Amplifying Resonant Repulsion with Inflated Young Planets, Overlooked Inner Planets, and Non-zero Initial $\Delta$

TL;DR

This paper investigates whether eccentricity tides can explain the observed deviations from resonance in multi-planet systems, considering additional effects like planet inflation, overlooked inner planets, and initial conditions, and concludes they are insufficient alone.

Contribution

The study introduces three overlooked effects that amplify eccentricity tides and assesses their impact on the tidal quality factor, showing these effects are inadequate to fully explain observed planetary configurations.

Findings

Eccentricity tides alone cannot account for the observed period deviations.

Inflated young planets and overlooked inner planets modestly increase tidal dissipation.

Additional mechanisms beyond eccentricity tides are necessary to explain planetary system architectures.

Abstract

Most multi-planet systems around mature ($\sim 5$-Gyr-old) host stars are non-resonant. Even the near-resonant planet pairs still display 1-2\% positive deviation from perfect period commensurabilities ($\Delta$) near first-order mean motion resonances (MMR). Resonant repulsion due to eccentricity tides was one of the first mechanisms proposed to explain the observed positive $\Delta$. However, the inferred rates of tidal dissipation are often implausibly rapid (with a reduced tidal quality factor $Q_p^\prime \lesssim 10$). In this work, we attempt to amplify eccentricity tides with three previously ignored effects. 1) Planets tend to be inflated when they were younger. 2) Kepler-like Planets likely form as resonant chains parked at the disk inner edge, overlooked inner planets could have contributed to tidal dissipation of the whole system. 3) Disk migration captures planets into first-order MMR with non-zero initial deviation $\Delta$, thereby lowering the amount of dissipation needed. We show that even after accounting for all three effects, $Q_p^\prime$ can only be amplified by about one order of magnitude, and still falls short of $Q_p^\prime$ values of Solar System planets. Therefore, eccentricity tides alone cannot fully explain the observed $\Delta$ distribution. Other effects such as obliquity tides, planetesimal scattering, expanding disk inner edge, disk turbulence, divergent encounters, and dynamical instabilities must have contributed to dislodging planets from first-order MMR.