Pith. sign in

REVIEW 4 major objections 4 minor 298 references

A spin-spin resonance between the two stars of a binary can swing the secondary's tilt to near 90 degrees, even when the primary is nearly aligned.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-01 04:45 UTC pith:Q6QINAPF

load-bearing objection Spin-spin resonance is a plausible new obliquity-excitation pathway, cleanly derived but with hand-picked examples and one contradictory appendix description. the 4 major comments →

arxiv 2607.22423 v1 pith:Q6QINAPF submitted 2026-07-24 astro-ph.SR astro-ph.EP

Spin-spin coupling in stellar binaries

Alexandre C. M. Correia This is my paper
classification astro-ph.SR astro-ph.EP
keywords spin-spin resonancestellar binariesobliquityCassini statesmagnetic brakingtidal dissipationspin-orbit misalignmentsecular dynamics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper claims that a spin-spin resonance, which appears when the two stellar spin-precession frequencies become commensurate, can excite the secondary star's obliquity to high values while the primary remains only weakly tilted. Magnetic braking, which slows the primary's rotation, sweeps the binary through the resonance and can permanently (or temporarily) establish a high-obliquity state; tidal dissipation acts in the opposite direction and can erase it. If correct, the mechanism provides an intrinsic, binary-internal explanation for the observed diversity of spin-orbit misalignment in young binaries, without requiring primordial misalignment or a third body. The author demonstrates the effect in two concrete systems, TOI-2119 and EBLM J2025-45, and maps the conditions under which capture occurs.

Core claim

The central discovery is a previously overlooked coupling: in the secular (orbit-averaged) spin dynamics of a stellar binary, the two stellar spins are not independent but interact via a resonance at φ̇0 ≈ φ̇1, where the precession frequencies of the two spins match. As the primary's rotation period lengthens under magnetic braking, the system crosses this resonance; the secondary's spin can then be captured into a high-obliquity Cassini state, with obliquity rising adiabatically as the period ratio continues to grow. In the absence of tides, the tilt can approach 90° even for a nearly aligned primary. Tides on either star damp the obliquity and, once the primary's tilt is reduced to near ze

What carries the argument

The spin-spin resonance: a commensurability of the two stellar spin-precession frequencies, φ̇i = -αi xi/Si (with xi the obliquity cosine and Si the spin angular momentum), which occurs when the rotation periods are close. The dynamics is governed by an integrable, orbit-averaged Hamiltonian whose stationary solutions are Cassini states; the resonance appears as a libration island around a high-obliquity state that emerges as the primary's rotation period crosses the secondary's. The mechanism is driven by the secular evolution of the rotation periods — magnetic braking lengthening the primary's period and tides competing — which sweeps the system into or away from the commensurability.

Load-bearing premise

The mechanism only operates if a binary actually reaches the spin-spin commensurability with suitable capture conditions; the paper's examples deliberately start with nearly equal rotation periods and a small secondary obliquity, while many real binaries may have period ratios far from unity or initial tilts outside the capture region.

What would settle it

A survey of young binaries measuring stellar rotation periods and obliquities would falsify the mechanism if no system with P0≈P1 shows a secondary tilted above ~30° while the primary is nearly aligned; conversely, finding even one such system with no alternative explanation (third body, primordial tilt) would support it.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the spin-spin resonance operates, binary obliquity can change substantially during the system's life, so a binary's current spin-orbit angle need not equal its primordial value.
  • The mechanism predicts that binaries with rotation periods near a 1:1 commensurability are the most likely to show strong secondary tilts, providing a diagnosable signature.
  • In compact binaries where tides are efficient, high-obliquity states are temporary; persistent high obliquity would imply weak tidal dissipation or recent resonance crossing.
  • Because the resonance requires fast initial rotation and near-equal periods, it is most relevant for young binaries soon after disk dispersal, connecting stellar rotation evolution to obliquity statistics.

Where Pith is reading between the lines

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

  • The same spin-spin coupling might operate in star-planet systems where the planet's spin and the star's spin are both precessing, though the extreme mass ratio would make capture less likely; this is an extension the paper does not explore.
  • One could test the mechanism statistically: in a young cluster with binaries, systems with period ratios close to unity should show a bimodal obliquity distribution (a low and a high branch), whereas systems with very unequal periods should be predominantly aligned.
  • The high-obliquity state in the absence of tides survives indefinitely (per the paper's example), so the mechanism might leave 'fossil' tilts in wide, older binaries; a search for highly tilted secondaries in wide binaries with slowly rotating primaries could discriminate between this and primordial-misalignment models.
  • If magnetic braking alone drives capture, the effect is insensitive to tidal model details; comparing the two examples (one with a brown dwarf, one with two stars) suggests the key parameter is simply the ratio of spin precession rates, so the mechanism may be generic to any two-spin binary.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper studies the secular spin dynamics of a stellar binary, starting from a quadrupolar Hamiltonian and deriving Cassini states as equilibria of the two spins. It identifies a spin-spin resonance that occurs when the two stellar spin-precession frequencies become commensurate, and argues that this resonance can excite the secondary's obliquity to high values even when the primary is only weakly tilted. Magnetic braking drives the system through the resonance, while tidal dissipation damps the obliquity. The claim is illustrated with numerical secular evolution of two example systems, TOI-2119 and EBLM J2025-45, using the author's previous secular formalism with added magnetic-braking and tidal torques.

