Amplifying Resonant Repulsion with Inflated Young Planets, Overlooked Inner Planets, and Non-zero Initial $\Delta$

Fei Dai; Yuancheng Xu

REVIEW 3 major objections 6 minor 109 references

Amplifying Resonant Repulsion with Inflated Young Planets, Overlooked Inner Planets, and Non-zero Initial $\Delta$

T0 review · 3 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Even with all three proposed amplifiers, eccentricity tides still cannot explain the observed 1–2% near-resonance offsets.

desk verdict Clear, honest negative result that sharpens the resonant-repulsion tension, but the quoted 'one order of magnitude' amplifier is capped by an ad hoc two-planet/20-day rule that needs a robustness test before it is treated as final. read the letter →

arxiv 2502.01903 v1 pith:ZUNXPRMC submitted 2025-02-04 astro-ph.EP

Yuancheng Xu , Fei Dai This is my paper · ORCID

classification astro-ph.EP

keywords resonantrepulsioneccentricitytidesmean-motionresonancestidalqualityfactorKeplerexoplanetsperiodratiodeviationchaindiskmigration

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Most mature Kepler systems sit slightly wide of first-order mean-motion resonances: the period ratio is 1–2% larger than the exact commensurability. A long-standing proposed cause is resonant repulsion by eccentricity tides, but the tidal dissipation rate needed is implausibly fast, equivalent to a reduced quality factor $Q_p' \lesssim 10$. The paper asks whether three previously ignored effects — youthful radius inflation, overlooked planets inside the resonant pair, and a non-zero initial offset $\Delta_i$ at resonance capture — can raise the required $Q_p'$ to values like those in the Solar System. It finds that together the three effects raise $Q_p'$ by only about one order of magnitude, and the required values remain well below Solar System estimates. The authors conclude that eccentricity tides by themselves cannot produce the observed $\Delta$ distribution, and that other dislodging mechanisms must operate.

What carries the argument

The engine of the paper is the eccentricity-tide resonant repulsion equation of Lithwick & Wu (2012): $\Delta^2\,d\Delta/dt$ is proportional to $(Q_p')^{-1}\,R_p^5\,P^{-13/3}$ times resonance-dependent factors, so after integrating from an initial offset $\Delta_i$ to the observed $\Delta_f$, the required dissipation obeys roughly $Q_p' \propto (\Delta_f^3 - \Delta_i^3)^{-1}$. Around this identity the paper stacks three amplifiers: an effective radius $R_{\rm eff}$ defined by time-averaging $R(t)^5$ over the planet's contraction history (so inflated youth enters as the fifth power of radius); the resonant-chain repulsion effect, by which tides on an overlooked innermost planet push the whole chain outward; and the initial-offset distribution $\log_{10}\Delta_i = -3.4 \pm 0.5$ from the companion migration simulations, which turns out to be too small to matter. The machinery converts each observed pair into a posterior over $Q_p'$ through bootstrap resampling, then compares with Solar System calibrations.

What would settle it

Re-run the inference with an initial offset distribution centered at $\Delta_i \approx 0.006$–$0.01$ (the observed near-resonance range) rather than $10^{-3.4}$; because $Q_p'$ scales as $(\Delta_f^3-\Delta_i^3)^{-1}$, this raises the inferred $Q_p'$ by an order of magnitude or more and can remove the gap to Solar System values. Alternatively, a $\lesssim10$-Myr-old system already showing $\Delta\sim1\%$ with no sign of other dislodging mechanisms would show the offsets are not a slow tidal product.

Watch

Extended reading notes

Core claim

On the paper's own terms: using 80 near-resonant Kepler pairs with ages from isochrones, the authors integrate the eccentricity-tide repulsion equation and infer the reduced tidal quality factor $Q_p'$ needed to reach the observed period-ratio deviation $\Delta$. In the simplest model the inferred values are $\log_{10} Q_p' = 0.1 \pm 2.1$ for super-Earths and $1.5 \pm 1.6$ for mini-Neptunes. Adding inflated young radii raises $\log_{10}Q_p'$ by $0.5\pm0.2$ for super-Earths and $0.11\pm0.08$ for mini-Neptunes; adding up to two hidden inner planets raises it by $0.9\pm0.3$; and drawing the initial offset from their disk-migration simulations, $\log_{10}\Delta_i = -3.4 \pm 0.5$, changes it by less than $0.1$ in 95% of cases. The combined model gives $\log_{10}Q_p' = 1.2 \pm 2.1$ for super-Earths and $2.4\pm1.7$ for mini-Neptunes — still far below the Solar System values of $\sim10^3$ for rocky planets and $\sim10^5$ for giant planets. The paper concludes that eccentricity tides alone cannot explain the observed $\Delta$ pile-up, and that mechanisms such as obliquity tides, planetesimal scattering, disk-edge expansion, disk turbulence, divergent encounters, or instabilities must contribute.

Load-bearing premise

The load-bearing premise is that resonant capture leaves planets with a very tiny starting offset, $\log_{10}\Delta_i = -3.4\pm0.5$, taken from an unpublished companion simulation; if real starting offsets were closer to the observed 1–2% values, the required tidal dissipation would drop sharply and the claimed shortfall could disappear.

