Amplifying Resonant Repulsion with Inflated Young Planets, Overlooked Inner Planets, and Nonzero Initial Δ

Abstract Most multiplanet systems around mature (∼5 Gyr old) host stars are nonresonant. Even the near-resonant planet pairs still display 1%–2% positive deviation from perfect period commensurabilities (Δ) near first-order mean motion resonances (MMRs). Resonant repulsion due to eccentricity tides was one of the first mechanisms proposed to explain the observed positive Δ. However, the inferred rates of tidal dissipation are often implausibly rapid (with a reduced tidal quality factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>≲</mml:mo> <mml:mn>10</mml:mn> </mml:math> ). 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 nonzero initial deviation Δ, thereby lowering the amount of dissipation needed. We show that even after accounting for all three effects, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> can only be amplified by about 1 order of magnitude, and still falls short of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> values of solar system planets. Therefore, eccentricity tides alone cannot fully explain the observed Δ 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.