pith. sign in

arxiv: 2606.20803 · v2 · pith:EU3VR6K5new · submitted 2026-06-18 · 🌌 astro-ph.EP

Planet-Planet Secular Migration Predicts a Stellar Obliquity-Period Anti-Correlation

Hareesh Gautham Bhaskar , Cristobal Petrovich , Diego J. Mu\~noz This is my paper

Pith reviewed 2026-06-26 15:26 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords hot Jupitersstellar obliquitysecular migrationvon Zeipel-Lidov-Kozaihigh-eccentricity migrationplanet-planet interactions
0
0 comments X

The pith

Secular planet-planet migration produces an obliquity-period anti-correlation for hot Jupiters.

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

The paper shows that high-eccentricity migration driven by a distant planetary companion reproduces the observed pattern in which misaligned hot Jupiters are mostly short-period while longer-period ones stay aligned. Shortest-period planets arise from the von Zeipel-Lidov-Kozai channel with inclined companions, yielding a wide range of final stellar obliquities. Longer-period planets form through slower coplanar migration that keeps obliquities low. A reader would care because the mechanism ties migration channel directly to an observable stellar property and supplies a concrete prediction for companion orbits that differs from tidal explanations.

Core claim

In N-body simulations, the shortest-period hot Jupiters are produced by the von Zeipel-Lidov-Kozai mechanism driven by highly inclined companions, resulting in a broad range of final stellar obliquities, while the longest-period hot Jupiters are produced over longer timescales by coplanar high-eccentricity migration, which preserves low obliquities.

What carries the argument

Secular high-eccentricity migration driven by a distant planetary companion, operating through two channels: von Zeipel-Lidov-Kozai from inclined orbits versus coplanar migration.

If this is right

  • Intermediate-period hot Jupiters display a moderate range of obliquities as the two channels overlap.
  • Shortest-period hot Jupiters should have distant companions with broadly distributed mutual inclinations.
  • Companions of longer-period hot Jupiters should reside in nearly coplanar orbits.

Where Pith is reading between the lines

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

  • Gaia astrometry of companion inclinations offers a direct test of the two-channel picture.
  • The same secular process may shape obliquity distributions in other classes of close-in planets.

Load-bearing premise

The observed obliquity-period trend cannot be explained by tidal dissipation in the star.

What would settle it

Measurement of the mutual inclinations of distant companions, which should be broadly distributed for short-period hot Jupiters and nearly coplanar for long-period ones.

Figures

Figures reproduced from arXiv: 2606.20803 by Cristobal Petrovich, Diego J. Mu\~noz, Hareesh Gautham Bhaskar.

Figure 1
Figure 1. Figure 1: The observed projected obliquity distribution of HJs (with mass > 1 MJup) around single stars (with mass > 0.5 M⊙). The final semi-major axis of the planets (af = a[1− e 2 ]) are shown on the x-axis, and their projected obliquities are shown on the y-axis. The colors show the eccentricities of the planets. In general, planets on close-in orbits (af < 0.06 AU) have low eccentricity (e ∼ 0.1) and broad range… view at source ↗
Figure 2
Figure 2. Figure 2: Final semi-major axes and obliquities of HJs formed in our fiducial simulations. Panel (a): the final semi-major axis of HJs are shown on the x-axis, and the final obliquities are shown on the y-axis. The color indicates the migration timescale. Close-in HJs exhibit a broad range of obliquities, whereas wider-orbit HJs tend to have low obliquities. The distribution shows an envelope that constrains the max… view at source ↗
Figure 3
Figure 3. Figure 3: Weighted distributions of the final semi-major axes and obliquities of HJs formed in our simulations. In our fiducial simulations, the initial eccentricities and mutual inclinations of the planets are sampled on a uniform grid. In this figure, we assign weights to each HJ to reflect different assumed underlying distributions of initial eccentricities and mutual inclinations. Specifically, we compute the we… view at source ↗
Figure 4
Figure 4. Figure 4: Marginalized distributions of companion eccentricity (panel a), HJ obliquity (panel b), and final orbital period (panel c) from our simulations. The colored curves correspond to different assumed underlying distributions of the planets’ initial eccentricities and mutual inclinations. We focus on three regimes: the ZLK limit, the CHEM limit, and an intermediate case. In panel (a), the black curve shows the … view at source ↗
Figure 5
Figure 5. Figure 5: Projected obliquities and inclinations of HJs from our simulations. The x-axis shows the final projected mutual inclination between the two planets in the system, while the y-axis shows the projected stellar obliquity of the inner planet. Panel (a) shows results for HJs with final semi-major axes af < 0.035 AU. Panels (b) and (c) show results for 0.035 AU < af < 0.045 AU and af > 0.045 AU, respectively. Th… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of analytical expression for obliquity envelope with secular simulations. In panel (a), we show the final semi-major axis on the x-axis, and the final obliquity on the y-axis. Panel (b) shows final obliquity as a function of the initial mutual inclination. In the panel (c), we show the initial mutual inclination between the planets as a function of the final semi￾major axis of the HJ. The analyt… view at source ↗
Figure 7
Figure 7. Figure 7: The final obliquity and semi-major axis of HJs in our secular simulations. The black dots show results from our simulations, and the contours show the two dimensional kernel density estimate. Results from our fiducial simulations (panel a) are compared to an additional set of simulations in which the tidal dissipation in the planet is enhanced (panel b). Rest of the initial conditions are kept same. We can… view at source ↗
Figure 8
Figure 8. Figure 8: Distribution of final obliquities and semi-major axes of HJs in our three-planet simulations. Panel (a) corresponds to our fiducial setup. In panels (b), (c), and (d), we include an additional outer planet with mass 8 MJup. The location of the outermost planet is set by the parameter R (see text for details): it lies farthest out for R = 0.01 and closest in for R = 0.4. Panels (a) and (b) are similar, indi… view at source ↗
read the original abstract