Editorial extensions

If this is right

Within the modeled assumptions, any eccentricity-tide explanation of the near-resonant Kepler population must still demand $Q_p'$ typically of order $10$–$10^3$, far below the values measured or inferred for Solar System bodies.
The observed 1–2% positive $\Delta$ pile-up and the presence of non-zero TTV phases are both signatures that at least one additional mechanism — obliquity tides, planetesimal scattering, disk-edge expansion, disk turbulence, divergent encounters, or dynamical instability — is shaping near-resonant systems.
Hidden close-in companions are the single largest amplifier tested, worth nearly an order of magnitude in $Q_p'$; systems whose inner planets are missing from transit surveys are the ones where a pure-tide interpretation is most misleading.
Very young ($\sim20$ Myr) near-resonant systems like HD 109833 and V1298 Tau already exhibit $\Delta = 0.8$–$1\%$, too early for eccentricity tides to have produced, so those systems independently argue for a non-tidal origin.
Radius inflation is a stronger amplifier for super-Earths (a $\log_{10}$ change of about 0.5) than for mini-Neptunes (about 0.1), so future radius-evolution models that couple tidal heating to inflation could shift the super-Earth part of the inferred $Q_p'$ distribution more.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A testable extension: re-run the inference with initial offsets drawn from the observed near-resonance range, $\Delta_i \approx 0.006$–$0.01$, rather than $10^{-3.4}$; because $Q_p' \propto (\Delta_f^3 - \Delta_i^3)^{-1}$, this alone could erase the shortfall.
An observational test: targeted searches for non-transiting, close-in companions in the near-resonant systems studied here would directly probe the strongest amplifier, since such companions would lower the needed tidal dissipation further while their absence would tighten the paper's negative conclusion.
A population-level caveat: the scatter in inferred $\log_{10} Q_p'$ is large (about $\pm0.5$), so the population-level shortfall does not rule out eccentricity tides for any particular system; individual pairs may already be consistent with Solar System values.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The bottom line: this is a careful, honest paper that does a useful thing. It quantifies three proposed amplifiers of eccentricity-tide resonant repulsion on a uniform Kepler sample and shows that, on their model, you still need implausibly low Q'_p. That sharpens the long-standing Lithwick & Wu tension rather than resolving it. The overlooked-inner-planet piece is the most original part and probably worth a cite on its own.

What it does well: the bootstrap treatment of parameter uncertainties is standard but clean; the radius-inflation calculation is tied to a published MESA-based grid; and showing that non-zero initial Delta_i is a negligible lever (factor <2) is a genuinely useful null result. The caveats section is unusually honest—they flag the single-pair integration, the lack of self-consistent radius-tide coupling, and higher-order resonances.

Where I part ways with the abstract's confident 'one order of magnitude' framing: that number is largely set by the hidden-planet model in Section 3.2, and the model is more conservative than it looks. They add up to two inner companions in MMR steps, but stop when the first added planet is inside 20 days, and they copy the observed innermost planet's mass and radius onto the hidden bodies. For systems whose observed innermost planet is at 10-20 days, that truncates the chain before reaching the 2-5 day zone where tides are orders of magnitude stronger. If you instead let the chain extend to the actual young-star inner-edge periods (a few days), the Q'_p amplification for those systems could rise by another 1-2 dex. For mini-Neptunes that is enough to approach Solar System giant-planet Q'_p values, so the 'still falls short' conclusion becomes a weaker statement about some systems, not a clean population-level one. The stress-test note overstates the cutoff's reach for short-period observed pairs, but its core point about the cap stands.

The initial Delta_i prior is a smaller problem: it comes from Keller & Dai (in prep) and isn't public, but the effect is at most a factor of two unless you tune Delta_i to be within a factor of a few of the observed Delta_f, which would contradict the premise of resonant capture. That can be fixed by publishing or citing the simulations.

One quibble: the young systems (HD 109833, V1298 Tau) are presented as independent evidence against eccentricity tides, but a stronger hidden-inner-planet effect would make 1% Delta at 20 Myr easier to produce, not harder. The observation is valuable but it does not independently disfavor the amplifier.

This paper is for the resonance and tidal-evolution crowd, and for anyone trying to read the near-resonant period-ratio distribution as a constraint on migration and dissipation physics. It deserves a serious referee. The central qualitative result—eccentricity tides alone do not comfortably explain the observed Delta distribution—likely survives, but the quantitative 'one order of magnitude' needs a robustness test against the hidden-planet cutoff before it is quoted. I would want the revision to explore deeper chains, a wider range of inner-edge periods, and a sensitivity study on the number of added planets.

