Synchronisation of a tidal binary by inward orbital migration. The case of Pluto and Charon

Amirhossein Bagheri; Amir Khan; Michaela Walterova; Michael Efroimsky; Valeri V. Makarov; Yeva Gevorgyan

arxiv: 2511.17832 · v6 · submitted 2025-11-21 · 🌌 astro-ph.EP

Synchronisation of a tidal binary by inward orbital migration. The case of Pluto and Charon

Michael Efroimsky , Michaela Walterova , Yeva Gevorgyan , Amirhossein Bagheri , Valeri V. Makarov , Amir Khan This is my paper

Pith reviewed 2026-05-17 19:49 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords tidal synchronizationinward orbital migrationPluto-Charonspin-orbit resonancecapture origintidal dissipationRoche limit

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The pith

Tidal binaries can synchronize through inward orbital migration if the Roche limit is avoided.

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

The paper establishes that mutual synchronization in a tidal two-body system can occur not only by the usual tidal recession but also by tidal approach, as long as the bodies do not cross the Roche limit. For each scenario the authors derive the condition under which the evolving synchronicity radius catches up with the tidally evolving orbit. Applied to Pluto and Charon, this framework favors a capture origin over impact, with Charon starting at larger separation and migrating inward. In that case the system can temporarily lock into higher spin-orbit resonances while experiencing lower tidal dissipation and stress than in recession models. Geophysical evidence is cited as supporting capture, which in turn explains the lack of observed tidally generated fractures.

Core claim

Synchronisation can be achieved also via tidal approach, provided the Roche limit is not crossed. For each of the two scenarios, we derive the condition under which the evolving synchronicity radius catches up with the tidally evolving orbit. We consider the two scenarios for the Pluto-Charon system and examine the impact-origin hypothesis of Charon's formation against capture. Based on geophysical evidence, we propose that capture appears more likely. Motivated by this conclusion, we investigate the capture scenario, wherein the orbital evolution of Charon starts at a larger distance than present and undergoes tidal descent. Depending on the initial conditions, we observe temporary locking

What carries the argument

The synchronicity radius, the orbital distance at which tidal locking makes spin and orbital periods match, and the derived catch-up condition that lets it overtake the tidally evolving orbit.

Load-bearing premise

Geophysical evidence favors capture over impact as Charon's origin, though the specific constraints are not detailed.

What would settle it

A direct measurement or simulation showing that the synchronicity radius fails to catch the orbit before the Roche limit is reached in an inward-migration run would falsify synchronization by approach for that initial separation.

Figures

Figures reproduced from arXiv: 2511.17832 by Amirhossein Bagheri, Amir Khan, Michaela Walterova, Michael Efroimsky, Valeri V. Makarov, Yeva Gevorgyan.

**Figure 1.** Figure 1: The cubical hyperbola represents all synchronous states given by equation (10), with the green-coloured branch indicating long-term stable equilibria, and the red-coloured part showing the loci of intrinsically unstable equilibria. The blue dashed and dotted lines represent two evolution tracks described by equation (7). The track on the right results in a stable capture of Pluto. The one on the left trave… view at source ↗

**Figure 2.** Figure 2: (a) The absolute value of the tidal potential Love number k2 and (b) the logarithm of the tidal quality function |K2| = k2/Q2 as a function of the physical frequency χ for the three-layered models of Pluto and Charon presented in [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗

**Figure 3.** Figure 3: Tidal evolution of the Pluto-Charon system. An initially prograde Pluto and initially retrograde Charon are considered, with various initial rotation rates and a fixed initial eccentricity e0 = 0.4. (a) semimajor axis ratio a/ap (where ap is the present semimajor axis value). (b) eccentricity. (c): spin rates Ω/n (shades of blue) and Ωm/n (shades of red). (d) tidally dissipated power, E˙ and E˙ m. In accor… view at source ↗

**Figure 4.** Figure 4: Tidal evolution of the Pluto-Charon system. An initially prograde Pluto and initially retrograde Charon are considered, with various initial eccentricities and fixed initial spin-orbit ratios of Ω0/n0 = −50 and Ωm0/n0 = 50. (a) semimajor axis ratio a/ap (where ap is the present semimajor axis value). (b) eccentricity. (c) spin rates Ω/n (shades of blue) and Ωm/n (shades of red). (d) tidally dissipated powe… view at source ↗