Significance. If the mechanism is robust, it would offer a new dynamical pathway for generating the observed diversity of spin-orbit misalignment in young stellar binaries, independent of primordial misalignment or tertiary forcing. The analytical derivation is clear and internally consistent, and the approximate Cassini-state expressions in Appendix C are a useful contribution. However, the paper's population-level conclusion currently rests on a small number of hand-picked initial conditions, and the capture process itself is not characterized quantitatively. The strengths are the clean Hamiltonian formulation and the explicit closed-form approximations for the Cassini states under S_1 << L; the weakness is that the demonstrated excitation may depend on fine-tuned initial phases and periods.

major comments (4)
  1. [§3, Eq. (13); §5 and Appendix F] The secular dynamics depend on the relative precession angle Delta_phi through u = sin(theta_1) cos(Delta_phi). The numerical examples specify initial P0, P1, theta_0, and theta_1, but never Delta_phi. For theta_1 = 1 or 5 deg, the sign of u selects which Cassini branch the system follows after the bifurcation, and therefore determines whether the obliquity is excited. As written, the capture outcome is underdetermined by the stated initial conditions. Please report the initial Delta_phi used in each integration and provide a capture map over the initial phase (and, ideally, over the initial obliquities).
  2. [Appendix F, Fig. F.3] The text around Fig. F.3 is internally inconsistent about the crossing direction. The left panel describes a crossing with decreasing P0/P1 and states that resonant capture is not possible. The right panel says that tides make P1 increase faster than P0 and then states that the system crosses the resonance with an increasing P0/P1. But if P1 increases faster than P0, the ratio P0/P1 decreases, not increases. Both panels therefore describe a decreasing P0/P1 crossing. If the right panel nevertheless exhibits capture, the distinction must come from an unstated initial phase or from the additional effect of tidal obliquity damping. Please correct the description and clarify the mechanism responsible for capture in the tidal case.
  3. [§6 and examples] The examples adopt initial rotation periods deliberately near resonance (P0 = 1 d, P1 = 2 d for TOI-2119; P0/P1 = 1.5/2.0 or 2.0/1.5 for EBLM J2025-45) and arbitrary initial secondary obliquities (1 or 5 deg). The manuscript itself concedes that larger initial period ratios 'may delay or prevent the onset of obliquity excitation'. Since the stated goal is to explain observed obliquity diversity, the lack of a quantitative map over initial period ratio, initial theta_1, Delta_phi, and tidal strength means the activation fraction and robustness of the mechanism are unquantified. A schematic parameter-space study is needed to support the population-level conclusion, or the conclusion must be substantially tempered.
  4. [Appendix E] The tidal time-lag parameters are fixed at Delta_t = 0.05 s for m < 0.8 M_sun and Delta_t = 0.005 s for m > 0.8 M_sun, with no sensitivity test. Since the Discussion states that tidal dissipation can vary by orders of magnitude and may either suppress or allow high-obliquity states, the illustrative outcomes are tied to these unvarying choices. Please show how the resonant excitation depends on the tidal strength over a plausible range (e.g., Q = 10^5-10^7) or state which range of Delta_t is required for the mechanism to operate.
minor comments (4)
  1. [Fig. 1 and §3] Figure 1 caption states P0 = 2.1 day and P1 = 2.0 day, while the text says 'P0 ~ P1 = 2 day'. Please harmonize the stated parameters.
  2. [Eq. (C.1)] The approximation delta_1 ~ zeta_1 (R_1/a)^2 should perhaps indicate the omitted factor C_1/(m_1 R_1^2) = zeta_1 and any constants; as written, the scaling is clear but the exact expression would help readers.
  3. [Fig. F.3 caption] The phrase 'allowing resonant capture and subsequent excitation' in the right-panel description should be reconciled with the corrected crossing-direction text (see major comment).
  4. [Appendix B] The ages in Table B.1 are given as ranges (e.g., 0.7-5.1 Gyr) but the simulations appear to use fixed stellar parameters. A sentence explaining which age/structural values were chosen would remove ambiguity.