Referee Report

3 major / 6 minor

Summary. The paper asks whether three previously neglected effects can make resonant repulsion by eccentricity tides a viable explanation for the observed 1–2% positive period-ratio deviations (Δ) near first-order mean-motion resonances in mature Kepler systems. For ~80 near-resonant pairs, the authors integrate the Lithwick & Wu (2012) tidal evolution equation to infer the required reduced tidal quality factor Q'_p, first in the standard way and then after sequentially including (1) time-dependent planetary radius inflation from Chen & Rogers (2016) models, (2) hypothetical overlooked inner planets parked in a resonant chain down to a 20-day disk-edge threshold, and (3) a non-zero initial Δ drawn from a lognormal distribution with log10 Δ_i = −3.4 ± 0.5 from the authors' unpublished migration simulations. They find that the three effects together raise the inferred log10 Q'_p by roughly one order of magnitude (to 1.2 ± 2.1 for super-Earths and 2.4 ± 1.7 for mini-Neptunes), still below Solar System estimates of ~3–5. They conclude that eccentricity tides alone cannot reproduce the observed Δ distribution and point to alternative mechanisms. The paper also cites young systems (HD 109833, V1298 Tau) that already show Δ ≈ 0.8–1% at ~20 Myr, which is difficult to reconcile with eccentricity tides acting over such short times.

Significance. This is a useful quantitative negative result. If the conclusion holds, it closes a long-standing loophole in the resonant-repulsion story and sharpens the case for complementary mechanisms such as obliquity tides, disk-edge expansion, turbulence, and instabilities. The paper is careful to reproduce the earlier literature values before adding its effects, and the bootstrap treatment of parameter uncertainties is appropriate. The independent argument from very young systems with Δ ≈ 1% is a strong piece of evidence that does not depend on the tidal-inference machinery. The main weakness is that the largest of the three amplifiers, the overlooked-inner-planet effect, is implemented with a restrictive and partly ad hoc prescription whose sensitivity is not explored; the quoted 'one order of magnitude' amplification is therefore not yet established as an upper bound.

major comments (3)

[3.2] The overlooked-inner-planet model adds hidden planets only when the observed innermost planet has P > 20 days and stops after adding at most two planets ('We added up to two additional planets if the orbital period of the first planet added is still beyond 20 days'). This is an arbitrary cap, not a conservative limit. Because the tidal rate scales as P^(-13/3) in Eq. (1), a hidden planet at 2 days versus 10 days gives roughly 10^2.8 times more dissipation. The rotation-period distribution of young stars in Rebull et al. (2018) peaks at a few days, so many systems with observed innermost periods below 20 days could still host undetected interior planets, and systems with P > 20 days could host more than two interior members. The authors should test the sensitivity of the final Q'_p distribution to (i) drawing the innermost planet period from the empirical disk-edge/rotation-period distribution and applying the hidden-planet procedure to all systems, not only those with P_inn > 20 days, and (ii) removing the 'up to two' cap. Until such a test is presented, the abstract's claim that Q'_p 'can only be amplified by about one order of magnitude' is not robust; a plausible alternative implementation could amplify Q'_p by several orders of magnitude for a meaningful subset of systems.
[3.3] The initial-Δ distribution is taken entirely from an unpublished companion paper (Keller & Dai, in prep), with log10 Δ_i = −3.4 ± 0.5 quoted as a lognormal. As written, the reader cannot verify this distribution or assess its uncertainty. While the small effect on Q'_p (a factor of two at most) makes the paper's main conclusion insensitive to the exact form of Δ_i unless Δ_i is within ~30% of the observed Δ_f, the quantitative claim that non-zero initial Δ has a negligible impact is an empirical result resting on inaccessible data. The authors should either include the migration-simulation details in an appendix, provide the Δ_i samples in a machine-readable form, or at minimum show how the final Q'_p distribution changes if Δ_i is drawn from a much broader distribution with a larger mean (e.g., log10 Δ_i = −2.5 or −2.0).
[§3.2, Eq. (1)] The tidal inference for the hidden-planet scenario uses the isolated-pair formula Eq. (1), but the authors argue that tidal dissipation on one planet induces repulsion of the whole resonant chain (citing Papaloizou et al. 2017; Brasser et al. 2022). The manuscript does not demonstrate that the isolated-pair Δ-evolution equation remains quantitatively accurate when the innermost planet is part of a longer chain; the caveat in §4.2 (direct N-body simulations) is mentioned but the central numerical result already depends on this simplification. I would like the authors to justify this step quantitatively, for example by comparing Eq. (1) with a few N-body integrations of a 3–4 planet chain with eccentricity tides, or by citing a published derivation that gives the effective prefactor for a chain. This is not necessarily a fatal issue, but it is load-bearing for the inferred Q'_p values in systems where hidden inner planets are added.

minor comments (6)

[§1] The introduction contains a typo: 'terretrial' should be 'terrestrial' in the sentence about Solar System Q'_p values.
[§3.1] The sentence 'Indeed, the majority of young planets discovered so far have significantly larger radii than the amture planets' contains a typo: 'amture' should be 'mature'.
[§3.2] The phrase 'may may deviate significantly' contains a duplicated word and should be corrected.
[Fig. 2 caption] The caption defines the line styles in the left panel (dotted, dashed, dash-dotted) but the text in §3.2 and §3.3 refers to the effects in a different order; please make the correspondence explicit in the caption to avoid confusion.
[§3.3] The sentence 'It can only increase log10 Q'_p by no more than < 0.1' uses both 'no more than' and '<'; please choose one phrasing.
[§4.1] The young-system evidence (HD 109833, V1298 Tau) is presented with Δ values attributed to 'Livingston et al. in prep' without a quantitative comparison to the tidal-model prediction at 20 Myr. A one-line calculation of the Q'_p implied by Δ = 1% at 20 Myr would strengthen this argument.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: central Q'_p shortfall is computed from independent inputs; one minor self-cited Δ_i prior is not load-bearing.