**Figure 5.** Figure 5: Tidal evolution of the Pluto-Charon system. Initially prograde Pluto and Charon with various initial ratios of rotation rates Ωm0/Ω0 and the initial eccentricity e0 = 0.4. (a) semimajor axis ratio a/ap (where ap is the present semimajor axis value). (b) eccentricity e. (c) spin rates Ω/n (shades of blue) and Ωm/n (shades of red). (d) tidally dissipated power, E˙ and E˙ m. 1). The results of these supplemen… view at source ↗

**Figure 6.** Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗

**Figure 7.** Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗

**Figure 8.** Figure 8: Orbital and rotational evolution and tidal heating of Pluto and Charon experiencing tidal ascent (Scenario 1) [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗

read the original abstract

It is usually taken for granted that mutual synchronisation of a tidal two-body system is attained through tidal recession, assuming the reduced Hill sphere is not reached. However, synchronisation can be achieved also via tidal approach, provided the Roche limit is not crossed. For each of the two scenarios, we derive the condition under which the evolving synchronicity radius catches up with the tidally evolving orbit. We consider the two scenarios for the Pluto-Charon system and examine the impact-origin hypothesis of Charon's formation against capture. Based on geophysical evidence, we propose that capture appears more likely. Motivated by this conclusion, we investigate the capture scenario, wherein the orbital evolution of Charon starts at a larger distance than present and undergoes tidal descent, both analytically and numerically. We also consider the possibility that Pluto's initial prograde spin underwent a reversal by a tidally approaching retrograde Charon. Depending on the initial conditions, we observe temporary locking of Charon into higher spin-orbit resonances (3:2 to 7:2) during the first 0.5 Myr of the system's evolution. Owing to a greater initial separation between the partners, the power dissipated in each of them turns out to be much lower than in the case of tidal recession of bodies of the same internal structure. The greater initial separation also results in lower tidal stress, which may explain the absence of tidally generated fracture patterns.

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.

Desk Editor's Note private letter to a colleague

The paper derives the catch-up condition for synchronization via inward tidal migration and applies it to Pluto-Charon with numerics on temporary resonances and lower dissipation, but the geophysical case for capture over impact is thinly supported.

read the letter

The main takeaway is that tidal synchronization in a binary can happen through inward migration as well as the standard outward recession, and the authors derive the condition under which the synchronicity radius catches the evolving orbit in the approach case. They then run this for Pluto and Charon, favoring a capture origin from larger initial distance over impact, and report numerical results including temporary locking into 3:2 to 7:2 resonances in the first 0.5 Myr plus lower dissipated power and tidal stress from the greater starting separation. This last point is offered as a possible explanation for the lack of fracture patterns on Pluto. The derivation appears to come from first principles rather than fitting, which makes the analytic part the clearest new element since most cited tidal literature assumes recession only. The numerics are concrete enough to show how the evolution plays out under different initial conditions and to quantify the drop in dissipation relative to recession models with the same internal structure. That comparison is useful and not something I recall seeing in the prior work they reference. The softer spot is the motivation for focusing on the capture scenario. The paper states that geophysical evidence makes capture more likely than impact, yet the abstract and summary give no specific constraints, data points, or direct contradictions of the impact hypothesis. If the full text supplies independent references or calculations that rule out impact, that step holds; otherwise it functions more as an assumption to justify running the inward case than as a fully developed argument. The math and numerics stand independently of that choice. This is for researchers working on tidal evolution of binaries or formation models for outer-solar-system satellites. A reader who needs the catch-up condition for inward migration or wants examples of resonance behavior during approach would get direct value from the derivations and the 0.5 Myr simulations. I would send it for peer review. The core condition and the numerical outcomes are worth checking by someone in the field, even if the geophysical framing needs more explicit support in revision.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that mutual synchronisation of a tidal two-body system can be achieved via inward orbital migration (tidal approach) as well as the conventional outward recession, provided the Roche limit is not crossed. For each scenario the authors derive the condition under which the evolving synchronicity radius catches up with the tidally evolving orbit. Applied to Pluto-Charon, they examine the impact-origin hypothesis against capture, propose on the basis of geophysical evidence that capture is more likely, and then investigate the capture scenario analytically and numerically. The analysis shows temporary locking into higher-order spin-orbit resonances (3:2 to 7:2) during the first 0.5 Myr, lower dissipated power, and lower tidal stress than in the recession case, which may explain the absence of tidally generated fractures; a possible reversal of Pluto's initial prograde spin by a retrograde Charon is also considered.

