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arxiv: 2606.06230 · v1 · pith:LWJUJ6SLnew · submitted 2026-06-04 · 🌌 astro-ph.EP

Peas and USPs: Can Stellar Spindown and Peas in a Pod Replicate Ultra-Short-Period Planet Characteristics?

Adam Distler , Juliette Becker This is my paper

Pith reviewed 2026-06-27 23:26 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords exoplanetspeas in a podultra-short-period planetssecular resonancesstellar spindownplanetary migrationorbital dynamics
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The pith

Strictly regular peas-in-a-pod systems cannot decouple their inner planet through stellar spindown resonance crossings.

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

The paper tests whether stellar spindown can explain why ultra-short-period planets differ from peas-in-a-pod chains in inclination, age, and size. It applies Laplace-Lagrange secular theory to the expected drop in stellar J2 and finds that regular planet spacings prevent the resonance crossings needed to decouple the innermost planet. Inner-planet migration must occur first for any crossing to happen. This removes any fixed inner edge beyond which all peas-in-a-pod systems would automatically produce decoupled planets. Crossing times vary with stellar evolution tracks and initial obliquity, providing a potential test of migration history.

Core claim

Strictly PIAP systems with regular spacings cannot undergo secular resonance crossings for the expected stellar J2 evolution, and that we instead require the inner planet to migrate inward to undergo this resonance crossing. As a result, there is no inner edge to PIAP systems where systems will always cross a secular resonance and decouple the inner planet. Using expected J2 evolution tracks from stellar evolution models, we find a diversity of expected resonance crossing times, highlighting the ability to test migration pathways and initial stellar obliquities using this framework.

What carries the argument

Laplace-Lagrange secular theory that tracks how changing stellar J2 alters planet precession rates and drives resonance crossings.

If this is right

  • Inner-planet migration is required before secular resonance crossing can occur in regular peas-in-a-pod systems.
  • Resonance crossing times depend on the star's J2 track and initial obliquity.
  • No universal inner boundary exists that forces all peas-in-a-pod systems to decouple their innermost planet.

Where Pith is reading between the lines

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

  • Observed ultra-short-period planets may arise from initial configurations that are not strictly regular or from processes beyond secular resonance.
  • Age and inclination measurements in young multi-planet systems could distinguish migration pathways.

Load-bearing premise

Stellar J2 follows the tracks from standard stellar evolution models and initial planet spacings remain strictly regular with no extra perturbations.

What would settle it

Detection of a regularly spaced peas-in-a-pod system whose age exceeds the calculated resonance-crossing time yet shows no inner-planet decoupling or migration.

Figures

Figures reproduced from arXiv: 2606.06230 by Adam Distler, Juliette Becker.

Figure 1
Figure 1. Figure 1: Left Panel: comparison between the solar system, typical Peas-in-a-Pod (PIAP) systems, and USP-hosting sys￾tems. Shown are USP-hosting systems such as TOI-125 (Nielsen et al. 2020) and TOI-561 (Piotto et al. 2024); Ke￾pler -342 - a non-USP system with an inner gap (Morton et al. 2016); PIAP systems from the California Kepler Sur￾vey (identifier begins with a ”K0”; Petigura et al. 2017; Weiss et al. 2018); … view at source ↗
Figure 2
Figure 2. Figure 2: Minimum distances as a function of Pinner and ∆ using the PIAP configuration (γ = 1) across a variety of different outer planet masses. We let ζ = 0.25, 1, 4, corresponding to planets of super-Earth, mini-Neptune, and Neptune masses, respectively. We observe that the minimum distances are not dependent on the innermost period, and they tend to decrease as the outer planets’ masses increase. None of the str… view at source ↗
Figure 3
Figure 3. Figure 3: Display of the proximity to a secular resonance as a function of ∆ and γ. For each heat map, the initial inner period was fixed to 5 d, and the zeta was varied between 0.25 and 4. Each heat map displays a star, corresponding to a specific example eigenfrequency evolution in the bottom right panel. We note that the upper colorbar bound of D ≤ 0.15 is arbitrary, and is used to highlight the shift in D across… view at source ↗
Figure 4
Figure 4. Figure 4: J2 and eigenfrequency evolution for the Kepler -80 system (MacDonald et al. 2016), K2-266 Rodriguez et al. (2018), and TOI-125 (Quinn et al. 2019) systems. Top panels: J2 evolution for each system as described by § 2.3 across a range of initial frequencies (Ω∗/Ωb,∗ = 0.01, 0.05, 0.1, 0.3). The median rotator A19 models are shown as a dotted curve . For each system, the line of the last secular resonance cr… view at source ↗
read the original abstract

Peas-in-a-Pod (PIAP) systems have been shown to be common across exoplanet systems, with regular planet spacings and similar planet sizes. In contrast, ultra-short-period planets have displayed distinct differences from PIAP systems, including higher mutual inclinations, ages, and planet sizes. Using Laplace-Lagrange secular theory, we investigate the ability of stellar spindown to decouple PIAP systems. We find that strictly PIAP systems with regular spacings cannot undergo secular resonance crossings for the expected stellar $J_2$ evolution, and that we instead require the inner planet to migrate inward to undergo this resonance crossing. As a result, there is no inner edge to PIAP systems where systems will always cross a secular resonance and decouple the inner planet. Using expected $J_2$ evolution tracks from stellar evolution models, we find a diversity of expected resonance crossing times, highlighting the ability to test migration pathways and initial stellar obliquities using this framework.