Circularity Check

0 steps flagged

No significant circularity: the Cassini-state and spin-spin resonance dynamics are derived from the Hamiltonian, and the examples are conditional demonstrations with acknowledged free initial conditions.

full rationale

The central derivation is self-contained. The paper starts from the standard quadrupolar Hamiltonian (Eq. 3), averages over the orbit (Eq. 5), derives the secular precession equations (Eqs. 6-7), reduces the problem to the direction cosines (Eqs. 9-20), and obtains the Cassini states as stationary points of the Hamiltonian (Eqs. 22-25). The high-obliquity branch is a property of these equilibria as the rotation-period ratio changes (Figs. 2 and F.1), not a fitted parameter. The examples set initial rotation periods near resonance and initial secondary obliquities arbitrarily (theta1 = 1 deg or 5 deg), and Section 6 explicitly labels this a convenience: 'we adopted initial rotation periods near resonance, so that the resonance crossing occurs after a short time. Larger initial period ratios may delay or prevent the onset of obliquity excitation.' This is a robustness caveat, not an equation that reduces to its input. The cited works (Boue & Laskar 2009; Correia 2015, 2016) are published derivations with stated assumptions, and the paper re-derives the integrable reduction and equilibria in its own equations rather than merely importing the result. No fitted value is renamed as a prediction. The review concerns about unspecified initial delta-phi, the F.3 crossing-direction description, and the unquantified capture fraction concern the mechanism's applicability and internal consistency, but none makes the claimed excitation equivalent by construction to an input. The paper is therefore best assessed as non-circular: the derivation chain is analytic and the limitations are explicitly acknowledged.

Axiom & Free-Parameter Ledger

6 free parameters · 8 axioms · 0 invented entities

No new particles, forces, or physical entities are introduced. The spin-spin resonance is a configuration of existing angular-momentum vectors. The ledger captures the main hand-chosen inputs: initial periods near resonance, arbitrary secondary obliquities, tidal time lags, and stellar structural parameters. These are the quantities a reader would need to vary to test whether the mechanism is robust or merely an artifact of the chosen examples.

free parameters (6)
  • Initial primary rotation period P0 (TOI-2119) = 1 day
    Chosen near the 2-day secondary period so magnetic braking crosses the spin-spin resonance within the integration time; the paper notes larger ratios may delay or prevent excitation (§5, §6).
  • Initial secondary rotation period P1 (TOI-2119) = 2 day
    Taken from observed brown-dwarf rotation distributions; places the system near commensurability with the primary.
  • Initial secondary obliquity θ1 = 1° (TOI-2119), 5° (EBLM J2025-45)
    Set arbitrarily in §5 and §F; the outcome depends on the capture side and phase, so this choice matters for the excitation.
  • Initial period choices for EBLM J2025-45 = P0=1.5/P1=2.0 d and P0=2.0/P1=1.5 d
    Two experiments chosen to illustrate capture and non-capture; not tied to measured initial periods of the system.
  • Tidal time lag Δt_i = 0.05 s (m<0.8 M☉), 0.005 s (m>0.8 M☉)
    Chosen by hand to correspond to Q≈1e6–1e7; the text acknowledges tidal dissipation can vary by orders of magnitude (§E, §6).
  • Love numbers k2i and structure constants ζi = Table B.1 values
    Estimated from stellar evolution models (Leconte et al. 2011; Claret 2023; Sethi et al. 2026). They set the precession frequency scale and the relative α1/α0, hence the resonance location.
axioms (8)
  • standard math Gyroscopic approximation: each star's spin is aligned with its maximum moment of inertia, with C_i=ζ_i m_i R_i²
    Introduced in §2 before Eq. (1); standard for secular spin dynamics of oblate stars.
  • domain assumption Quadrupolar expansion: terms in (R_i/r)^3 are neglected
    §2 after Eq. (3); valid for the systems considered but excludes higher-order gravitational coupling.
  • domain assumption Secular averaging over one orbital period
    §2, Eq. (5); assumes spin precession is much slower than orbital motion, which is standard for these systems.
  • standard math Total angular momentum J is conserved in the dissipation-free problem
    Eq. (8); follows from the Hamiltonian and is used to reduce the system to two degrees of freedom.
  • domain assumption Small spin-to-orbit ratios S_i ≪ L
    Appendix C, Eq. (C.1): δ1≈ζ1(R1/a)^2≪1; used for the approximate Cassini-state expressions.
  • domain assumption Magnetic braking prescription with Rossby-number saturation
    Appendix D, Eqs. (D.1)–(D.3); adopted from Wright et al. (2018) and Matt et al. (2015, 2019).
  • domain assumption Constant-time-lag tidal model with frequency-independent Δt
    Appendix E, Eq. (E.1); acknowledged as a simplification because the frequency dependence of Δt is unknown.
  • domain assumption The secondary's magnetic braking is negligible in TOI-2119 and slower in EBLM J2025-45
    §5: 'The rotation period of the secondary is not expected to change significantly because it is a brown dwarf'; for EBLM both stars undergo braking but the M-dwarf secondary evolves more slowly.