Stellar obliquities provide a fossil record of hot Jupiter (HJ) migration. An emerging observational trend in single-star systems is that strongly misaligned HJs are largely confined to short orbital periods, while longer-period HJs are preferentially aligned. This pattern cannot be explained by tidal dissipation in the star and may instead preserve clues to the migration pathway. We show that secular high-eccentricity migration driven by a distant planetary companion naturally produces such an obliquity--period correlation. In our simulations, the shortest-period HJs tend to be produced by the von Zeipel--Lidov--Kozai mechanism driven by highly inclined companions, which results in a broad range of final stellar obliquities. The longest-period HJs, on the other hand, are produced over longer timescales by coplanar high-eccentricity migration, which preserves low obliquities. The transition between these two limits is not abrupt, with intermediate-period HJs displaying a moderate range of obliquities. According to this interpretation, we predict that the shortest-period HJs should have distant planetary companions with broadly distributed mutual inclinations, whereas the companions of longer-period HJs should reside in nearly coplanar orbits. Upcoming Gaia astrometric constraints will provide a key test of this picture.

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

3 major / 2 minor

Summary. The manuscript claims that N-body simulations of planet-planet secular high-eccentricity migration naturally reproduce the observed stellar obliquity–orbital period anti-correlation among hot Jupiters in single-star systems. Short-period HJs arise primarily via the von Zeipel–Lidov–Kozai mechanism driven by inclined outer companions and exhibit a broad range of final obliquities, while longer-period HJs form via coplanar high-eccentricity migration that preserves low obliquities; the transition is gradual. The work predicts that short-period HJs should have broadly inclined distant companions while longer-period HJs should have nearly coplanar ones, testable with Gaia astrometry.

Significance. If the simulation results hold, the paper supplies a dynamical mechanism that accounts for the trend without invoking stellar tidal dissipation and generates concrete, falsifiable predictions about companion mutual inclinations. The isolation of two distinct secular channels and the explicit link to an observable anti-correlation constitute a substantive contribution to the migration debate.

major comments (3)
  1. [§3] §3 (Simulation Setup): the manuscript does not specify the initial semi-major axis and eccentricity distributions, the number of realizations per channel, the integrator timestep, or whether general relativity and stellar tides are included; without these parameters it is impossible to verify that the reported obliquity–period separation is not an artifact of the chosen initial conditions or neglected physics.
  2. [§4.2] §4.2 (Obliquity–Period Distributions): the transition between the vZLK and coplanar regimes is described qualitatively; the central claim would be strengthened by reporting a quantitative statistic (e.g., Spearman rank correlation or binned median obliquity vs. period) together with bootstrap uncertainties rather than visual inspection of scatter plots alone.
  3. [§5] §5 (Predictions): the statement that Gaia will provide a key test is not accompanied by a forward-modelled distribution of mutual inclinations or an estimate of the astrometric precision required to distinguish the two populations; this leaves the falsifiability claim unquantified.
minor comments (2)
  1. [Abstract, §1] The abstract and §1 use both “correlation” and “anti-correlation” interchangeably; consistent terminology would improve clarity.
  2. [Figure captions] Figure captions should explicitly state the number of simulated systems shown and whether error bars represent 1σ or interquartile ranges.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We appreciate the referee's thorough review and positive evaluation of our work. Below we respond point-by-point to the major comments, indicating where revisions will be made to the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (Simulation Setup): the manuscript does not specify the initial semi-major axis and eccentricity distributions, the number of realizations per channel, the integrator timestep, or whether general relativity and stellar tides are included; without these parameters it is impossible to verify that the reported obliquity–period separation is not an artifact of the chosen initial conditions or neglected physics.

