inward movement before final stabilization.

Contribution

It introduces an analytic model for orbital migration and resonance maintenance in multi-planet systems, applied specifically to Kepler 444, and validates it with numerical simulations.

Findings

Migration times are comparable to protoplanetary disk lifetimes.

Observed deviations from resonance suggest weak convergent migration.

Significant inward migration requires shorter migration times and closer resonances.

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).