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 / 1 minor

Summary. The paper applies Laplace-Lagrange secular theory to Peas-in-a-Pod (PIAP) systems and concludes that strictly regular planet spacings cannot produce secular resonance crossings under the J2(t) evolution tracks predicted by standard stellar-evolution models. Consequently, an inner planet must migrate inward to experience a resonance crossing, implying that no universal inner edge exists at which all PIAP systems decouple. The work also reports a range of resonance-crossing times that could be used to test migration pathways and initial stellar obliquities.

Significance. If the central claim is robust, the result supplies a dynamical mechanism that can help account for the observed differences in mutual inclination, age, and size between PIAP systems and ultra-short-period planets. The framework is built on standard secular theory and published stellar J2 tracks, which is a methodological strength; the diversity of crossing times offers a concrete, observationally testable prediction.

major comments (2)
  1. [Abstract and stellar-evolution section] The central claim that regular spacings preclude resonance crossings rests on the specific functional form and timescale of the adopted J2(t) tracks. No sensitivity tests to alternative initial rotation rates, magnetic-braking prescriptions, or non-standard spindown laws are reported; a modest change in the J2 decay rate could move the resonance condition into the regular-spacing regime.
  2. [Secular-theory methods] The manuscript states that the secular frequencies are computed from Laplace-Lagrange theory with time-dependent J2, yet neither the explicit matrix elements nor the numerical criterion used to identify a resonance crossing are provided. Without these details the assertion that regular spacings never satisfy the crossing condition cannot be independently verified.
minor comments (1)
  1. Notation for the stellar quadrupole moment should be defined at first use (J2 versus J_2) and kept consistent throughout.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which help clarify the presentation of our results. We address each major comment below. Revisions will be made to improve reproducibility and to discuss the dependence on stellar models.

read point-by-point responses

  1. Referee: [Abstract and stellar-evolution section] The central claim that regular spacings preclude resonance crossings rests on the specific functional form and timescale of the adopted J2(t) tracks. No sensitivity tests to alternative initial rotation rates, magnetic-braking prescriptions, or non-standard spindown laws are reported; a modest change in the J2 decay rate could move the resonance condition into the regular-spacing regime.

    Authors: Our central result is that, for the J2(t) evolution predicted by standard stellar models, strictly regular PIAP spacings do not produce secular resonance crossings. We agree that the outcome depends on the adopted spindown law. In revision we will add a short discussion in the stellar-evolution section noting the sensitivity to initial rotation rate and braking prescriptions, with references to alternative models in the literature. Full parameter sweeps lie outside the scope of the present work, but the added text will make the dependence explicit. revision: partial

  2. Referee: [Secular-theory methods] The manuscript states that the secular frequencies are computed from Laplace-Lagrange theory with time-dependent J2, yet neither the explicit matrix elements nor the numerical criterion used to identify a resonance crossing are provided. Without these details the assertion that regular spacings never satisfy the crossing condition cannot be independently verified.

    Authors: We agree that the explicit matrix and crossing criterion should be provided. In the revised manuscript we will include, in a new appendix, the Laplace-Lagrange secular matrix with the time-dependent J2 contribution and state the numerical criterion used to flag a crossing (a secular eigenfrequency passing through the stellar spin-axis precession rate). These additions will allow independent reproduction of the result that regular spacings do not satisfy the crossing condition. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses external J2 tracks and standard secular theory

full rationale

The central claim follows from applying Laplace-Lagrange secular theory to J2 evolution tracks taken from standard stellar evolution models (external inputs). The conclusion that strictly regular PIAP systems do not cross secular resonances is a direct computational outcome of those inputs rather than a redefinition, fitted parameter renamed as prediction, or self-citation chain. No load-bearing steps reduce by construction to the paper's own definitions or prior self-citations.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of Laplace-Lagrange secular theory to these systems and on the accuracy of J2 evolution tracks taken from prior stellar models; no new free parameters or invented entities are introduced in the abstract.

free parameters (1)
  • stellar J2 evolution tracks
    Drawn from external stellar evolution models whose internal parameters are not re-derived here.
axioms (1)
  • domain assumption Laplace-Lagrange secular theory applies to these multi-planet systems
    Invoked to investigate secular resonance crossings driven by stellar spindown.

pith-pipeline@v0.9.1-grok · 5706 in / 1228 out tokens · 29759 ms · 2026-06-27T23:26:43.205849+00:00 · methodology

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