    Authors: We agree that these simulation parameters must be clearly specified to allow verification of the results. In the revised manuscript, we will expand §3 to explicitly detail the initial semi-major axis and eccentricity distributions, the number of realizations per channel, the integrator timestep, and whether general relativity and stellar tides are included. revision: yes

  2. Referee: [§4.2] §4.2 (Obliquity–Period Distributions): the transition between the vZLK and coplanar regimes is described qualitatively; the central claim would be strengthened by reporting a quantitative statistic (e.g., Spearman rank correlation or binned median obliquity vs. period) together with bootstrap uncertainties rather than visual inspection of scatter plots alone.

    Authors: We acknowledge that providing a quantitative statistic would strengthen the presentation of the obliquity–period anti-correlation. We will add the Spearman rank correlation coefficient and binned median obliquities with bootstrap uncertainties to the revised §4.2. revision: yes

  3. Referee: [§5] §5 (Predictions): the statement that Gaia will provide a key test is not accompanied by a forward-modelled distribution of mutual inclinations or an estimate of the astrometric precision required to distinguish the two populations; this leaves the falsifiability claim unquantified.

    Authors: We agree that quantifying the Gaia test would make the prediction more concrete. In the revision, we will include a forward-modelled distribution of mutual inclinations and an estimate of the required astrometric precision to distinguish the populations in the updated §5. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central claim is that N-body simulations of secular high-eccentricity migration (von Zeipel-Lidov-Kozai vs. coplanar channels) produce the observed obliquity-period anti-correlation as an emergent output. No evidence appears of fitting parameters to the target trend, self-defining the result via the inputs, or relying on load-bearing self-citations whose content reduces to the present claim. The derivation is presented as independent dynamical modeling whose predictions (e.g., companion inclination distributions) are testable externally. This is the normal case of a simulation-based prediction without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are identifiable from the provided text.

axioms (1)
  • domain assumption The observed obliquity-period trend is real and cannot be produced by tidal dissipation alone.
    Stated directly in the abstract as the motivation for seeking an alternative explanation.

pith-pipeline@v0.9.1-grok · 5770 in / 1368 out tokens · 24513 ms · 2026-06-26T15:26:43.802376+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

246 extracted references · 232 canonical work pages · 92 internal anchors

  1. [1]

    The Disk Substructures at High Angular Resolution Project (DSHARP). I. Motivation, Sample, Calibration, and Overview. , keywords =. doi:10.3847/2041-8213/aaf741 , archivePrefix =. 1812.04040 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/2041-8213/aaf741 2041

  2. [2]

    Secular Evolution of Hierarchical Planetary Systems

    Secular Evolution of Hierarchical Planetary Systems. , keywords =. doi:10.1086/375857 , archivePrefix =. astro-ph/0304454 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/375857

  3. [3]

    arXiv e-prints , keywords =

    Formation of inner planets in the presence of a Cold Jupiter: orbital evolution and relative velocities of planetesimals. arXiv e-prints , keywords =. doi:10.48550/arXiv.2308.14347 , archivePrefix =. 2308.14347 , primaryClass =

    work page doi:10.48550/arxiv.2308.14347

  4. [4]

    , keywords =

    Accretion discs in astrophysics. , keywords =. doi:10.1146/annurev.aa.19.090181.001033 , adsurl =

    work page doi:10.1146/annurev.aa.19.090181.001033

  5. [5]

    Secular Evolution Driven by Massive Eccentric Disks/Rings: An Apsidally Aligned Case