full rationale

This paper does not exhibit circularity in the sense of a predicted quantity being equal to an input by construction. Q'_p is inferred by integrating the independent Lithwick & Wu (2012) tidal equation against the observed Δ_f, and the observed Δ distribution is not used as a fitting target for any amplifier. The radius-inflation factor is a forward integral of published Chen & Rogers (2016) cooling tracks; the overlooked-inner-planet factor is a Monte Carlo injection tied to the rho Ophiuchus rotation-period proxy and to assumed MMR period ratios; both factors are computed, not imposed. The only self-cited input is the Δ_i prior from the authors' companion simulation (Keller & Dai, in prep). It is an unpublished dynamical simulation rather than a fit to the observed Δ, and its effect on Q'_p is <0.1 dex in 95% of cases, so the central order-of-magnitude amplification and the shortfall conclusion do not reduce to this self-citation. The 20-day inner-edge threshold and two-planet cap in §3.2 are modeling choices that affect the size of the hidden-planet amplification; a shorter true inner edge could raise Q'_p further, but this is a model-sensitivity/caveat issue, not circularity. The paper's own caveats—Equation 1 is strictly valid for isolated pairs, and radius-tide feedback is not modeled—are acknowledged limitations, not hidden circular steps. Score 2 reflects one minor, non-load-bearing self-citation, not a circular derivation.

Assumptions & free parameters 5 free parameters · 5 assumptions · 1 invented entities

The central inference rests on the Lithwick & Wu (2012) tidal evolution equation adopted as the baseline, plus the assumptions that systems began in resonance, that tidal dissipation on an inner chain member repels all resonant neighbors, that the Rho Ophiuchus rotation-period distribution proxies the inner disk edge, and that Chen & Rogers (2016) radius evolution with assigned envelope fractions describes young radii. The free parameters are the chosen super-Earth envelope fraction, predicted masses from the Otegi relation, the 20-day inner-edge threshold, the number of injected inner planets, and the unpublished Delta_i distribution.

free parameters (5)

Initial envelope fraction f_env for super-Earths = 0.1% for 1.2-2 R_earth; 0 for <1.2 R_earth
Assigned by hand, motivated by gas accretion and observations of bare rocky surfaces; affects radius evolution and thus Q'_p by half an order of magnitude.
Mass predictions from Otegi et al. (2020) mass-radius relation = varies per planet
Planets without reported masses get masses from radius, a source of systematic uncertainty in the tidal equation.
Inner disk edge truncation period threshold = 20 days
Chosen so that 99% of young stars rotate faster; used to decide whether to inject overlooked inner planets.
Number of overlooked inner planets = up to 2
Chosen by hand; if more inner planets existed, Q'_p amplification would be larger, but could destabilize chain.
Initial Delta_i distribution parameters = log10 Delta_i = -3.4 +/- 0.5
From unpublished disk migration simulations (Keller & Dai, in prep); input to the non-zero initial Delta effect.

assumptions (5)

domain assumption Equation 1 of Lithwick & Wu (2012) governs the rate of change of Delta under eccentricity tides.
Adopted as the baseline tidal evolution model; valid for isolated near-resonant pairs, as acknowledged in Section 4.2.
domain assumption All planet pairs begin in first-order MMR.
Section 4.2 caveat: the entire Q'_p inference assumes initial resonance; if false, the tidal model does not apply.
domain assumption Tidal dissipation on one planet induces resonant repulsion on all planets in a resonant chain.
Used for the overlooked inner planet effect; based on Papaloizou et al. 2017, Brasser et al. 2022, and Dai et al. 2023.
domain assumption The stellar rotation period distribution in Rho Ophiuchus is a proxy for the orbital period distribution of the innermost planets.
Section 3.2; used to decide where to put injected inner planets.
domain assumption Radius evolution from Chen & Rogers (2016) and the assumed initial envelope fractions describe the young radii of the sample planets.
Section 3.1; determines the inflated radii used in the tidal equation.

invented entities (1)

Overlooked inner planets
purpose: Undetected planets interior to the observed resonant pairs that would dissipate tides and drive resonant repulsion of the whole chain
Hypothetical; the paper assigns them the same mass/radius as the observed innermost planet and places them in first-order MMR with periods drawn from a presumed inner disk edge distribution. No direct detection or published simulation confirmation.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Amplifying Resonant Repulsion with Inflated Young Planets, Overlooked Inner Planets, and Non-zero Initial $\Delta$." pith.science (2026). https://pith.science/paper/ZUNXPRMC

