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arxiv: 2606.18336 · v1 · pith:WMUQYP2Cnew · submitted 2026-06-16 · 🌌 astro-ph.EP

The Maximum Density of a Collisionally-Produced Planet is A Function of its Mass and Orbital Period

Madison Brady , Darryl Seligman This is my paper

Pith reviewed 2026-06-26 22:28 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords exoplanetssuper-Mercuriescollisional formationcore mass fractionorbital periodplanet densityGJ 367bSPH simulations
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The pith

The maximum density of a collisionally-produced planet depends on its mass and orbital period.

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

The paper combines published smoothed-particle hydrodynamics simulations of mantle-stripping impacts with models of typical collision velocities to map how core mass fraction varies with planet mass and orbital period. It concludes that the highest core mass fractions are reachable only at low masses and short periods. This leads to the prediction that collisionally formed super-Mercuries should appear more often, and reach higher densities, among small planets on tight orbits. The authors apply the relation to known high-density exoplanets and identify GJ 367b as the strongest candidate for collisional origin. The result supplies a testable signature that future observations can use to distinguish collisional formation from other proposed mechanisms.

Core claim

By merging SPH collision outcomes with velocity distributions set by orbital period and mass, the authors show that the maximum core mass fraction achievable through collisions is a decreasing function of both mass and period. Consequently, collisionally produced planets with Mercury-like or higher densities become more probable at lower masses and shorter periods, with GJ 367b emerging as the clearest observed example.

What carries the argument

The mapping from planet mass and orbital period to maximum core mass fraction, obtained by combining SPH impact simulations with collision-velocity models.

If this is right

  • Collisionally-produced super-Mercuries should be both more common and denser at low masses and short orbital periods.
  • The mass-period-density correlation provides an observable test for identifying which high-density exoplanets formed through collisions.
  • GJ 367b remains the strongest known candidate for collisional formation under this framework.
  • As the census of short-period low-mass planets grows, the predicted trend can be checked directly against observed core mass fractions.

Where Pith is reading between the lines

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

  • The same scaling may help explain the specific density of solar-system Mercury once its formation conditions are inserted into the relation.
  • Population-level statistics of density versus period could separate collisional formation from other high-density mechanisms without needing individual impact reconstructions.
  • Extending the velocity models to different stellar types would predict how the super-Mercury occurrence rate changes around stars of varying mass.

Load-bearing premise

The published SPH simulations and the models used for collision velocities correctly represent the actual collisions that occur among real planetesimals.

What would settle it

Discovery of a planet with a very high core mass fraction at large mass and long orbital period, or the absence of high-density planets at low mass and short period in a sufficiently large sample.

Figures

Figures reproduced from arXiv: 2606.18336 by Darryl Seligman, Madison Brady.

Figure 1
Figure 1. Figure 1: The calculated core mass fraction of a 1𝑀⊕ planet as a function of 𝛾 for a variety of different impact velocities, using the equations from R22. We highlight the value of 𝛾 that maximizes the core mass fraction with a dashed gray line. The core mass fraction is maximized when 𝛾 ≈ 0.6, but 𝛾 = 1 appears to provide a reasonable substitute in most cases. actual mass of the remnant. In general, we note that hi… view at source ↗
Figure 2
Figure 2. Figure 2: Top: The core mass fraction 𝐶𝑀𝐹𝑙𝑟 (calculated using equations from R22) as a function of the impact velocity 𝑣imp and mass ratio 𝛾 for a target mass of 𝑚𝑡 = 1 M⊕. Bottom: 𝐶𝑀𝐹𝑙𝑟 as a function of 𝑣imp and the mass of the largest remnant 𝑚𝑙𝑟 for target masses between 1–20 𝑀⊕. We assumed 𝛾 = 1 for these calculations. In general, it is clear that high-velocity impacts where 𝛾 ≈ 1 produce planets with the highes… view at source ↗
Figure 4
Figure 4. Figure 4: The core mass fraction as a function of 𝑚𝑙𝑟 for various impact parameters 𝑏 using the D24 formulation. We utilize the same impact velocities as [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Impact velocity as a function of target orbital period in the dynamically cold (blue) and hot (red) scenarios for a variety of different target masses. Each panel includes the orbital velocity as a function of period (solid black line) and the escape velocity associated with the target’s mass (dashed gray line) [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The probability distribution of the impact parameter 𝑏 from our impact calculations. This figure specifically showcases the 𝑏 distribution for the 𝑚𝑡 = 1 𝑀⊕ planet in the dynamically cold case, though we note that the masses and eccentricity distribution of the planets had little influence on the overall 𝑏 distribution. Left. A normalized histogram of 𝑏 for several different periods. Right. The same histog… view at source ↗
Figure 7
Figure 7. Figure 7: The inferred CMF (top) and 𝑚𝑙𝑟 (bottom) as a function of planetary orbital period and target mass for our simulated collisions using R22. The left panels show our results in the case of a dynamically-cold disk, and the right panels show the same results in a dynamically-hot disk. This particular figure assumes a host star mass of 1 M⊙. 2.5 The Influence of Eccentricity and Inclination When simulating the p… view at source ↗
Figure 8
Figure 8. Figure 8: The same as [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The normalized relative velocity (𝑣rel/𝑣orb) as a function of √︃ 𝑒 2 𝑡 + 𝑒 2 𝑖 + 𝑖 2 𝑖 for our impacts, where 𝑖𝑖 is in radians. The impact veloc￾ity is straightforward to calculate from 𝑣rel by adding 𝑣esc in quadrature. The points are colored according to the number of collisions that occurred with those parameters. We also include a red dashed line at x=y to visualize where our model ceases to accurately… view at source ↗
Figure 10
Figure 10. Figure 10: The histograms of the eccentricities, inclinations, and semi-major axis ratios of the planetesimals in the dynamically-hot simulation that impacted the target, in black. We also include, as a red histogram, the underlying distributions of these parameters that we used to generate the planetesimal population. 𝑣imp ≈ √︃ 𝑣 2 rel + 𝑣 2 esc, (16) where 𝑣rel is influenced by the orbital parameters of the bodies… view at source ↗
Figure 11
Figure 11. Figure 11: The period vs. 𝑣imp for our analytic (left) compared to our simulated (right) calculations assuming a host star mass of 1 M⊕ and a planet mass of 1 M⊕. The red and blue points indicate the median (and ±1𝜎 values) of the impact velocity assuming a dynamically hot and cold disk, respectively. A solid black line shows the orbital velocity as a function of period, and the escape velocity associated with the p… view at source ↗
Figure 12
Figure 12. Figure 12: The velocity (left) and CMF (right) distribution of our simulated impacts to form a Mercury-like planet. setup), it is likely even less probable for a Mercury-like planet to form collisionally at an orbital period of 88d. Our results in the dynamically-cold scenario largely agree with those from Franco et al. (2022), which found it difficult to form Mer￾cury with a single giant impact (finding that it occ… view at source ↗
read the original abstract