pith-pipeline@v1.3.0-alltime-deepseek · 11228 in / 16720 out tokens · 180004 ms · 2026-08-01T04:45:50.138278+00:00 · methodology

0 comments
read the original abstract

Spin-orbit misalignment is increasingly observed in binary stars, but its origin remains uncertain. We study the secular spin dynamics of stellar binaries and derive the associated Cassini states. We isolate a spin-spin resonance that arises when the two stellar spin-precession frequencies become commensurate. This resonance can excite the obliquity of the secondary to high values even when the primary is only weakly tilted. Magnetic braking favors the formation of high-obliquity states, whereas tidal dissipation may suppress them. Spin-spin coupling may thus help explain the observed diversity of obliquities in young stellar binaries.

Figures

Figures reproduced from arXiv: 2607.22423 by Alexandre C. M. Correia.

Figure 1
Figure 1. Figure 1: Secular trajectories in the TOI-2119 system (Table B.1) adopting P0 = 2.1 day and P1 = 2.0 day. We show the spin axis of the secondary, s1, projected on the orbital plane. These trajectories are obtained by plotting the level curves H0(u, v, x⋆) = const (Eq. (20)). The stationary solutions (Cassini states) are marked with a dot. Following Correia (2016), we can get z from expression (13), z = x0 x1 + u (1 … view at source ↗
Figure 2
Figure 2. Figure 2: Cassini states as a function of the rotation period of the pri￾mary, P0, for the TOI-2119 system (Table B.1) with P1 = 2 day. These equilibria are obtained by solving Eq. (25). The vertical dashed line cor￾responds to the configuration shown in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Secular spin evolution of the TOI-2119 binary stars as a function of time. We show the obliquity (top), rotation period (middle), and precession frequency ratio (bottom). The primary and secondary spins are shown in blue and red, respectively. The left column shows the evolution under magnetic braking alone, while the right column also includes tidal effects for both stars. 6. Discussion In this Letter, we… view at source ↗

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

298 extracted references · 41 linked inside Pith

  1. [1]

    IAU Minor Planet Center

  2. [2]

    Handbook of Mathematical Functions

  3. [3]

    , year = 1996, month = jan, volume = 44, pages =

    Ancillary data services of NASA's Navigation and Ancillary Information Facility. , year = 1996, month = jan, volume = 44, pages =. doi:10.1016/0032-0633(95)00107-7 , adsurl =

    doi:10.1016/0032-0633(95)00107-7 1996

  4. [4]

    Science , year = 1999, month = apr, volume = 284, pages =

    Global Distribution of Crustal Magnetization Discovered by the Mars Global Surveyor MAG/ER Experiment. Science , year = 1999, month = apr, volume = 284, pages =

    1999

  5. [5]

    , archivePrefix = "arXiv", eprint =

    Twenty-one New Light Curves of OGLE-TR-56b: New System Parameters and Limits on Timing Variations. , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/741/2/102 , adsurl =

    doi:10.1088/0004-637x/741/2/102

  6. [6]

    , archivePrefix = "arXiv", eprint =

    On the stability of extrasolar planetary systems and other closely orbiting pairs. , archivePrefix = "arXiv", eprint =. doi:10.1093/mnras/stu2397 , adsurl =

    doi:10.1093/mnras/stu2397

  7. [7]

    , year = 1999, month = nov, volume = 142, pages =

    On the Character and Consequences of Large Impacts in the Late Stage of Terrestrial Planet Formation. , year = 1999, month = nov, volume = 142, pages =. doi:10.1006/icar.1999.6201 , adsurl =

    arXiv 1999

  8. [8]

    , year = 2006, month = may, volume = 441, pages =

    Neptune's capture of its moon Triton in a binary-planet gravitational encounter. , year = 2006, month = may, volume = 441, pages =. doi:10.1038/nature04792 , adsurl =

    doi:10.1038/nature04792 2006

  9. [9]

    , keywords =

    Detectability of shape deformation in short-period exoplanets. , keywords =. doi:10.1051/0004-6361/201834215 , archivePrefix =. 1812.04538 , primaryClass =

    Pith/arXiv arXiv

  10. [10]

    , keywords =

    Misaligned spin and orbital axes cause the anomalous precession of DI Herculis. , keywords =. doi:10.1038/nature08408 , archivePrefix =. 0909.2861 , primaryClass =

    Pith/arXiv arXiv

  11. [11]