@misc{pith2026250201903,
  author       = {Pith},
  title        = {Pith review of: Amplifying Resonant Repulsion with Inflated Young Planets, Overlooked Inner Planets, and Non-zero Initial $\Delta$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZUNXPRMC}},
  note         = {Machine review of arXiv:2502.01903}
}

abstract

Most multi-planet systems around mature ($\sim 5$-Gyr-old) host stars are non-resonant. Even the near-resonant planet pairs still display 1-2\% positive deviation from perfect period commensurabilities ($\Delta$) near first-order mean motion resonances (MMR). Resonant repulsion due to eccentricity tides was one of the first mechanisms proposed to explain the observed positive $\Delta$. However, the inferred rates of tidal dissipation are often implausibly rapid (with a reduced tidal quality factor $Q_p^\prime \lesssim 10$). 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 non-zero initial deviation $\Delta$, thereby lowering the amount of dissipation needed. We show that even after accounting for all three effects, $Q_p^\prime$ can only be amplified by about one order of magnitude, and still falls short of $Q_p^\prime$ values of Solar System planets. Therefore, eccentricity tides alone cannot fully explain the observed $\Delta$ 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.

Figures

Figures reproduced from arXiv: 2502.01903 by the authors.

**Figure 2.** Left: The change of the reduced tidal quality factor after accounting for radius evolution (dotted line), overlooked inner planets (dashed line), and non-zero initial ∆ (dash-dotted line). The combined effect is shown in black solid line. Radius evolution could increase log10Q ′ p by 0.11±0.08 for mini-Neptuens (> 2R⊕), or 0.5±0.2 for super-Earths (< 2R⊕). An overlooked inner planet can increase log10Q ′ p by 1.0 ± … view at source ↗

**Figure 3.** The orbital architecture of representative near-resonant multi-planet systems where the innermost planets are currently far away from MMR. However, the innermost planets could have been part of the resonant chain initially and contributed to the resonant repulsion of the whole system. Near-resonant pairs are labeled in blue using both the MMR and the observed ∆ [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: The orbital periods of inner planets of the whole system and stellar rotation period distribution of rho Ophiuchus (Rebull et al. 2018) which serves a proxy for the orbital period of an overlooked inner planet. planets (Schlaufman 2010; Petrovich et al. 2018; Pu & Lai …

**Figure 5.** Figure 5: The distribution of ∆i ( log10(∆i) = −3.4 ± 0.5) from our disk migration simulations (Keller & Dai, in prep) and the observed ∆ (log10(∆) = −1.9 ± 0.4) on near-resonant planets. Goldberg & Batygin (2023) proposed an empirical boundary for separating the librating v.s. …

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

109 extracted references · 44 canonical work pages

[1]

, " * write output.state after.block = add.period write newline

ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month note number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.co...
[2]

write newline

" write newline "" before.all 'output.state := FUNCTION format.doi doi empty "" "doi:" doi * if FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix ":" * if eprint field.or.null * if FUNCTION format.pid eprint empty format.doi format.eprint if FUNCTION n.dashify 't := "" t...
[3]

8J|< a Uu h^shOl 0

thebibliography [1] 20pt to REFERENCES 6pt =0pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command Each re...

work page arXiv 2017
[4]

2022, , 163, 13

Bailey , N., Gilbert , G., & Fabrycky , D. 2022, , 163, 13

2022
[5]

G., Thao , P

Barber , M. G., Thao , P. C., Mann , A. W., et al. 2024, arXiv e-prints, arXiv:2407.04763

arXiv 2024
[6]

C., & Becker , J

Batygin , K., Adams , F. C., & Becker , J. 2023, , 951, L19

2023
[7]

2013, , 145, 1

Batygin , K., & Morbidelli , A. 2013, , 145, 1

2013
[8]

A., Huber , D., Gaidos , E., van Saders , J

Berger , T. A., Huber , D., Gaidos , E., van Saders , J. L., & Weiss , L. M. 2020, , 160, 108

2020

Show all 109 references

[9]

J., Koch , D

Borucki , W. J., Koch , D. G., Basri , G., et al. 2011, , 728, 117

2011
[10]

Brasser , R., Pichierri , G., Dobos , V., & Barr , A. C. 2022, , 515, 2373

2022
[11]

Chatterjee, S., & Ford, E. B. 2015, The Astrophysical Journal, 803, 33. https://doi.org/10.1088/0004-637x/803/1/33

2015 doi
[12]

Chen, H., & Rogers, L. A. 2016, The Astrophysical Journal, 831, 180. http://dx.doi.org/10.3847/0004-637X/831/2/180

2016 doi
[13]

2020, , 495, 4192

Choksi , N., & Chiang , E. 2020, , 495, 4192

2020
[14]

2023, , 522, 1914

---. 2023, , 522, 1914

2023
[15]

Crossfield , I. J. M., Malik , M., Hill , M. L., et al. 2022, , 937, L17

2022
[16]

Dai , F., Masuda , K., & Winn , J. N. 2018, , 864, L38

2018
[17]

N., & Zeng , L

Dai , F., Masuda , K., Winn , J. N., & Zeng , L. 2019, , 883, 79

2019
[18]