    Secular Evolution Driven by Massive Eccentric Disks/Rings: An Apsidally Aligned Case. , keywords =. doi:10.3847/1538-4357/aad3ba , archivePrefix =. 1809.02625 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/aad3ba

  6. [6]

    The California Legacy Survey. III. On the Shoulders of (Some) Giants: The Relationship between Inner Small Planets and Outer Massive Planets. , keywords =. doi:10.3847/1538-4365/ac7230 , archivePrefix =. 2112.03399 , primaryClass =

    work page doi:10.3847/1538-4365/ac7230

  7. [7]

    , keywords =

    Pericenter precession induced by a circumstellar disk on the orbit of massive bodies: comparison between analytical predictions and numerical results. , keywords =. doi:10.1051/0004-6361/201527610 , adsurl =

    work page doi:10.1051/0004-6361/201527610

  8. [8]

    Celestial Mechanics and Dynamical Astronomy , keywords =

    Secular resonance sweeping and orbital excitation in decaying disks. Celestial Mechanics and Dynamical Astronomy , keywords =. doi:10.1007/s10569-019-9942-0 , archivePrefix =. 1912.09118 , primaryClass =

    work page doi:10.1007/s10569-019-9942-0 1912

  9. [9]

    Formation of Gaps in Self-gravitating Debris Disks by Secular Resonance in a Single-planet System. I. A Simplified Model. , keywords =. doi:10.3847/1538-4357/abda46 , archivePrefix =. 2010.15617 , primaryClass =

    work page doi:10.3847/1538-4357/abda46 2010

  10. [10]

    Celestial Mechanics and Dynamical Astronomy , keywords =

    Secular Resonances in the Primitive Solar Nebula. Celestial Mechanics and Dynamical Astronomy , keywords =. doi:10.1007/BF00048587 , adsurl =

    work page doi:10.1007/bf00048587

  11. [11]

    An Observational Perspective of Transitional Disks

    An Observational Perspective of Transitional Disks. Protostars and Planets VI , year = 2014, editor =. doi:10.2458/azu_uapress_9780816531240-ch022 , archivePrefix =. 1402.7103 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.2458/azu_uapress_9780816531240-ch022 2014

  12. [12]

    Wind-driven Accretion in Protoplanetary Disks. II. Radial Dependence and Global Picture. , keywords =. doi:10.1088/0004-637X/772/2/96 , archivePrefix =. 1305.7232 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/772/2/96

  13. [13]

    , keywords =

    Homogeneous studies of transiting extrasolar planets - IV. Thirty systems with space-based light curves. , archivePrefix = "arXiv", eprint =. doi:10.1111/j.1365-2966.2011.19399.x , adsurl =

    work page doi:10.1111/j.1365-2966.2011.19399.x 2011

  14. [15]

    Angular momentum evolution of young low-mass stars and brown dwarfs: observations and theory

    Angular Momentum Evolution of Young Low-Mass Stars and Brown Dwarfs: Observations and Theory. Protostars and Planets VI , year = 2014, editor =. doi:10.2458/azu_uapress_9780816531240-ch019 , archivePrefix =. 1309.7851 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.2458/azu_uapress_9780816531240-ch019 2014

  15. [16]

    Magnetic braking of T Tauri stars

    Magnetic braking of T Tauri stars. , keywords =. doi:10.1093/mnras/280.2.458 , archivePrefix =. astro-ph/9512018 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/280.2.458

  16. [17]

    Andrews and D

    Sean M. Andrews and D. J. Wilner and A. M. Hughes and Chunhua Qi and C. P. Dullemond , title =. doi:10.1088/0004-637x/723/2/1241 , url =

    work page doi:10.1088/0004-637x/723/2/1241

  17. [18]

    Fulton and Lee J

    Benjamin J. Fulton and Lee J. Rosenthal and Lea A. Hirsch and Howard Isaacson and Andrew W. Howard and Cayla M. Dedrick and Ilya A. Sherstyuk and Sarah C. Blunt and Erik A. Petigura and Heather A. Knutson and Aida Behmard and Ashley Chontos and Justin R. Crepp and Ian J. M. Crossfield and Paul A. Dalba and Debra A. Fischer and Gregory W. Henry and Stephen...

    work page doi:10.3847/1538-4365/abfcc1

  18. [19]

    Revisiting the pre-main-sequence evolution of stars. I. Importance of accretion efficiency and deuterium abundance. , keywords =. doi:10.1051/0004-6361/201628260 , archivePrefix =. 1702.07901 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201628260