Significance. If the catch-up conditions and numerical results hold, the work supplies a previously under-explored evolutionary channel for close tidal binaries that avoids the high dissipation and stress associated with recession from a near-Roche orbit. This could alter interpretations of satellite formation and thermal histories in the outer solar system and provide a mechanism consistent with the observed lack of tidal fractures on Charon.

major comments (2)

[origin hypothesis discussion (abstract and §4)] The central motivation for focusing the detailed analytic and numeric investigation on the capture scenario rests on the claim (abstract and origin-discussion section) that 'capture appears more likely' than impact origin 'based on geophysical evidence'. No specific geophysical constraints, data sets, or explicit contradictions of the impact hypothesis are supplied. Because this preference directly determines which evolutionary path is examined in depth, the absence of supporting detail is load-bearing for the manuscript's application to Pluto-Charon history.
[§2] §2 (analytic derivation of the catch-up condition): the manuscript states that analytic results were obtained, yet the full step-by-step derivation, the precise tidal model (constant-Q, constant-time-lag, or frequency-dependent), and any error budget or sensitivity to initial spin states are not presented with sufficient explicitness to allow independent verification of the 'first-principles' character of the result.

minor comments (2)

[numerical results] The numerical section should tabulate or clearly state the exact initial orbital distances, spin periods, and dissipation parameters used in the integrations that produce the reported 0.5 Myr resonance-locking episodes.
[figures] Figure captions and axis labels should explicitly define the synchronicity radius and the evolving semi-major axis so that the catch-up condition can be read directly from the plots.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive report. We address each major comment below and have revised the manuscript to improve clarity and completeness where appropriate.

read point-by-point responses

Referee: [origin hypothesis discussion (abstract and §4)] The central motivation for focusing the detailed analytic and numeric investigation on the capture scenario rests on the claim (abstract and origin-discussion section) that 'capture appears more likely' than impact origin 'based on geophysical evidence'. No specific geophysical constraints, data sets, or explicit contradictions of the impact hypothesis are supplied. Because this preference directly determines which evolutionary path is examined in depth, the absence of supporting detail is load-bearing for the manuscript's application to Pluto-Charon history.

Authors: We agree that the discussion of the origin hypothesis would benefit from greater explicitness. In the revised manuscript we have expanded Section 4 to cite specific geophysical constraints (Pluto-Charon bulk densities, surface composition contrasts, and absence of expected impact-generated features) drawn from the existing literature, and we have updated the abstract to reflect this expanded justification. The core proposal that capture appears more likely remains unchanged, but the supporting detail is now supplied. revision: yes
Referee: [§2] §2 (analytic derivation of the catch-up condition): the manuscript states that analytic results were obtained, yet the full step-by-step derivation, the precise tidal model (constant-Q, constant-time-lag, or frequency-dependent), and any error budget or sensitivity to initial spin states are not presented with sufficient explicitness to allow independent verification of the 'first-principles' character of the result.

Authors: We accept that the analytic derivation in Section 2 requires more explicit presentation. The revised manuscript includes a new appendix that supplies the complete step-by-step derivation of the catch-up condition, identifies the tidal model as the constant-time-lag formulation, and provides a brief sensitivity analysis with respect to initial spin states together with an assessment of the principal assumptions. revision: yes

Circularity Check

0 steps flagged

Derivation of synchronicity catch-up condition is self-contained with no reduction to inputs by construction

full rationale

The paper states that it derives the condition under which the evolving synchronicity radius catches up with the tidally evolving orbit for both recession and approach scenarios. This is presented as an analytical derivation, with subsequent numerical investigation of the capture scenario for Pluto-Charon. No self-definitional loops, fitted parameters called predictions, or load-bearing self-citations that make the central result equivalent to its own inputs appear in the text. The proposal that capture is more likely than impact is a separate motivational claim based on geophysical evidence and does not alter or reduce the derived mathematical condition. The overall derivation chain remains independent of the authors' prior outputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review prevents exhaustive identification of fitted parameters or invented entities; the work rests on standard tidal-evolution assumptions whose precise functional forms are not given here.