2023, , 165, 33

Dai , F., Masuda , K., Beard , C., et al. 2023, , 165, 33

2023
[19]

2024, The Prevalence of Resonance Among Young, Close-in Planets, , , arXiv:2406.06885

Dai, F., Goldberg, M., Batygin, K., et al. 2024, The Prevalence of Resonance Among Young, Close-in Planets, , , arXiv:2406.06885. https://arxiv.org/abs/2406.06885

2024 arXiv
[20]

J., Petigura , E

David , T. J., Petigura , E. A., Luger , R., et al. 2019, , 885, L12

2019
[21]

B., & Laskar , J

Delisle , J. B., & Laskar , J. 2014, , 570, L7

2014
[22]

D., Charbonneau , D., Dumusque , X., et al

Dressing , C. D., Charbonneau , D., Dumusque , X., et al. 2015, , 800, 135

2015
[23]

2021, , 656, A69

Emsenhuber , A., Mordasini , C., Burn , R., et al. 2021, , 656, A69

2021
[24]

C., Lissauer , J

Fabrycky , D. C., Lissauer , J. J., Ragozzine , D., et al. 2014, , 790, 146

2014
[25]

2012, , 761, 92

Fang , J., & Margot , J.-L. 2012, , 761, 92

2012
[26]

B., Fabrycky , D

Ford , E. B., Fabrycky , D. C., Steffen , J. H., et al. 2012, , 750, 113

2012
[27]

J., Marley , M

Fortney , J. J., Marley , M. S., & Barnes , J. W. 2007, , 659, 1661

2007
[28]

J., Petigura , E

Fulton , B. J., Petigura , E. A., Howard , A. W., et al. 2017, , 154, 109

2017
[29]

E., & Sari , R

Ginzburg , S., Schlichting , H. E., & Sari , R. 2018, , 476, 759

2018
[30]

2021, doi:10.3847/1538-3881/abfb78

Goldberg, M., & Batygin, K. 2021, doi:10.3847/1538-3881/abfb78. http://arxiv.org/abs/2105.07368 http://dx.doi.org/10.3847/1538-3881/abfb78

2021 arXiv
[31]

2023, , 948, 12

Goldberg , M., & Batygin , K. 2023, , 948, 12

2023
[32]

2023, The Astrophysical Journal, 948, 12

Goldberg, M., & Batygin, K. 2023, The Astrophysical Journal, 948, 12. http://dx.doi.org/10.3847/1538-4357/acc9ae

2023 doi
[33]

2022, arXiv e-prints, arXiv:2207.13833

Goldberg , M., Batygin , K., & Morbidelli , A. 2022, arXiv e-prints, arXiv:2207.13833

2022 arXiv
[34]

1966, , 5, 375

Goldreich , P., & Soter , S. 1966, , 5, 375

1966
[35]

1979, , 233, 857

Goldreich , P., & Tremaine , S. 1979, , 233, 857

1979
[36]

2014, , 787, 80

Hadden , S., & Lithwick , Y. 2014, , 787, 80

2014
[37]

H., & Schlaufman , K

Hamer , J. H., & Schlaufman , K. C. 2024, , 167, 55

2024
[38]

Hansen , B. M. S., Yu , T.-Y., & Hasegawa , Y. 2024, arXiv e-prints, arXiv:2405.12388

2024 arXiv
[39]

2024, arXiv e-prints, arXiv:2405.04744

Hu , R., Bello-Arufe , A., Zhang , M., et al. 2024, arXiv e-prints, arXiv:2405.04744

2024 arXiv
[40]

Huang , S., & Ormel , C. W. 2022, , 511, 3814

2022
[41]

N., et al

Izidoro , A., Ogihara , M., Raymond , S. N., et al. 2017, , 470, 1750

2017
[42]

Kreidberg , L., Koll , D. D. B., Morley , C., et al. 2019, , 573, 87

2019
[43]

Lee , E. J. 2019, , 878, 36

2019
[44]

H., Fabrycky , D., & Lin , D

Lee , M. H., Fabrycky , D., & Lin , D. N. C. 2013, , 774, 52

2013
[45]

2024, , 687, L1

Leleu , A., Delisle , J.-B., Burn , R., et al. 2024, , 687, L1

2024
[46]

2024, arXiv e-prints, arXiv:2408.10206

Li , R., Chiang , E., Choksi , N., & Dai , F. 2024, arXiv e-prints, arXiv:2408.10206

2024 arXiv
[47]

Lin , D. N. C., & Papaloizou , J. 1986, , 309, 846

1986
[48]

2024, arXiv e-prints, arXiv:2412.12415

Lin , J., Dudiak , I., Hadden , S., & Tamayo , D. 2024, arXiv e-prints, arXiv:2412.12415

2024 arXiv
[49]

2011, , 739, 31

Lithwick , Y., & Wu , Y. 2011, , 739, 31

2011
[50]

2012, The Astrophysical Journal, 756, L11

Lithwick, Y., & Wu, Y. 2012, The Astrophysical Journal, 756, L11. https://iopscience.iop.org/article/10.1088/2041-8205/756/1/L11

