A Pluto-Charon Sonata III. Growth of Charon from a Circum-Pluto Ring of Debris

Benjamin C. Bromley; Scott J. Kenyon

A Pluto-Charon Sonata III. Growth of Charon from a Circum-Pluto Ring of Debris

T0 review · 0 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Graze-and-merge impact cannot explain Pluto's small moons if debris was 145–230 km rocks

desk verdict A well-executed simulation study that identifies a new debris-clearing mechanism, but the headline negative result is explicitly conditional on the debris size distribution, so it narrows rather than closes the graze-and-merge channel. read the letter →

arxiv 1908.01776 v1 pith:6OZT5B5Q submitted 2019-08-05 astro-ph.EP astro-ph.SR

Scott J. Kenyon , Benjamin C. Bromley This is my paper · ORCID

classification astro-ph.EPastro-ph.SR

keywords Pluto-Charonsatelliteformationgraze-and-mergeimpactcircumplanetarydiskn-bodysimulationscoagulationcircumbinarysatellitesKuiperbeltobjects

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tests the graze-and-merge origin of the Pluto–Charon system by simulating Charon's growth from a ring of debris around Pluto. It finds that Charon-mass satellites form within weeks from planetesimals 145–230 km in radius, reaching orbits of 5–6 Pluto radii with eccentricities 0.1–0.3. The same growth, however, causes the Pluto–Charon binary to eject several leftover 100–200 km bodies through the orbital plane, and these ejections sweep away essentially all small debris within 10–100 years. If that is how Charon formed, there would be no circumbinary disk left to build Styx, Nix, Kerberos, and Hydra, so the graze-and-merge channel would be ruled out for large-planetesimal debris. The authors note the channel stays viable only if the debris consisted of bodies no larger than about 10–20 km.

What carries the argument

The machinery is a hybrid coagulation and n-body code that tracks massive planetesimals plus 14,000 massless tracer particles around Pluto. Tracers act as proxies for small collisional debris; the dynamical channel that carries the argument is the ejection of leftover 145–230 km planetesimals by the growing Pluto–Charon binary, which sweeps through the tracers' orbital plane and removes them on decade timescales.

What would settle it

Run the same growth calculation with an initial swarm of 10–20 km planetesimals including collisional fragmentation. If a Charon analog still forms but a circumbinary ring of tracers survives at 30–60 Pluto radii for 100 years, the paper's negative conclusion would fail for that debris size; additionally, measuring the actual size distribution of debris in SPH graze-and-merge simulations would show whether the 145–230 km population used here is realistic.

Watch

Extended reading notes

Core claim

The central claim is that a Pluto–Charon binary formed by graze-and-merge cannot simultaneously produce Charon and the four small circumbinary satellites, when the debris disk is made of 145–230 km planetesimals. In the simulations, a Charon analog assembles in roughly 30–100 days on an orbit similar to hit-and-run survivors, but the newly formed binary dynamically ejects several leftover massive planetesimals through the disk plane; each such ejection scatters and removes the small tracer particles that stand in for the debris from which the small moons would form. At 10–100 years, systems that form a Charon-mass satellite retain at most a handful of tracers, and usually none. The authors conclude that the known small satellites cannot be the leftover of a graze-and-merge impact under these initial conditions, while leaving open the possibility that much smaller debris (10–20 km bodies) could survive.

Load-bearing premise

The argument assumes the debris left by a graze-and-merge impact was dominated by planetesimals 145–230 km in radius and that fragmentation debris from their collisions is negligible; if the real debris was mostly bodies smaller than about 10–20 km, the small particles could survive and the graze-and-merge channel would remain plausible.

Editorial extensions

If this is right

If Charon forms by accretion in a circum-Pluto disk of 145–230 km planetesimals, the small satellites Styx, Nix, Kerberos, and Hydra cannot be debris left over from the same event.
Charon analogs reach their final mass in weeks, so the tidal expansion of the Pluto–Charon binary would begin from orbits similar to those produced by hit-and-run encounters.
The clearing of small debris takes only 10–100 yr, much faster than the million-year tidal expansion, so any circumbinary material must either be delivered later or survive as much smaller particles.
If the debris disk is instead dominated by 10–20 km bodies, graze-and-merge remains a plausible formation channel for both Charon and the small satellites.