  19. [20]

    Magnetic Origins of the Stellar Mass-Obliquity Correlation in Planetary Systems

    Magnetic Origins of the Stellar Mass-Obliquity Correlation in Planetary Systems. , keywords =. 2015. doi:10.1088/0004-637X/811/2/82 , archivePrefix =. 1508.02365 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/811/2/82 2015

  20. [21]

    Star-Disc-Binary Interactions in Protoplanetary Disc Systems and Primordial Spin-Orbit Misalignments

    Star-disc-binary interactions in protoplanetary disc systems and primordial spin-orbit misalignments. , keywords =. 2014. doi:10.1093/mnras/stu485 , archivePrefix =. 1402.1907 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stu485 2014

  21. [22]

    A Mechanism of Exciting Planetary Inclination and Eccentricity through a Residual Gas Disk

    Mechanism for Exciting Planetary Inclination and Eccentricity through a Residual Gas Disk. , keywords =. 2013. doi:10.1088/0004-637X/769/1/26 , archivePrefix =. 1303.6736 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/769/1/26 2013

  22. [23]

    L., Nichol, R., Bamford, S., et al

    Eccentricity pumping of a planet on an inclined orbit by a disc. , keywords =. 2010. doi:10.1111/j.1365-2966.2010.16295.x , archivePrefix =. 1001.0657 , primaryClass =

    work page doi:10.1111/j.1365-2966.2010.16295.x 2010

  23. [25]

    Mass constraint for a planet in a protoplanetary disk from the gap width

    Mass constraint for a planet in a protoplanetary disk from the gap width. , keywords =. 2016. doi:10.1093/pasj/psw037 , archivePrefix =. 1603.03853 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/pasj/psw037 2016

  24. [26]

    An introduction to the study of stellar structure. 1939

    1939

  25. [27]

    , archivePrefix = "arXiv", eprint =

    The Gravitational Interaction between Planets on Inclined Orbits and Protoplanetary Disks As the Origin of Primordial Spin-Orbit Misalignments. , archivePrefix = "arXiv", eprint =. doi:10.3847/1538-3881/153/2/60 , adsurl =

    work page doi:10.3847/1538-3881/153/2/60

  26. [28]

    , archivePrefix = "arXiv", eprint =

    Inclined massive planets in a protoplanetary disc: gap opening, disc breaking, and observational signatures. , archivePrefix = "arXiv", eprint =. doi:10.1093/mnras/sty3358 , adsurl =

    work page doi:10.1093/mnras/sty3358

  27. [32]

    , archivePrefix = "arXiv", eprint =

    Hiding Planets behind a Big Friend: Mutual Inclinations of Multi-planet Systems with External Companions. , archivePrefix = "arXiv", eprint =. doi:10.3847/1538-3881/153/1/42 , adsurl =

    work page doi:10.3847/1538-3881/153/1/42

  28. [33]

    Science , archivePrefix = "arXiv", eprint =

    Stellar Spin-Orbit Misalignment in a Multiplanet System. Science , archivePrefix = "arXiv", eprint =. doi:10.1126/science.1242066 , adsurl =

    work page doi:10.1126/science.1242066

  29. [34]

    Celestial Mechanics , keywords =

    A Second Fundamental Model for Resonance. Celestial Mechanics , keywords =. doi:10.1007/BF01234306 , adsurl =

    work page doi:10.1007/bf01234306

  30. [35]

    Secular transport during disk dispersal: the case of Kepler-419

    Secular Transport during Disk Dispersal: The Case of Kepler-419. , keywords =. doi:10.3847/1538-3881/aaeed9 , archivePrefix =. 1809.03510 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-3881/aaeed9

  31. [36]

    Why do Earth satellites stay up?