    The BANANA Project. V. Misaligned and Precessing Stellar Rotation Axes in CV Velorum. , keywords =. doi:10.1088/0004-637X/785/2/83 , archivePrefix =. 1403.0583 , primaryClass =

    Pith/arXiv arXiv

  12. [12]

    , year = 1973, month = aug, volume = 23, pages =

    The Weak Friction Approximation and Tidal Evolution in Close Binary Systems. , year = 1973, month = aug, volume = 23, pages =. doi:10.1007/BF00645172 , adsurl =

    doi:10.1007/bf00645172 1973

  13. [13]

    , eprint =

    Formation and structure of the three Neptune-mass planets system around HD 69830. , eprint =. doi:10.1051/0004-6361:20065697 , adsurl =

    doi:10.1051/0004-6361:20065697

  14. [14]

    , eprint =

    Models of giant planet formation with migration and disc evolution. , eprint =. doi:10.1051/0004-6361:20042032 , adsurl =

    doi:10.1051/0004-6361:20042032

  15. [15]

    semi-major axis

    Theoretical models of planetary system formation: mass vs. semi-major axis. , archivePrefix = "arXiv", eprint =. doi:10.1051/0004-6361/201321690 , adsurl =

    doi:10.1051/0004-6361/201321690

  16. [16]

    From 0.2 to 1.5 M _ at seven metallicities from PMS to TAMS

    First grids of low-mass stellar models and isochrones with self-consistent treatment of rotation. From 0.2 to 1.5 M _ at seven metallicities from PMS to TAMS. , keywords =. doi:10.1051/0004-6361/201935160 , archivePrefix =. 1905.08516 , primaryClass =

    Pith/arXiv arXiv 1905

  17. [17]

    , year = 1973, month = nov, volume = 20, pages =

    Pluto: New Photometry and a Determination of the Axis of Rotation. , year = 1973, month = nov, volume = 20, pages =. doi:10.1016/0019-1035(73)90004-3 , adsurl =

    doi:10.1016/0019-1035(73)90004-3 1973

  18. [18]

    Geophysical Journal International , keywords =

    The frequency dependence of Q in the Earth and implications for mantle rheology and Chandler wobble. Geophysical Journal International , keywords =. doi:10.1111/j.1365-246X.1979.tb01033.x , adsurl =

    doi:10.1111/j.1365-246x.1979.tb01033.x 1979

  19. [19]

    , year = 1987, month = sep, volume = 71, pages =

    The mass, gravity field, and ephemeris of Mercury. , year = 1987, month = sep, volume = 71, pages =. doi:10.1016/0019-1035(87)90033-9 , adsurl =

    doi:10.1016/0019-1035(87)90033-9 1987

  20. [20]

    Science , year = 1998, month = sep, volume = 281, pages =

    Europa's Differentiated Internal Structure: Inferences from Four Galileo Encounters. Science , year = 1998, month = sep, volume = 281, pages =. doi:10.1126/science.281.5385.2019 , adsurl =

    arXiv 1998

  21. [21]

    , year = 2001, month = sep, volume = 153, pages =

    Shape, Mean Radius, Gravity Field, and Interior Structure of Callisto. , year = 2001, month = sep, volume = 153, pages =. doi:10.1006/icar.2001.6664 , adsurl =

    arXiv 2001

  22. [22]

    , archivePrefix = "arXiv", eprint =

    Formation and stellar spin-orbit misalignment of hot Jupiters from Lidov-Kozai oscillations in stellar binaries. , archivePrefix = "arXiv", eprint =. doi:10.1093/mnras/stv2906 , adsurl =

    doi:10.1093/mnras/stv2906

  23. [23]

    , keywords =

    Eccentricity and spin-orbit misalignment in short-period stellar binaries as a signpost of hidden tertiary companions. , keywords =. doi:10.1093/mnras/stx293 , archivePrefix =. 1610.02626 , primaryClass =

    Pith/arXiv arXiv

  24. [24]

    , keywords =

    Excitation of Spin-Orbit Misalignments in Stellar Binaries with Circumbinary Disks: Application to DI Herculis. , keywords =. doi:10.3847/1538-4357/abcda2 , archivePrefix =. 2010.15122 , primaryClass =

    Pith/arXiv arXiv 2010

  25. [25]

    Cours de M\' e canique C\' e leste

  26. [26]

    On the Rigidity of the Earth. Proc. R. Soc. Lond. A , year = 1910, volume = 84, pages =

    1910

  27. [27]

    ArXiv e-prints , archivePrefix = "arXiv", eprint =

    How eccentric orbital solutions can hide planetary systems in 2:1 resonant orbits. ArXiv e-prints , archivePrefix = "arXiv", eprint =

  28. [28]