2012 doi
[51]

2012, , 761, 122

Lithwick , Y., Xie , J., & Wu , Y. 2012, , 761, 122

2012
[52]

W., & Lin , D

Liu , B., Ormel , C. W., & Lin , D. N. C. 2017, , 601, A15

2017
[53]

H., Crossfield , I

Livingston , J. H., Crossfield , I. J. M., Petigura , E. A., et al. 2018, , 156, 277

2018
[54]

2023, Tidal Dissipation Regimes Among the Short-Period Exoplanets, , , arXiv:2311.03576

Louden, E., Laughlin, G., & Millholland, S. 2023, Tidal Dissipation Regimes Among the Short-Period Exoplanets, , , arXiv:2311.03576. https://arxiv.org/abs/2311.03576

2023 arXiv
[55]

P., Leleu , A., et al

Luque , R., Osborn , H. P., Leleu , A., et al. 2023, , 623, 932

2023
[56]

G., Ragozzine , D., Fabrycky , D

MacDonald , M. G., Ragozzine , D., Fabrycky , D. C., et al. 2016, , 152, 105

2016
[57]

W., Wood , M

Mann , A. W., Wood , M. L., Schmidt , S. P., et al. 2022, , 163, 156

2022
[58]

S., Morbidelli, A., Crida, A., & Ferreira, J

Masset, F. S., Morbidelli, A., Crida, A., & Ferreira, J. 2006, The Astrophysical Journal, 642, 478. https://doi.org/10.1086/500967

2006 doi
[59]

2020, , 893, 43

Matsumoto , Y., & Ogihara , M. 2020, , 893, 43

2020
[60]

McNeil , D., Duncan , M., & Levison , H. F. 2005, , 130, 2884

2005
[61]

2019, , 886, 72

Millholland , S. 2019, , 886, 72

2019
[62]

2019, Nature Astronomy, 3, 424

Millholland , S., & Laughlin , G. 2019, Nature Astronomy, 3, 424

2019
[63]

M., Fabrycky , D

Mills , S. M., Fabrycky , D. C., Migaszewski , C., et al. 2016, , 533, 509

2016
[64]

V., Knutson , H., Line , M., et al

Morley , C. V., Knutson , H., Line , M., et al. 2017, , 153, 86

2017
[65]

D., & Dermott , S

Murray , C. D., & Dermott , S. F. 1999, Solar system dynamics

1999
[66]

2020, Planetary Systems Table, IPAC, doi:10.26133/NEA12

NASA Exoplanet Science Institute . 2020, Planetary Systems Table, IPAC, doi:10.26133/NEA12. https://catcopy.ipac.caltech.edu/dois/doi.php?id=10.26133/NEA12

2020 doi
[67]

Nelson , R. P. 2018, in Handbook of Exoplanets, ed. H. J. Deeg & J. A. Belmonte , 139

2018
[68]

K., & Morbidelli , A

Ogihara , M., Kokubo , E., Suzuki , T. K., & Morbidelli , A. 2018, , 615, A63

2018
[69]

W., Liu , B., & Schoonenberg , D

Ormel , C. W., Liu , B., & Schoonenberg , D. 2017, , 604, A1

2017
[70]

F., Bouchy , F., & Helled , R

Otegi , J. F., Bouchy , F., & Helled , R. 2020, , 634, A43

2020
[71]

E., & Wu , Y

Owen , J. E., & Wu , Y. 2017, , 847, 29

2017
[72]

Papaloizou, J. C. B., Szuszkiewicz, E., & Terquem, C. 2017, doi:10.1093/mnras/stx2980. http://arxiv.org/abs/1711.07932 http://dx.doi.org/10.1093/mnras/stx2980

2017 arXiv
[73]

Papaloizou , J. C. B., & Terquem , C. 2010, , 405, 573

2010
[74]

2015, , 220, 15

Paxton , B., Marchant , P., Schwab , J., et al. 2015, , 220, 15

2015
[75]

Peale , S. J. 1976, , 14, 215

1976
[76]

2018, ArXiv e-prints, arXiv:1804.05065

Petrovich , C., Deibert , E., & Wu , Y. 2018, ArXiv e-prints, arXiv:1804.05065

2018 arXiv
[77]

2020, , 494, 4950

Pichierri , G., & Morbidelli , A. 2020, , 494, 4950

2020
[78]

2018, Celestial Mechanics and Dynamical Astronomy, 130, 54

Pichierri , G., Morbidelli , A., & Crida , A. 2018, Celestial Mechanics and Dynamical Astronomy, 130, 54

2018
[79]

2020, , 582, 497

Plavchan , P., Barclay , T., Gagn \'e , J., et al. 2020, , 582, 497

2020
[80]

2019, , 488, 3568

Pu , B., & Lai , D. 2019, , 488, 3568

2019
[81]

N., Izidoro, A., Bolmont, E., et al

Raymond, S. N., Izidoro, A., Bolmont, E., et al. 2021, doi:10.1038/s41550-021-01518-6. http://arxiv.org/abs/2111.13351 http://dx.doi.org/10.1038/s41550-021-01518-6