    Why do Earth satellites stay up?. American Journal of Physics , keywords =. doi:10.1119/1.4874853 , archivePrefix =. 1309.5244 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1119/1.4874853

  32. [37]

    MNRAS , author =

    Reducing the probability of capture into resonance. , keywords =. doi:10.1111/j.1365-2966.2005.09826.x , archivePrefix =. astro-ph/0507477 , primaryClass =

    work page doi:10.1111/j.1365-2966.2005.09826.x 2005

  33. [38]

    , keywords =

    Migration Timescale Thresholds for Resonant Capture in the Plutino Problem. , keywords =. doi:10.1086/318880 , adsurl =

    work page doi:10.1086/318880

  34. [39]

    Celestial Mechanics , keywords =

    A Simple Derivation of Capture Probabilities for the J+1:J and J+2:J Orbit-Orbit Resonance Problems. Celestial Mechanics , keywords =. doi:10.1007/BF01231120 , adsurl =

    work page doi:10.1007/bf01231120

  35. [40]

    arXiv e-prints , keywords =

    Exponential growth of eccentricity in secular theory. arXiv e-prints , keywords =

  36. [41]

    , archivePrefix = "arXiv", eprint =

    Outer-planet scattering can gently tilt an inner planetary system. , archivePrefix = "arXiv", eprint =. doi:10.1093/mnras/stw2180 , adsurl =

    work page doi:10.1093/mnras/stw2180

  37. [43]

    , keywords =

    Spin-Orbit Alignment of the Pictoris Planetary System. , keywords =. doi:10.3847/2041-8213/ab9d27 , archivePrefix =. 2006.10784 , primaryClass =

    work page doi:10.3847/2041-8213/ab9d27 2041

  38. [44]

    Shadows cast by a warp in the HD 142527 protoplanetary disk

    Shadows Cast by a Warp in the HD 142527 Protoplanetary Disk. , keywords =. doi:10.1088/2041-8205/798/2/L44 , archivePrefix =. 1412.4632 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/2041-8205/798/2/l44 2041

  39. [45]

    , keywords =

    Dust-depleted Inner Disks in a Large Sample of Transition Disks through Long-baseline ALMA Observations. , keywords =. doi:10.3847/1538-4357/ab7b63 , archivePrefix =. 2003.00079 , primaryClass =

    work page doi:10.3847/1538-4357/ab7b63 2003

  40. [46]

    Kepler-108: A Mutually Inclined Giant Planet System

    Kepler-108: A Mutually Inclined Giant Planet System. , keywords =. doi:10.3847/1538-3881/153/1/45 , archivePrefix =. 1606.04485 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-3881/153/1/45

  41. [47]

    , keywords =

    Evidence for a high mutual inclination between the cold Jupiter and transiting super Earth orbiting Men. , keywords =. doi:10.1093/mnras/staa2033 , archivePrefix =. 2007.01871 , primaryClass =

    work page doi:10.1093/mnras/staa2033 2007

  42. [48]

    , year = 2012, month = nov, volume =

    A primordial origin for misalignments between stellar spin axes and planetary orbits. , year = 2012, month = nov, volume =. doi:10.1038/nature11560 , adsurl =

    work page doi:10.1038/nature11560 2012

  43. [49]

    HAT-P-11: Discovery of a Second Planet and a Clue to Understanding Exoplanet Obliquities

    HAT-P-11: Discovery of a Second Planet and a Clue to Understanding Exoplanet Obliquities. , keywords =. doi:10.3847/1538-3881/aabfec , archivePrefix =. 1805.09352 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-3881/aabfec

  44. [50]

    , keywords =

    Why do warm Neptunes present nonzero eccentricity?. , keywords =. doi:10.1051/0004-6361/201936967 , archivePrefix =. 2005.02700 , primaryClass =

    work page doi:10.1051/0004-6361/201936967 2005

  45. [52]

    Planets Near Mean-Motion Resonances

    Planets near Mean-motion Resonances. , keywords =. doi:10.1088/0004-637X/770/1/24 , archivePrefix =. 1211.5603 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/770/1/24

  46. [53]

    Solar System Dynamics

  47. [54]

    , year = 1968, month = apr, volume = 73, pages =

    Dynamical evolution of triple stars. , year = 1968, month = apr, volume = 73, pages =. doi:10.1086/110614 , adsurl =

    work page doi:10.1086/110614 1968

  48. [55]

    , year = 1966, month = sep, volume =

    Quasi-periodic Solutions for the three-body problem. , year = 1966, month = sep, volume =. doi:10.1086/109964 , adsurl =

    work page doi:10.1086/109964 1966

  49. [56]

    In Situ Formation and Dynamical Evolution of Hot Jupiter Systems

    In Situ Formation and Dynamical Evolution of Hot Jupiter Systems. , keywords =. doi:10.3847/0004-637X/829/2/114 , archivePrefix =. 1511.09157 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/0004-637x/829/2/114

  50. [57]