Reading between the lines

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

A general lesson likely extends beyond Pluto: a massive moon growing inside a circumplanetary debris ring may clean the outer region by flinging leftover planetesimals through it, so systems that combine a large moon with small outer moons require either small debris or a later source of material.
The paper's tracer-clearing mechanism suggests a testable distinction between formation channels: hit-and-run should leave more small debris in the 30–60 Pluto-radius zone than graze-and-merge, which could be checked with high-resolution simulations of each impact geometry.
If future simulations with 10–20 km planetesimals and fragmentation succeed, the main obstacle to graze-and-merge would shift from the growth of Charon to the survival of small debris through tidal expansion of the binary.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague, here's the take on 1908.01776. The paper is the first simulation of Charon growing from a circum-Pluto planetesimal ring, and it finds a specific mechanism that matters: a growing Charon-mass object ejects leftover 100–200 km planetesimals through the disk plane, and those ejections sweep out the small debris that would otherwise form Styx, Nix, Kerberos, and Hydra. That mechanism is new and physically plausible, and the simulations are done carefully: a real grid over initial mass, planetesimal size, and eccentricity, with statistical tests on the outcomes and data/plots available online. Credit where due: this is a real result, not a parameter-fit to the observed satellites.

The soft spot is the one the authors themselves flag. The negative conclusion—that graze-and-merge cannot produce the circumbinary system—rests on the assumption that the post-impact debris is composed of 145–230 km planetesimals and that fragmentation is negligible. Section 2 states this directly. Section 5.3 then shows that 10–20 km leftovers would only stir small particles to ~10% of escape speed, so those particles could survive. The abstract says the same thing. So the paper does not rule out graze-and-merge; it rules out one debris-size regime, and it is honest about that. The reader's conditional verdict is right.

Other caveats are minor. The initial disk is more radially extended than the SPH disks of Canup, and the assumed solid density matches Charon rather than the lower-density ice-rich debris Canup favors. The authors address both, and neither changes the central dynamical point. The simulations are internally consistent, with no obvious signs of tuning.

Who should read this: anyone working on Pluto-Charon formation or on satellite formation from impact debris. It's a useful constraint, not a settlement. The paper deserves a serious referee—the mechanism could be important, and the conditional claim is testable with more detailed impact models. I'd accept it for review with the expectation that the authors emphasize the conditional nature and, ideally, run even a simple fragmentation case. My own verdict: conditionally sound, with the condition clearly stated in the paper.

Referee Report

0 major / 4 minor

Summary. This paper uses the Orchestra hybrid n-body/coagulation code to simulate the growth of a Charon-mass satellite from a circum-Pluto disk of planetesimals and the concurrent dynamical evolution of massless tracer particles intended to represent small debris. A broad grid of initial swarm masses (0.85–1.75 Charon masses), planetesimal radii (145, 185, 230 km), and eccentricities (0.1–0.4) is explored with 12–15 realizations per setup. Charon analogs form on timescales of 10–100 days with semimajor axes of 5–6 Pluto radii and eccentricities of 0.1–0.3. In systems where the analog reaches roughly 0.9–1.1 Charon masses, the Pluto–Charon binary ejects leftover 145–230 km planetesimals that remove nearly all tracers within 10–100 years, leaving no circumbinary debris. The authors conclude that graze-and-merge formation is ruled out when the debris has this size distribution, while explicitly leaving open the possibility that a disk of 10–20 km objects could retain the small circumbinary satellites.

Significance. If the simulations are correct, they provide a sharp, falsifiable constraint on the graze-and-merge scenario: the survival of Styx, Nix, Kerberos, and Hydra depends on the size distribution of the debris produced by the giant impact. The paper has several strengths. The ensemble is large (~475 calculations), the outcomes are characterized with K-S, Pearson, Spearman, and Kendall statistics, the results are insensitive to initial eccentricity, and the simulation outputs and reading software are publicly available through a DOI. No parameters are fitted to reproduce Charon; the initial conditions bracket SPH impact outcomes, and the comparison to observed satellite masses is an evaluation, not a fit. The principal limitation, acknowledged in the manuscript, is that the decisive condition—debris dominated by 145–230 km planetesimals—is an input assumption rather than a derived outcome of giant-impact modeling. I regard the conditional framing as a strength rather than a flaw, provided the concluding sections keep the condition visible.

minor comments (4)

