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<p>The Kepler space telescope was a successful mission that used the transit method. Multi–planetary systems are interesting because they are dynamically rich due to the planets’ interactions. Kepler’s mission was the first to find a system with four planets all in resonance, that is <i>Kepler–223</i>. The <i>Kepler–223</i> system is of unique dynamical interest as the first exoplanetary system confirmed to host four sub–Neptune planets in a precise 3:4:6:8 resonant chain. Previous dynamical studies have struggled to fully recover the long–term phase protection mechanisms, often finding that higher–order resonant angles circulate rather than librate. In this work, we re–examine the dynamical state of <i>Kepler–223</i> by performing high–resolution N–body integrations and constructing detailed stability maps in the <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>e</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(a,e)$</EquationSource> </InlineEquation> phase space, we demonstrate that the system is locked in a deeper resonant state than previously thought. Crucially, we find that all resonant arguments, exhibit robust libration over secular timescales. Our stability maps reveal that the planets reside in clearly defined stability islands that allow for higher eccentricities than previous estimates. We further compare these numerical islands with analytical resonance widths and find excellent agreement for the inner three planets, while the outermost planet (<i>Kepler–223</i>e) exhibits a stability region wider than first–order analytical theories predict, suggesting complex multi–body stabilization effects at the edge of the chain.</p>

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The dynamical environment of Kepler–223 planetary system

  • 期刊论文

  • 发表日期：

    2026年5月4日

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  • Carlos E. Chavez,
  • Adrián Fierro,
  • Ándres Avilés

摘要

The Kepler space telescope was a successful mission that used the transit method. Multi–planetary systems are interesting because they are dynamically rich due to the planets’ interactions. Kepler’s mission was the first to find a system with four planets all in resonance, that is Kepler–223. The Kepler–223 system is of unique dynamical interest as the first exoplanetary system confirmed to host four sub–Neptune planets in a precise 3:4:6:8 resonant chain. Previous dynamical studies have struggled to fully recover the long–term phase protection mechanisms, often finding that higher–order resonant angles circulate rather than librate. In this work, we re–examine the dynamical state of Kepler–223 by performing high–resolution N–body integrations and constructing detailed stability maps in the ( a , e ) $(a,e)$ phase space, we demonstrate that the system is locked in a deeper resonant state than previously thought. Crucially, we find that all resonant arguments, exhibit robust libration over secular timescales. Our stability maps reveal that the planets reside in clearly defined stability islands that allow for higher eccentricities than previous estimates. We further compare these numerical islands with analytical resonance widths and find excellent agreement for the inner three planets, while the outermost planet (Kepler–223e) exhibits a stability region wider than first–order analytical theories predict, suggesting complex multi–body stabilization effects at the edge of the chain.