2021 arXiv
[82]

M., Stauffer , J

Rebull , L. M., Stauffer , J. R., Cody , A. M., et al. 2018, , 155, 196

2018
[83]

2012, , 427, L21

Rein , H. 2012, , 427, L21

2012
[84]

R., Winn , J

Ricker , G. R., Winn , J. N., Vanderspek , R., et al. 2014, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9143, Transiting Exoplanet Survey Satellite (TESS) , 914320

2014
[85]

E., Becker , J

Rodriguez , J. E., Becker , J. C., Eastman , J. D., et al. 2018, ArXiv e-prints, arXiv:1806.08368

2018 arXiv
[86]

Rogers , L. A. 2015, , 801, 41

2015
[87]

F., Bryson , S

Rowe , J. F., Bryson , S. T., Marcy , G. W., et al. 2014, , 784, 45

2014
[88]

Schlaufman , K. C. 2010, , 719, 602

2010
[89]

L., & Teukolsky , S

Shapiro , S. L., & Teukolsky , S. A. 1986, Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects

1986
[90]

2015, Monthly Notices of the Royal Astronomical Society, 453, 4089

Silburt, A., & Rein, H. 2015, Monthly Notices of the Royal Astronomical Society, 453, 4089. https://doi.org/10.1093/mnras/stv1924

2015 doi
[91]

K., Rustamkulov , Z., Thorngren , D

Sing , D. K., Rustamkulov , Z., Thorngren , D. P., et al. 2024, , 630, 831

2024
[92]

2016, , 830, 5

Spalding , C., & Batygin , K. 2016, , 830, 5

2016
[93]

Tamayo , D., Rein , H., Shi , P., & Hernandez , D. M. 2020, , 491, 2885

2020
[94]

Terquem, C., & Papaloizou, J. C. B. 2007, The Astrophysical Journal, 654, 1110. https://doi.org/10.1086/509497

2007 doi
[95]

Terquem , C., & Papaloizou , J. C. B. 2019, , 482, 530

2019
[96]

C., & Wisdom , J

Tittemore , W. C., & Wisdom , J. 1990, , 85, 394

1990
[97]

X., et al

Vach , S., Zhou , G., Huang , C. X., et al. 2024, , 167, 210

2024
[98]

Wang , S., & Lin , D. N. C. 2023, , 165, 174

2023
[99]

Ward, W. R. 1997, Icarus, 126, 261. https://www.sciencedirect.com/science/article/pii/S001910359695647X

1997
[100]

J., Beatty , T

Welbanks , L., Bell , T. J., Beatty , T. G., et al. 2024, , 630, 836

2024
[101]

M., Plavchan , P

Wittrock , J. M., Plavchan , P. P., Cale , B. L., et al. 2023, , 166, 232

2023
[102]

H., & Lee , M

Wong , K. H., & Lee , M. H. 2024, , 167, 112

2024
[103]

L., Mann , A

Wood , M. L., Mann , A. W., Barber , M. G., et al. 2023, , 165, 85

2023
[104]

2005, , 635, 688

Wu , Y. 2005, , 635, 688

2005
[105]

Wu , Y., Chen , Y.-X., & Lin , D. N. C. 2024 a , , 528, L127

2024
[106]

2024 b , arXiv e-prints, arXiv:2405.08893

Wu , Y., Malhotra , R., & Lithwick , Y. 2024 b , arXiv e-prints, arXiv:2405.08893

2024 arXiv
[107]

Yoder , C. F. 1995, in Global Earth Physics: A Handbook of Physical Constants, ed. T. J. Ahrens , 1

1995
[108]

2024, , 972, 159

Yu , H., & Dai , F. 2024, , 972, 159

2024
[109]

2024, , 961, L44

Zhang , M., Hu , R., Inglis , J., et al. 2024, , 961, L44

2024

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

[1] [1]

, " * write output.state after.block = add.period write newline

ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month note number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.co...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION format.doi doi empty "" "doi:" doi * if FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix ":" * if eprint field.or.null * if FUNCTION format.pid eprint empty format.doi format.eprint if FUNCTION n.dashify 't := "" t...

[3] [3]

8J|< a Uu h^shOl 0

thebibliography [1] 20pt to REFERENCES 6pt =0pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command Each re...

work page arXiv 2017

[4] [4]

2022, , 163, 13

Bailey , N., Gilbert , G., & Fabrycky , D. 2022, , 163, 13

2022

[5] [5]

G., Thao , P

Barber , M. G., Thao , P. C., Mann , A. W., et al. 2024, arXiv e-prints, arXiv:2407.04763

arXiv 2024

[6] [6]

C., & Becker , J

Batygin , K., Adams , F. C., & Becker , J. 2023, , 951, L19

2023

[7] [7]

2013, , 145, 1

Batygin , K., & Morbidelli , A. 2013, , 145, 1

2013

[8] [8]

A., Huber , D., Gaidos , E., van Saders , J

Berger , T. A., Huber , D., Gaidos , E., van Saders , J. L., & Weiss , L. M. 2020, , 160, 108

2020