[Abstract and §6] The abstract and §6 already state the size dependence, but the summary sentence 'Thus, there is no circumbinary disk of solids in which to grow satellites with properties similar to the known small satellites' could be misread as a general conclusion. I suggest adding an explicit qualifier such as 'for a debris disk dominated by 100–200 km solids' at the start of that sentence to preserve the conditional nature of the result in the concluding section.
[Abstract] The abstract refers to '100–200 km particles' while the simulations and Table 1 use r0 = 145, 185, and 230 km; please harmonize the reported size range.
[§5.2, Eq. (7)] Equation (7) is inconsistent with the preceding relation U = NkT = E/2: if U = NkT, then T = E/(2Nk), not E/(3Nk). The quoted T ≈ 70–90 K follows from the E/(3Nk) version, so either the text should justify the factor 3 or the equation and the derived temperatures should be corrected.
[§4, paragraph following Fig. 8] In the sentence 'seven have ft ≲ 10−3 at 150–30 d', the time range should read '150–300 d'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central result is an emergent n-body dynamical outcome, with initial conditions bracketing prior SPH debris states and no parameter fitted to the observed satellites.

full rationale

Walking the paper's derivation chain, the central claim is not equivalent to its inputs by construction. The simulations start from circum-Pluto debris disks with M0 = 0.85-1.75 Charon masses, planetesimal radii r0 = 145, 185, or 230 km, and eccentricities e0 = 0.1-0.4. These choices bracket the outcomes of published SPH graze-and-merge impact calculations rather than being tuned to reproduce the observed Pluto-Charon circumbinary satellites. The key tracer-clearing result is an emergent dynamical outcome: the growing Charon analog ejects leftover massive n-bodies, and those ejections remove the massless tracers. The surviving tracer fraction ft is measured from the simulations, not imposed. The constraint Ms ~ ft fs M0 with MSNKH <~ 1e20 g is an evaluation of the simulation output against observed satellite masses, not a fit. The negative conclusion is explicitly conditional: the paper states that graze-and-merge formation is ruled out 'when the formation of Charon within a circum-Pluto disk leads to the ejection of several 100-200 km particles,' and immediately acknowledges that 'If a growing Charon ejects only much smaller particles, however, graze-and-merge impacts are a plausible formation channel.' The main assumption, ignoring fragmentation, is stated in Section 2 and is an input restriction rather than a disguised prediction; the paper also verifies internally that collisions eject less than 1% of the combined mass. Self-citations to Kenyon & Bromley for growth-time scaling, collisional damping, and Nix/Hydra mass constraints are used as consistency checks or independent inputs, not as the derivation of the central tracer-clearing result. No fitted parameter is renamed as a prediction, and no load-bearing claim reduces to a self-citation chain by construction.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the assumed initial size distribution of the debris disk (145-230 km planetesimals) and on the neglect of fragmentation; these are the main upstream assumptions. No parameters are fitted to the observed satellite system; the surveyed initial conditions bracket plausible impact outcomes. No new physical entities are postulated.

free parameters (6)

Initial planetesimal radius r0 = 145, 185, 230 km (surveyed)
Initial condition varied to bracket plausible debris sizes from SPH impact models; not fitted to the final satellite system.
Initial swarm mass M0 = 0.85, 1.25, 1.75 Charon masses (surveyed)
Initial condition bracketing Charon's mass, chosen to test sensitivity; not fitted.
Initial eccentricity e0 = 0.1, 0.2, 0.3, 0.4 (surveyed)
Initial condition covering SPH impact outcomes; varied to test trends.
Disk radial extent = 3-11 Pluto radii
Inner and outer radii chosen to match the Canup (2005) SPH debris distribution outside the Roche limit; not fitted.
Surface density slope n = 1.7-1.8
Adopted from Ida et al. (1997) for lunar formation disks because Canup (2005) does not quote the surface density profile; not fitted.
Mass density of solids rho0 = 1.75 g cm^-3
Set equal to Charon's density; the paper notes this runs counter to Canup's lower-density SPH debris. An assumption, not a fit.

assumptions (5)

domain assumption Two particles merge unless the sum of their radii exceeds their mutual Hill sphere (Eqs. 1-2).
Used in the n-body code to decide collision outcomes; a standard physical criterion for accretion in a planetocentric disk.
domain assumption 150-250 km solids are stable against tidal disruption outside about 2 Pluto radii and recover structure after passing inside the Roche limit.
Invoked in Section 2 to justify ignoring tidal shredding for the modeled planetesimal sizes.
domain assumption Fragmentation in collisions of 100+ km icy bodies removes less than 1% of mass as debris, so it can be neglected.
Stated in Section 2; load-bearing because a population of small debris could damp the ejections that clear tracers, as discussed in Section 5.3.
ad hoc to paper The initial disk has surface density distribution Sigma proportional to a^-n with n = 1.7-1.8 over 3-11 Pluto radii.
Adopted from lunar disk models (Ida et al. 1997) because Canup (2005) does not quote Sigma(a); not derived from SPH output in this paper.
domain assumption Massless tracers do not interact with each other or exert gravity; collisional damping is treated only in a simplified test model (Eqs. 3-5).
Simplifying assumption for the debris population; the authors add a damping test but do not include full fragmentation or tracer self-gravity.

