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arxiv: 2606.26343 · v1 · pith:BFEK5C32new · submitted 2026-06-24 · 🌌 astro-ph.EP

Architectures of Planetary Systems III: Excitation of Eccentricities and Inclinations

Alex R. Howe , Juliette C. Becker , Fred C. Adams This is my paper

Pith reviewed 2026-06-26 01:19 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords exoplanet architecturesorbital eccentricitydynamical excitationnormalized angular momentum deficitplanetary system classificationsolar system comparisonlong-period planets
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The pith

Large-gap planetary systems exhibit greater eccentricity dispersion than compact ones, rendering the solar system dynamically colder than typical.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper correlates a classification of planetary system architectures with measures of orbital excitation in eccentricity and inclination. It reports that systems with large gaps between planets show higher eccentricity dispersion and elevated eccentricity-specific normalized angular momentum deficit compared with closely spaced systems. Systems with detected outer planets likewise appear more excited. These patterns position the solar system as an outlier with lower excitation than expected for its architecture. The work additionally forecasts a population of highly inclined long-period planets that upcoming astrometric surveys should detect.

Core claim

Extending an earlier classification framework, the analysis finds statistically significant correlations between architecture type and eccentricity distributions. Systems separated by large gaps display more dynamical excitation than compact systems when measured by eccentricity dispersion and an eccentricity-specific NAMD metric. Systems with detected outer planets also register higher excitation levels, so that the solar system appears dynamically colder than most observed systems of similar architecture. Inclination data remain too compromised by selection effects for reliable conclusions, yet the patterns predict a reservoir of highly inclined long-period planets accessible to future ast

What carries the argument

Architecture classification framework that groups systems by inter-planet spacing and presence of outer planets, tested against eccentricity dispersion and eccentricity-specific normalized angular momentum deficit (NAMD).

If this is right

  • Large-gap architectures are expected to retain higher eccentricity dispersion as a signature of past dynamical interactions.
  • Detection of an outer planet correlates with elevated system-wide excitation in the eccentricity metrics.
  • The solar system constitutes an outlier whose low excitation level is atypical for systems with its spacing and outer-planet properties.
  • A population of highly inclined long-period planets remains undetected but should appear in upcoming astrometric data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The observed link between gap size and excitation may trace back to formation pathways that permit more violent scattering when planets are widely spaced.
  • Unbiased future surveys could test whether the solar system's cold state is intrinsically rare or an artifact of current detection limits.
  • The prediction of inclined long-period planets supplies a concrete target for distinguishing between migration and scattering scenarios in formation models.

Load-bearing premise

Eccentricity measurements and architectural classifications drawn from current detections are not substantially distorted by observational selection biases.

What would settle it

A larger, bias-corrected sample of planetary systems in which eccentricity dispersion shows no systematic difference between large-gap and compact architectures would falsify the central correlation.

Figures

Figures reproduced from arXiv: 2606.26343 by Alex R. Howe, Fred C. Adams, Juliette C. Becker.

Figure 1
Figure 1. Figure 1: Abridged quick-reference chart for our classification of planetary system architectures presented in Paper I. Each row corresponds to one planetary system, with horizontal spacing corresponding to orbital period on a log scale and point sizes corresponding to planet size. Colors correspond to planet type: jupiters in red, neptunes in yellow, sub-neptunes in blue, and earths in green. The details of our cla… view at source ↗
Figure 2
Figure 2. Figure 2: Corner plot showing the distributions of minimum eccentricity (emin), maximum eccentricity (emax), eccentricity dispersion (σe), and inclination dispersion (σi) for our dataset. The top three rows include all systems with usable eccentricity measurements; the bottom right panel includes all systems with usable inclination measurements, and the remainder of the bottom row includes systems with both eccentri… view at source ↗
Figure 3
Figure 3. Figure 3: Scatterplot of the system angular momentum deficit in eccentricity NAMDe (calculated by assuming i = 0) versus dispersion σe in eccentricity. Histograms of the two quantities are shown on the top and right of the plot. 4. RESULTS 4.1. Contribution of Eccentricity (Assuming Coplanar Orbits, i = 0) For planets with measured eccentricities, inclinations are available for only about one third of systems. Becau… view at source ↗
Figure 4
Figure 4. Figure 4: Scatterplot of the system angular momentum deficit in inclination NAMDi (calculated by as￾suming e = 0) versus dispersion σi in inclination. Histograms of the two quantities are shown on the top and right of the plot. 4.3. K-S Test Results Figures 2 and 3 show qualitatively that gapped systems and systems with detected outer planets both appear to be dynamically excited when compared with closely-spaced in… view at source ↗
Figure 5
Figure 5. Figure 5: Scatterplot comparing the contribution of inclination (NAMDi) versus eccentricity (NAMDe) to total NAMD. categories “overlap.” This allows us to probe our Paper I classes directly while still accounting for the effects of the greater angular momentum of giant outer planets. Ultimately, this proves not to have a significant effect on our results. To address the problem of multiple comparisons in our analysi… view at source ↗
read the original abstract