    , keywords =

    A terrestrial planet candidate in a temperate orbit around Proxima Centauri. , keywords =. doi:10.1038/nature19106 , archivePrefix =. 1609.03449 , primaryClass =

    Pith/arXiv arXiv

  29. [29]

    On Oort's Constant B. Pub. Astron. Soc. Japan , year = 1967, volume = 19, pages =

    1967

  30. [30]

    , year = 1969, volume = 74, pages =

    Friction between Mantle and Core of the Earth as a Cause of the Secular Change in Obliquity. , year = 1969, volume = 74, pages =. doi:10.1086/110808 , adsurl =

    doi:10.1086/110808 1969

  31. [31]

    ArXiv e-prints , archivePrefix = "arXiv", eprint =

    Thermal Tides in Short Period Exoplanets. ArXiv e-prints , archivePrefix = "arXiv", eprint =

  32. [32]

    , archivePrefix = "arXiv", eprint =

    Thermal Tides in Fluid Extrasolar Planets. , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/714/1/1 , adsurl =

    doi:10.1088/0004-637x/714/1/1

  33. [33]

    Physics of the Earth and Planetary Interiors , year = 1984, month = sep, volume = 34, pages =

    Thermal evolution of Venus. Physics of the Earth and Planetary Interiors , year = 1984, month = sep, volume = 34, pages =. doi:10.1016/0031-9201(84)90065-7 , adsurl =

    doi:10.1016/0031-9201(84)90065-7 1984

  34. [34]

    Celestial Mechanics and Dynamical Astronomy , keywords =

    Mutual gravitational potential and torque of solid bodies via inertia integrals. Celestial Mechanics and Dynamical Astronomy , keywords =. doi:10.1007/s10569-007-9092-7 , adsurl =

    doi:10.1007/s10569-007-9092-7

  35. [35]

    , archivePrefix = "arXiv", eprint =

    Impact of the frequency dependence of tidal Q on the evolution of planetary systems. , archivePrefix = "arXiv", eprint =. doi:10.1051/0004-6361/201322782 , adsurl =

    doi:10.1051/0004-6361/201322782

  36. [36]

    , archivePrefix = "arXiv", eprint =

    Atmospheric tides in Earth-like planets. , archivePrefix = "arXiv", eprint =. doi:10.1051/0004-6361/201628252 , adsurl =

    doi:10.1051/0004-6361/201628252

  37. [37]

    , archivePrefix = "arXiv", eprint =

    The rotation of planets hosting atmospheric tides: from Venus to habitable super-Earths. , archivePrefix = "arXiv", eprint =. doi:10.1051/0004-6361/201628701 , adsurl =

    doi:10.1051/0004-6361/201628701

  38. [38]

    , keywords =

    Generic frequency dependence for the atmospheric tidal torque of terrestrial planets. , keywords =. doi:10.1051/0004-6361/201834685 , archivePrefix =. 1902.00280 , primaryClass =

    Pith/arXiv arXiv 1902

  39. [39]

    Kosmicheskie Issledovaniia , keywords =

    Preliminary results of an investigation of the light regime in the atmosphere and on the surface of Venus. Kosmicheskie Issledovaniia , keywords =

  40. [40]

    Convectively generated internal gravity waves in the lower atmosphere of Venus. I. No wind shear. Journal of Atmospheric Sciences , keywords =. doi:10.1175/1520-0469(2000)057<0184:CGIGWI>2.0.CO;2 , adsurl =

    doi:10.1175/1520-0469(2000)057 2000

  41. [41]

    , archivePrefix = "arXiv", eprint =

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

    doi:10.1088/0004-637x/710/2/1724

  42. [42]

    , archivePrefix = "arXiv", eprint =

    HAT-P-20b-HAT-P-23b: Four Massive Transiting Extrasolar Planets. , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/742/2/116 , adsurl =

    doi:10.1088/0004-637x/742/2/116

  43. [43]

    , archivePrefix = "arXiv", eprint =

    HAT-P-34b-HAT-P-37b: Four Transiting Planets More Massive than Jupiter Orbiting Moderately Bright Stars. , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-6256/144/1/19 , adsurl =

    doi:10.1088/0004-6256/144/1/19

  44. [44]

    , keywords =

    A dynamical history of the inner Neptunian satellites. , keywords =. doi:10.1016/0019-1035(92)90155-Z , adsurl =

    doi:10.1016/0019-1035(92)90155-z

  45. [45]

    The Outer Solar System Origins Survey. I. Design and First-quarter Discoveries. , keywords =. doi:10.3847/0004-6256/152/3/70 , archivePrefix =. 1511.02895 , primaryClass =

    Pith/arXiv arXiv

  46. [46]