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Cite this review

Pith. "Pith review of A Pluto-Charon Sonata III. Growth of Charon from a Circum-Pluto Ring of Debris." pith.science (2026). https://pith.science/paper/6OZT5B5Q

@misc{pith2026190801776,
  author       = {Pith},
  title        = {Pith review of: A Pluto-Charon Sonata III. Growth of Charon from a Circum-Pluto Ring of Debris},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6OZT5B5Q}},
  note         = {Machine review of arXiv:1908.01776}
}

read the original abstract

Current theory considers two options for the formation of the Pluto-Charon binary (Canup 2005, 2011; Desch 2015). In the `hit-and-run' model, a lower mass projectile barely hits the more massive Pluto, kicks up some debris, and remains bound to Pluto (see also Asphaug et al. 2006). In a `graze-and-merge' scenario, the projectile ejects substantial debris as it merges with Pluto (see also Canup 2001). To investigate the graze-and-merge idea in more detail, we consider the growth of Charon-mass objects within a circum-Pluto ring of solids. Numerical calculations demonstrate that Charon analogs form rapidly within a swarm of planetesimals with initial radii of 145-230 km. On time scales of roughly 30-100 days, newly-formed Charon analogs have semimajor axes, a = 5-6 Pluto radii, and orbital eccentricities, e = 0.1-0.3, similar to Charon analogs that remain bound after hit-and-run collisions with Pluto. Although the early growth of Charon analogs generates rings of small particles at a = 50-275 Pluto radii, ejection of several 145-230 km leftovers by the central Pluto-Charon binary removes these small solids in 10-100 yr. Simple estimates suggest small particles might survive the passage of 10-20 km objects ejected by the central binary. Our results indicate that the Pluto-Charon circumbinary satellite system was not formed by a graze-and-merge impact when the formation of Charon within a circum-Pluto disk leads to the ejection of several 100-200 km particles through the orbital plane of the Pluto-Charon binary. If a growing Charon ejects only much smaller particles, however, graze-and-merge impacts are a plausible formation channel for the Pluto-Charon binary and an ensemble of small, circumbinary satellites.

Figures

Figures reproduced from arXiv: 1908.01776 by the authors.

**Figure 1.** — Time evolution of the number of n-bodies in the swarm for calculations with M0 = 1.25 mC and r0 = 145, 185, or 230 km as indicated in the legend. Within a few hours, several n-bodies merge to form larger objects. On time scales of 1–2 days (10–50 days), collisions reduce the number of n-bodies in half (to 1–2) [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗

**Figure 1.** Initially, all of the n-bodies have the same mass. Within a few hours, several have merged with other n-bodies and doubled, tripled, or quadrupled in mass. In some cases, one n-body gains mass more rapidly than the others and remains the most massive object until the end of the calculation ( [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗

**Figure 2.** — As in Fig. 1 for the masses of surviving [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

Figures from the paper (8 more)

**Figure 3.** Figure 3: — As in Fig. 1 for the semimajor axis. Once a single massive [PITH_FULL_IMAGE:figures/full_fig_p012_3.png]

**Figure 4.** Figure 4: — Cumulative probability for the final mass of the largest [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]

**Figure 5.** Figure 5: — Positions of massless tracers in the x − y plane at 150–300 d. In each panel, the density of tracers in arbitrary units ranges f rom low (cyan) to medium (purple) to high (magenta). The final mass of the Charon analog (in Charon masses) appears in the lower left or l…

**Figure 6.** Figure 6: — As in Fig. 5 for systems of tracers with large-scale spiral structure at 150–300 d. [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]

**Figure 7.** Figure 7: — Fraction of 14,000 tracers remaining after 150–300 d of dynamical evolution (when [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]

**Figure 8.** Figure 8: — As in Fig. 7 with color-coding by [PITH_FULL_IMAGE:figures/full_fig_p023_8.png]

**Figure 9.** Figure 9: — As in Fig. 7 with color-coding by [PITH_FULL_IMAGE:figures/full_fig_p025_9.png]

**Figure 10.** Figure 10: — As in Fig. 9 for a subset of systems after 10–100 yr of dynamical evolution. For [PITH_FULL_IMAGE:figures/full_fig_p026_10.png]

Discussion (0). Continue with ORCID to comment.

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