    , year = 1962, month = nov, volume =

    Secular perturbations of asteroids with high inclination and eccentricity. , year = 1962, month = nov, volume =. doi:10.1086/108790 , adsurl =

    work page doi:10.1086/108790 1962

  51. [58]

    , year = 1962, month = oct, volume =

    The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies. , year = 1962, month = oct, volume =. doi:10.1016/0032-0633(62)90129-0 , adsurl =

    work page doi:10.1016/0032-0633(62)90129-0 1962

  52. [60]

    , year = 1939, month = mar, volume =

    Apsidal motion in binary stars. , year = 1939, month = mar, volume =. doi:10.1093/mnras/99.5.451 , adsurl =

    work page doi:10.1093/mnras/99.5.451 1939

  53. [61]

    Equilibrium, Stability and Orbital Evolution of Close Binary Systems

    Equilibrium, Stability, and Orbital Evolution of Close Binary Systems. , keywords =. doi:10.1086/173812 , archivePrefix =. astro-ph/9307032 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/173812

  54. [62]

    , keywords =

    Gravity-darkening exponents and apsidal-motion constants for pre-main-sequence models. , keywords =. doi:10.1051/0004-6361/201218881 , adsurl =

    work page doi:10.1051/0004-6361/201218881

  55. [63]

    Hints for a Turnover at the Snow Line in the Giant Planet Occurrence Rate

    Hints for a Turnover at the Snow Line in the Giant Planet Occurrence Rate. , keywords =. doi:10.3847/1538-4357/ab0300 , archivePrefix =. 1812.05569 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ab0300

  56. [64]

    Constraints on the dynamical history of a multi-planet system

    Nearly polar orbit of the sub-Neptune HD 3167 c. Constraints on the dynamical history of a multi-planet system. , keywords =. doi:10.1051/0004-6361/201935944 , adsurl =

    work page doi:10.1051/0004-6361/201935944

  57. [65]

    The Dispersal of Planet-forming discs: Theory confronts Observations

    The dispersal of planet-forming discs: theory confronts observations. Royal Society Open Science , keywords =. doi:10.1098/rsos.170114 , archivePrefix =. 1704.00214 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1098/rsos.170114

  58. [66]

    The inner regions of protoplanetary disks

    The Inner Regions of Protoplanetary Disks. , keywords =. doi:10.1146/annurev-astro-081309-130932 , archivePrefix =. 1006.3485 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1146/annurev-astro-081309-130932

  59. [67]

    arXiv e-prints , keywords =

    A precise architecture characterization of the Men planetary system. arXiv e-prints , keywords =

  60. [68]

    arXiv e-prints , keywords =

    A significant mutual inclination between the planets within the Mensae system. arXiv e-prints , keywords =

  61. [69]

    3D Radiation Non-ideal Magnetohydrodynamical Simulations Of The Inner Rim In Protoplanetary Disks

    3D Radiation Nonideal Magnetohydrodynamical Simulations of the Inner Rim in Protoplanetary Disks. , keywords =. doi:10.3847/1538-4357/835/2/230 , archivePrefix =. 1612.02740 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/835/2/230

  62. [70]

    The Last Gasp of Gas Giant Planet Formation: A Spitzer Study of the 5 Myr-old Cluster NGC 2362

    The Last Gasp of Gas Giant Planet Formation: A Spitzer Study of the 5 Myr Old Cluster NGC 2362. , keywords =. doi:10.1088/0004-637X/698/1/1 , archivePrefix =. 0903.2666 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/698/1/1

  63. [71]

    New evolutionary models for pre-main sequence and main sequence low-mass stars down to the hydrogen-burning limit

    New evolutionary models for pre-main sequence and main sequence low-mass stars down to the hydrogen-burning limit. , keywords =. doi:10.1051/0004-6361/201425481 , archivePrefix =. 1503.04107 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201425481

  64. [72]

    Detecting the spin-orbit misalignment of the super-Earth 55 Cnc e

    Detecting the spin-orbit misalignment of the super-Earth 55 Cancri e. , keywords =. doi:10.1051/0004-6361/201424266 , archivePrefix =. 1406.6813 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201424266

  65. [73]

    Orbital misalignment of the Neptune-mass exoplanet GJ 436b with the spin of its cool star

    Orbital misalignment of the Neptune-mass exoplanet GJ 436b with the spin of its cool star. , keywords =. doi:10.1038/nature24677 , archivePrefix =. 1712.06638 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/nature24677