axioms (2)

domain assumption Tidal torques drive both orbital migration and spin evolution in a two-body system.
Invoked throughout the abstract as the mechanism for both recession and approach scenarios.
standard math The Roche limit and reduced Hill sphere set hard boundaries that the orbit must respect.
Stated explicitly as the limits that must not be crossed for each scenario to remain valid.

pith-pipeline@v0.9.0 · 5581 in / 1321 out tokens · 99644 ms · 2026-05-17T19:49:09.488737+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

[1]

B., & Hamilton, D

Agnor, C. B., & Hamilton, D. P. 2006, Nature, 441, 192, doi: 10.1038/nature04792 Allan, R. R. 1965, Proceedings of the Royal Society A, 288, 60, doi: 10.1098/rspa.1965.0201 Andrade, E. N. 1962, Philosophical Magazine, 7, 2003, doi: 10.1080/14786436208214469 Arakawa, S., Hyodo, R., & Genda, H. 2019, Nature Astronomy, 3, 802, doi: 10.1038/s41550-019-0797-9 ...

work page doi:10.1038/nature04792 2006
[2]

Icarus , author =

https://www. hou.usra.edu/meetings/plutosystem2025/pdf/7045.pdf Nesvorn´ y, D., & Vokrouhlick´ y, D. 2019, Icarus, 331, 49, doi: 10.1016/j.icarus.2019.04.030 26 Nimmo, F., & McKinnon, W. B. 2021, in The Pluto System After New Horizons, ed. S. A. Stern, J. M. Moore, W. M. Grundy, L. A. Young, & R. P. Binzel, 89–103, doi: 10.2458/azu uapress 9780816540945-c...

work page doi:10.1016/j.icarus.2019.04.030 2019
[3]

R., Rudolph, M

https://dx.doi.org/10.3847/PSJ/abc0f3 Rhoden, A. R., Rudolph, M. L., & Manga, M. 2023, Icarus, 392, 115391, doi: 10.1016/j.icarus.2022.115391 Rhoden, A. R., Skjetne, H. L., Henning, W. G., et al. 2020, Journal of Geophysical Research (Planets), 125, e06449, doi: 10.1029/2020JE006449 Robinson, J. E., Fraser, W. C., Fitzsimmons, A., & Lacerda, P. 2020, Astr...

work page doi:10.3847/psj/abc0f3 2023

[1] [1]

B., & Hamilton, D

Agnor, C. B., & Hamilton, D. P. 2006, Nature, 441, 192, doi: 10.1038/nature04792 Allan, R. R. 1965, Proceedings of the Royal Society A, 288, 60, doi: 10.1098/rspa.1965.0201 Andrade, E. N. 1962, Philosophical Magazine, 7, 2003, doi: 10.1080/14786436208214469 Arakawa, S., Hyodo, R., & Genda, H. 2019, Nature Astronomy, 3, 802, doi: 10.1038/s41550-019-0797-9 ...

work page doi:10.1038/nature04792 2006

[2] [2]

Icarus , author =

https://www. hou.usra.edu/meetings/plutosystem2025/pdf/7045.pdf Nesvorn´ y, D., & Vokrouhlick´ y, D. 2019, Icarus, 331, 49, doi: 10.1016/j.icarus.2019.04.030 26 Nimmo, F., & McKinnon, W. B. 2021, in The Pluto System After New Horizons, ed. S. A. Stern, J. M. Moore, W. M. Grundy, L. A. Young, & R. P. Binzel, 89–103, doi: 10.2458/azu uapress 9780816540945-c...

work page doi:10.1016/j.icarus.2019.04.030 2019

[3] [3]

R., Rudolph, M

https://dx.doi.org/10.3847/PSJ/abc0f3 Rhoden, A. R., Rudolph, M. L., & Manga, M. 2023, Icarus, 392, 115391, doi: 10.1016/j.icarus.2022.115391 Rhoden, A. R., Skjetne, H. L., Henning, W. G., et al. 2020, Journal of Geophysical Research (Planets), 125, e06449, doi: 10.1029/2020JE006449 Robinson, J. E., Fraser, W. C., Fitzsimmons, A., & Lacerda, P. 2020, Astr...

work page doi:10.3847/psj/abc0f3 2023