    OSSOS. VII. 800+ Trans-Neptunian Objects The Complete Data Release. , keywords =. doi:10.3847/1538-4365/aab77a , archivePrefix =. 1805.11740 , primaryClass =

    Pith/arXiv arXiv

  47. [47]

    Vistas in Astronomy , year = 1979, volume = 23, pages =

    CORAVEL - A new tool for radial velocity measurements. Vistas in Astronomy , year = 1979, volume = 23, pages =. doi:10.1016/0083-6656(79)90016-3 , adsurl =

    doi:10.1016/0083-6656(79)90016-3 1979

  48. [48]

    , year = 1996, month = oct, volume = 119, pages =

    ELODIE: A spectrograph for accurate radial velocity measurements. , year = 1996, month = oct, volume = 119, pages =

    1996

  49. [49]

    Transiting exoplanets from the CoRoT space mission. I. CoRoT-Exo-1b: a low-density short-period planet around a G0V star. , archivePrefix = "arXiv", eprint =. doi:10.1051/0004-6361:200809353 , adsurl =

    doi:10.1051/0004-6361:200809353

  50. [50]

    , year = 1975, month = jul, volume = 12, pages =

    Gravitational two-body problem with arbitrary masses, spins, and quadrupole moments. , year = 1975, month = jul, volume = 12, pages =. doi:10.1103/PhysRevD.12.329 , adsurl =

    doi:10.1103/physrevd.12.329 1975

  51. [52]

    , year = 1999, month = oct, volume = 141, pages =

    Mercurian Impact Craters: Implications for Polar Ground Ice. , year = 1999, month = oct, volume = 141, pages =. doi:10.1006/icar.1999.6165 , adsurl =

    arXiv 1999

  52. [53]

    , eprint =

    Measuring the Oblateness and Rotation of Transiting Extrasolar Giant Planets. , eprint =. doi:10.1086/373893 , adsurl =

    doi:10.1086/373893

  53. [54]

    Astrobiology , archivePrefix = "arXiv", eprint =

    Tides and the Evolution of Planetary Habitability. Astrobiology , archivePrefix = "arXiv", eprint =. doi:10.1089/ast.2007.0204 , adsurl =

    arXiv 2007

  54. [56]

    Astrobiology , archivePrefix = "arXiv", eprint =

    Tidal Venuses: Triggering a Climate Catastrophe via Tidal Heating. Astrobiology , archivePrefix = "arXiv", eprint =. doi:10.1089/ast.2012.0851 , adsurl =

    arXiv 2012

  55. [57]

    , archivePrefix = "arXiv", eprint =

    Revisiting the transits of CoRoT-7b at a lower activity level. , archivePrefix = "arXiv", eprint =. doi:10.1051/0004-6361/201423939 , adsurl =

    doi:10.1051/0004-6361/201423939

  56. [58]

    , keywords =

    Detection of the tidal deformation of WASP-103b at 3 with CHEOPS. , keywords =. doi:10.1051/0004-6361/202142196 , archivePrefix =. 2201.03328 , primaryClass =

    Pith/arXiv arXiv

  57. [59]

    Science Monthly , year = 1932, volume = 35, pages =

    Tides in the atmosphere. Science Monthly , year = 1932, volume = 35, pages =

    1932

  58. [60]

    , keywords =

    Dynamical evolution of triple-star systems by Lidov-Kozai cycles and tidal friction. , keywords =. doi:10.1093/mnras/sty1758 , archivePrefix =. 1807.05901 , primaryClass =

    Pith/arXiv arXiv

  59. [61]

    , archivePrefix = "arXiv", eprint =

    Determination of the Interior Structure of Transiting Planets in Multiple-Planet Systems. , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/704/1/L49 , adsurl =

    doi:10.1088/0004-637x/704/1/l49

  60. [62]

    , archivePrefix = "arXiv", eprint =

    Resolving the sin(I) Degeneracy in Low-mass Multi-planet Systems. , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/730/2/95 , adsurl =

    doi:10.1088/0004-637x/730/2/95

  61. [63]

    Celestial Mechanics and Dynamical Astronomy , archivePrefix = "arXiv", eprint =

    Onset of secular chaos in planetary systems: period doubling and strange attractors. Celestial Mechanics and Dynamical Astronomy , archivePrefix = "arXiv", eprint =. doi:10.1007/s10569-011-9361-3 , adsurl =

    doi:10.1007/s10569-011-9361-3

  62. [64]

    , archivePrefix = "arXiv", eprint =

    Analytical treatment of planetary resonances. , archivePrefix = "arXiv", eprint =. doi:10.1051/0004-6361/201220907 , adsurl =

    doi:10.1051/0004-6361/201220907

  63. [65]