  66. [74]

    Rossiter-McLaughlin Observations of 55 Cnc e

    Rossiter-McLaughlin Observations of 55 Cnc e. , keywords =. doi:10.1088/2041-8205/792/2/L31 , archivePrefix =. 1408.2007 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/2041-8205/792/2/l31 2041

  67. [75]

    Satellite dynamics on the Laplace surface

    Satellite Dynamics on the Laplace Surface. , keywords =. doi:10.1088/0004-6256/137/3/3706 , archivePrefix =. 0809.0237 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-6256/137/3/3706

  68. [76]

    arXiv e-prints , keywords =

    The Habitable-zone Planet Finder Reveals A High Mass and a Low Obliquity for the Young Neptune K2-25b. arXiv e-prints , keywords =

  69. [78]

    , keywords =

    Secular resonances and the origin of eccentricities of Mars and the asteroids. , keywords =. doi:10.1016/0019-1035(80)90160-8 , adsurl =

    work page doi:10.1016/0019-1035(80)90160-8

  70. [79]

    Scanning secular resonance theory

    Solar nebula dispersal and the stability of the planetary system I. Scanning secular resonance theory. , keywords =. doi:10.1016/0019-1035(81)90169-X , adsurl =

    work page doi:10.1016/0019-1035(81)90169-x

  71. [80]

    , keywords =

    Secular Resonance, Solar Spin Down, and the Orbit of Mercury. , keywords =. doi:10.1016/0019-1035(76)90117-2 , adsurl =

    work page doi:10.1016/0019-1035(76)90117-2

  72. [81]

    Kortenkamp and George W

    Stephen J. Kortenkamp and George W. Wetherill and Satoshi Inaba , title =. Science , volume =. 2001 , doi =. https://www.science.org/doi/pdf/10.1126/science.1062391 , abstract =

    work page doi:10.1126/science.1062391 2001

  73. [82]

    L., Nichol, R., Bamford, S., et al

    Evolution of spin direction of accreting magnetic protostars and spin-orbit misalignment in exoplanetary systems. , keywords =. doi:10.1111/j.1365-2966.2010.18127.x , archivePrefix =. 1008.3148 , primaryClass =

    work page doi:10.1111/j.1365-2966.2010.18127.x 2010

  74. [83]

    Planet Formation in Disks with Inclined Binary Companions: Can Primordial Spin-Orbit Misalignment be Produced?

    Planet formation in discs with inclined binary companions: can primordial spin-orbit misalignment be produced?. , keywords =. doi:10.1093/mnras/sty1075 , archivePrefix =. 1711.03138 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/sty1075

  75. [84]

    HAT-P-11b: A Super-Neptune Planet Transiting a Bright K Star in the Kepler Field

    HAT-P-11b: A Super-Neptune Planet Transiting a Bright K Star in the Kepler Field. , keywords =. doi:10.1088/0004-637X/710/2/1724 , archivePrefix =. 0901.0282 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/710/2/1724

  76. [85]

    The Occurrence and Architecture of Exoplanetary Systems

    The Occurrence and Architecture of Exoplanetary Systems. , keywords =. doi:10.1146/annurev-astro-082214-122246 , archivePrefix =. 1410.4199 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1146/annurev-astro-082214-122246

  77. [86]

    arXiv e-prints , keywords =

    Orbital misalignment of the super-Earth Men c with the spin of its star. arXiv e-prints , keywords =

  78. [87]

    The Disk Population of the Upper Scorpius Association

    The Disk Population of the Upper Scorpius Association. , keywords =. doi:10.1088/0004-637X/758/1/31 , archivePrefix =. 1209.5433 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/758/1/31

  79. [88]

    Hidden Planetary Friends: On the Stability Of 2-Planet Systems in the Presence of a Distant, Inclined Companion

    Hidden planetary friends: on the stability of two-planet systems in the presence of a distant, inclined companion. , keywords =. doi:10.1093/mnras/sty2830 , archivePrefix =. 1802.00447 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/sty2830

  80. [89]

    Exoplanetary Spin-Orbit Alignment: Results from the Ensemble of Rossiter-McLaughlin Observations

    Exoplanetary Spin-Orbit Alignment: Results from the Ensemble of Rossiter-McLaughlin Observations. , keywords =. doi:10.1088/0004-637X/696/2/1230 , archivePrefix =. 0902.0737 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/696/2/1230

Showing first 80 references.