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Rattle-and-Break: the Impact of Planetesimal Scattering on Super-Earth Resonant Chains

Sam Hadden, Yanqin Wu

Abstract

The spacings of super-Earths in multi-transiting systems exhibit a distribution that is broad and mostly featureless, with the exception of notable excesses of planet pairs situated a few percent wide of first-order mean motion resonances (MMRs). In this work, we extend the so-called "breaking-the-chains" model to account for both of these characteristics. Assuming that super-Earths are settled into stable chains of resonances after disk-driven migration, we show that scattering a planetesimal population that contains only a few percent of a system's mass can reorganize primordial chains in remarkable ways. The planetesimal scattering "rattles" the chains by repelling adjacent planet pairs wide of their initial MMRs. Some chains remain rattled but otherwise intact and make up the observed excesses wide of MMRs. In other systems, however, this initial rattling sows the seeds of later orbital instabilities that break the chains entirely. If individual planetesimals' masses are of order a Pluto mass or so, the onset of these instabilities can occur tens or hundreds of Myr after birth, naturally explaining the apparent disappearance of near-resonant pairs on this timescale. The origin of such Pluto-mass debris is currently unknown.

Rattle-and-Break: the Impact of Planetesimal Scattering on Super-Earth Resonant Chains

Abstract

The spacings of super-Earths in multi-transiting systems exhibit a distribution that is broad and mostly featureless, with the exception of notable excesses of planet pairs situated a few percent wide of first-order mean motion resonances (MMRs). In this work, we extend the so-called "breaking-the-chains" model to account for both of these characteristics. Assuming that super-Earths are settled into stable chains of resonances after disk-driven migration, we show that scattering a planetesimal population that contains only a few percent of a system's mass can reorganize primordial chains in remarkable ways. The planetesimal scattering "rattles" the chains by repelling adjacent planet pairs wide of their initial MMRs. Some chains remain rattled but otherwise intact and make up the observed excesses wide of MMRs. In other systems, however, this initial rattling sows the seeds of later orbital instabilities that break the chains entirely. If individual planetesimals' masses are of order a Pluto mass or so, the onset of these instabilities can occur tens or hundreds of Myr after birth, naturally explaining the apparent disappearance of near-resonant pairs on this timescale. The origin of such Pluto-mass debris is currently unknown.
Paper Structure (13 sections, 3 equations, 7 figures, 1 table)

This paper contains 13 sections, 3 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. MMR deficit and the Pile-up
  3. Our Proposal: "rattle-and-break"
  4. Rattling the Chains: Set-up
  5. Rattling the Chains -- Consequences
  6. the HD 110067 analogues
  7. the Kepler-223 analogues
  8. Discussion
  9. Comparison to observed trends
  10. A Dichotomy of Systems?
  11. Comparison to previous works
  12. Two Important Details
  13. Summary

Figures (7)

  • Figure 1: Period ratios of adjacent planets in transiting systems. The top panel shows the histogram of period ratios of all adjacent transiting planets in systems hosting two or more planets. The bottom panel plots the outer versus inner planet pair period ratios for adjacent trios of planets in systems with three or more planets. The loci of first order two-body MMRs and zeroth-order three-body MMRs are indicated by solid black and gray dashed lines, respectively. Young multi-planet systems analyzed by Dai2024 are indicated by stars. Mature resonant chains, shown as large circles, lie along three-body MMRs. Most multi-transiting systems eschew resonant configurations, but show a preference for period ratios just wide of the resonances. Data are taken from the NASA Exoplanet Archive exoplanet-archive-2013.
  • Figure 2: How a resonant chain can be rattled free by planetesimal scattering. Summary of simulation hd110067_ms1_K10_f0.1. The top panel shows the semi-major axes (solid lines) and apocenter-pericenter range (shaded regions) of each planet versus time. The next panel shows planets' orbital eccentricities. The third panel shows adjacent planet pairs' distance from resonance, Equation \ref{['eq:delta_def']}. The fourth panel shows the number of surviving bound planetesimals. The system undergoes a orbital instability after $13\,{\rm Myr}$, resulting in planet mergers, followed but another instability and merger around $40\,{\rm Myr}$, leaving a three-planet system.
  • Figure 3: Same as Fig. \ref{['fig:hd110067_evolution_example']} but now emphasize evolution in the three-body resonances, with each group depicting one adjacent trio in the system. In each panel, the top sub-panel shows the time evolution of a trio's three-body resonance angle, $\phi$ (Equation \ref{['eq:phi_def']}). Bottom sub-panels show the outer planet pair's period ratio versus the inner pair's, colored according to simulation time. The centers and libration widths of each three-body resonance, computed according to Equation C21 of Lammers2024, are indicated by gray lines. Planetesimal scattering causes adjacent planet pairs spread wide of nominal two-body resonance while closely following three-body resonances in the period-ratio plane until an orbital instability occurs after $13\,\rm{Myr}$.
  • Figure 4: The initial (in black) and final orbital architectures of HD 110067 analogue systems that underwent dynamical instabilities. The left-hand panel shows the orbital semi-major axes of planets, along with their apocenter and pericenter distances, indicated by error bars. Average eccentricities, computed over the last 10% of simulation time, are indicated above each planet. The right-hand panel shows, for systems with more than two surviving planets, where they fall in the period ratio-period ratio plane. Once the instabilities occur, all MMRs are disrupted.
  • Figure 5: Same as Figure \ref{['fig:hd110067_evolution_example']}, but for an Kepler-223 analogue (k223_ms1_K10_f0.1). In contrast with HD 110067 simulations, all simulations of Kepler-223 remain dynamically stable for at least $320\,{\rm Myr}$.
  • ...and 2 more figures