    , archivePrefix = "arXiv", eprint =

    Dissipative Divergence of Resonant Orbits. , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-6256/145/1/1 , adsurl =

    doi:10.1088/0004-6256/145/1/1

  64. [66]

    , archivePrefix = "arXiv", eprint =

    Capture of planets into mean-motion resonances and the origins of extrasolar orbital architectures. , archivePrefix = "arXiv", eprint =. doi:10.1093/mnras/stv1063 , adsurl =

    doi:10.1093/mnras/stv1063

  65. [67]

    , archivePrefix = "arXiv", eprint =

    Spin-Spin Coupling in the Solar System. , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/810/2/110 , adsurl =

    doi:10.1088/0004-637x/810/2/110

  66. [68]

    , archivePrefix = "arXiv", eprint =

    Chaotic Disintegration of the Inner Solar System. , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/799/2/120 , adsurl =

    doi:10.1088/0004-637x/799/2/120

  67. [69]

    , archivePrefix = "arXiv", eprint =

    Evidence for a Distant Giant Planet in the Solar System. , archivePrefix = "arXiv", eprint =. doi:10.3847/0004-6256/151/2/22 , adsurl =

    doi:10.3847/0004-6256/151/2/22

  68. [70]

    , keywords =

    Formation of Giant Planet Satellites. , keywords =. doi:10.3847/1538-4357/ab8937 , archivePrefix =. 2005.08330 , primaryClass =

    Pith/arXiv arXiv 2005

  69. [71]

    , archivePrefix = "arXiv", eprint =

    Detection of a Third Planet in the HD 74156 System Using the Hobby-Eberly Telescope. , archivePrefix = "arXiv", eprint =. doi:10.1086/523701 , adsurl =

    doi:10.1086/523701

  70. [72]

    Masses and orbital coplanarity for planets b and c

    The architecture of the GJ 876 planetary system. Masses and orbital coplanarity for planets b and c. , archivePrefix = "arXiv", eprint =. doi:10.1051/0004-6361/200811280 , adsurl =

    doi:10.1051/0004-6361/200811280

  71. [73]

    Celestial Mechanics and Dynamical Astronomy , keywords =

    Asymmetric Librations in Exterior Resonances. Celestial Mechanics and Dynamical Astronomy , keywords =. doi:10.1007/BF00693323 , adsurl =

    doi:10.1007/bf00693323

  72. [74]

    Application to the GJ876 planetary system

    Modelling the high-eccentricity planetary three-body problem. Application to the GJ876 planetary system. , keywords =. doi:10.1046/j.1365-8711.2003.06345.x , adsurl =

    arXiv 2003

  73. [75]

    , eprint =

    Extrasolar Planets in Mean-Motion Resonance: Apses Alignment and Asymmetric Stationary Solutions. , eprint =. doi:10.1086/376568 , adsurl =

    doi:10.1086/376568

  74. [76]

    , keywords =

    Planetary migration and extrasolar planets in the 2/1 mean-motion resonance. , keywords =. doi:10.1111/j.1365-2966.2005.09779.x , archivePrefix =. astro-ph/0404166 , primaryClass =

    arXiv 2005

  75. [77]

    , keywords =

    Co-orbital terrestrial planets in exoplanetary systems: a formation scenario. , keywords =. doi:10.1051/0004-6361:20066582 , adsurl =

    doi:10.1051/0004-6361:20066582

  76. [78]

    , archivePrefix = "arXiv", eprint =

    Multiple-planet Scattering and the Origin of Hot Jupiters. , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/751/2/119 , adsurl =

    doi:10.1088/0004-637x/751/2/119

  77. [79]

    , archivePrefix = "arXiv", eprint =

    Emerging Trends in a Period-Radius Distribution of Close-in Planets. , archivePrefix = "arXiv", eprint =. doi:10.1088/0004-637X/763/1/12 , adsurl =

    doi:10.1088/0004-637x/763/1/12

  78. [80]

    , eprint =

    Discovery of a cool planet of 5.5 Earth masses through gravitational microlensing. , eprint =. doi:10.1038/nature04441 , adsurl =

    doi:10.1038/nature04441

  79. [81]

    Journal of Geophysical Research (Planets) , keywords =

    Coupling mantle convection and tidal dissipation: Applications to Enceladus and Earth-like planets. Journal of Geophysical Research (Planets) , keywords =. doi:10.1029/2009JE003564 , adsurl =

    doi:10.1029/2009je003564

  80. [82]

    , archivePrefix = "arXiv", eprint =

    (47171) 1999 TC _ 36 , A transneptunian triple. , archivePrefix = "arXiv", eprint =. doi:10.1016/j.icarus.2009.12.017 , adsurl =

    doi:10.1016/j.icarus.2009.12.017 1999

Showing first 80 references.