The current census of planetary systems displays a wide range of architectures. Extending earlier work, this paper investigates the correlation between our classification framework for these architectures and the distribution of eccentricities and inclinations of planetary orbits using both dispersion and normalized angular momentum deficit (NAMD) metrics. Orbital inclinations prove to be too strongly affected by observational biases to yield meaningful results, but the patterns in eccentricities reveal significant correlations. We find that systems with large gaps between planets are more dynamically excited than closely-spaced systems, based on dispersion in eccentricity and an eccentricity-specific NAMD metric. Systems with detected outer planets also appear dynamically excited, to a degree where our own solar system appears to be dynamically colder than expected. We also predict the existence of a population of highly-inclined long-period planets that is likely to be observed by upcoming astrometric surveys.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper extends prior work on planetary system architectures by correlating classifications (large-gap vs. closely spaced systems; presence/absence of detected outer planets) with dynamical excitation, quantified via eccentricity dispersion and an eccentricity-specific normalized angular momentum deficit (NAMD). It reports that large-gap systems and those with outer planets are more excited, that the solar system is dynamically colder than typical, that inclinations are too biased for analysis, and that a population of highly inclined long-period planets should be detectable by future astrometry.

Significance. If the reported correlations survive bias corrections, the results would constrain formation and migration scenarios by linking architectural features to excitation levels. The adoption of an eccentricity-specific NAMD is a methodological strength for enabling mass-weighted comparisons across heterogeneous systems.

major comments (2)
  1. [Data and sample selection] The central comparison of eccentricity dispersion and NAMD between large-gap and closely-spaced systems (as summarized in the abstract) rests on direct use of catalogued values without forward-modeling of survey selection functions. RV semi-amplitude and transit completeness both favor higher-e and longer-period detections in a manner that correlates with gap size; no injection-recovery or Monte-Carlo test is described that would show the trend persists after these filters.
  2. [Results on systems with outer planets] Classification of systems as having 'detected outer planets' is performed on the same incomplete catalog used for the eccentricity metrics. The claim that such systems appear dynamically excited therefore requires explicit demonstration that the outer-planet detection threshold does not itself induce the reported excitation difference; this is load-bearing for the solar-system comparison.
minor comments (2)
  1. [Abstract] The abstract refers to an 'eccentricity-specific NAMD metric' without a defining equation or reference to its precise formulation; adding this would aid readers.
  2. [Inclination analysis] Inclination results are dismissed due to biases, but the paper could briefly quantify the bias strength (e.g., via a simple completeness estimate) to justify the decision.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments and the recommendation for major revision. We address each major comment below and outline the revisions we will make to strengthen the manuscript's handling of observational biases.

read point-by-point responses

  1. Referee: The central comparison of eccentricity dispersion and NAMD between large-gap and closely-spaced systems (as summarized in the abstract) rests on direct use of catalogued values without forward-modeling of survey selection functions. RV semi-amplitude and transit completeness both favor higher-e and longer-period detections in a manner that correlates with gap size; no injection-recovery or Monte-Carlo test is described that would show the trend persists after these filters.

    Authors: We acknowledge the validity of this concern. Our analysis is based on the directly observed catalog values, as is common in studies of exoplanet demographics. However, we agree that selection effects could potentially influence the results. In the revised manuscript, we will include a dedicated discussion of these biases and conduct a Monte-Carlo test to evaluate the persistence of the trend under assumed detection thresholds. This will be presented as a partial revision since a complete forward-modeling of all survey selection functions is a substantial undertaking that we will note as future work. revision: partial

  2. Referee: Classification of systems as having 'detected outer planets' is performed on the same incomplete catalog used for the eccentricity metrics. The claim that such systems appear dynamically excited therefore requires explicit demonstration that the outer-planet detection threshold does not itself induce the reported excitation difference; this is load-bearing for the solar-system comparison.

    Authors: We agree that this is a critical point for the interpretation, particularly regarding the solar system comparison. We will revise the manuscript to explicitly address this by adding an analysis that examines the excitation levels while accounting for the detection limits of outer planets, such as by restricting the comparison to systems with similar observational coverage. We will also clarify that the solar system is presented as a notable example rather than a statistical outlier based on the current sample. This revision will be incorporated in the next version. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical application of metrics to external catalog

full rationale

The paper classifies observed systems using a prior framework, then computes eccentricity dispersion and an eccentricity-specific NAMD on the same catalog to report correlations. No equation defines the output metric in terms of the architecture labels, no parameter is fitted to a subset and relabeled a prediction, and no uniqueness theorem or ansatz is imported via self-citation to force the result. The reported patterns are direct statistical comparisons against observed values; the forward prediction of inclined planets is likewise a non-circular extrapolation. The derivation chain therefore remains self-contained against the external data.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no information on free parameters, background axioms, or new postulated entities; full text would be required to audit these.

pith-pipeline@v0.9.1-grok · 5678 in / 1020 out tokens · 34174 ms · 2026-06-26T01:19:40.532471+00:00 · methodology

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