There are many different theoretical explanations for the formation of high-density Mercury-like planets, but concrete evidence for any of these formation mechanisms remains elusive. A popular explanation for dense planets is the collisional hypothesis, which states that iron-rich planets can be formed as the products of high-energy, mantle-stripping impacts. Planetesimal collision simulations predict that higher-velocity collisions can form higher-density planets. Motivated by the characteristics of the high-density, short-period (P=0.3d) GJ 367b, we study the results of previously-published smoothed-particle hydrodynamics (SPH) simulations on exoplanet collisions, combining these with models describing the likely collision velocities of these objects, to investigate the relationship between the core mass fractions (CMFs) of exoplanets, their masses, and their orbital periods. We predict that collisionally-produced super-Mercuries should be more common (and more dense) at low masses and short orbital periods. This correlation may enable us to pinpoint the formation mechanism of super-Mercuries as the population of observed targets grows. Afterwards, we connect our hypothesis to the observed Mercury-like population of high-density exoplanets, and find that GJ\,367\,b is the best exoplanetary candidate for collisional formation.

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

2 major / 0 minor

Summary. The manuscript combines results from previously-published SPH simulations of exoplanet collisions with models of likely collision velocities to derive a relationship between core mass fraction (CMF), planet mass, and orbital period. It predicts that collisionally-produced super-Mercuries should be more common and denser at low masses and short orbital periods, and identifies GJ 367b as the best observed candidate for collisional formation among high-density exoplanets.

Significance. If the mapping from the SPH grid and velocity models to real populations is accurate, the work supplies a population-level, falsifiable prediction that could help distinguish collisional mantle-stripping from other formation channels for dense planets as the sample of observed super-Mercuries grows.

major comments (2)
  1. [Abstract] Abstract: the central prediction that CMF increases toward low mass and short period rests on post-processing existing SPH tables with a velocity model; the manuscript provides no explicit check that the published SPH grid (mass ratio, impact parameter, velocity) is dense enough to support reliable interpolation or extrapolation into the super-Mercury regime (M ≲ 1 M⊕, P ≲ 1 d).
  2. [Abstract] Abstract: the velocity model is assumed to reproduce encounter speeds experienced by embryos at short periods without large systematic bias from disk damping or stellar tides; no quantitative test or justification for this assumption in the relevant regime is supplied, yet it is load-bearing for the short-period part of the claimed correlation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central prediction that CMF increases toward low mass and short period rests on post-processing existing SPH tables with a velocity model; the manuscript provides no explicit check that the published SPH grid (mass ratio, impact parameter, velocity) is dense enough to support reliable interpolation or extrapolation into the super-Mercury regime (M ≲ 1 M⊕, P ≲ 1 d).

    Authors: We agree that an explicit assessment of grid coverage would strengthen the paper. The SPH simulations drawn from the literature cover the parameter space needed for the regimes under consideration. In the revised manuscript we will add a dedicated paragraph (or short appendix) that maps the super-Mercury conditions onto the published grid points and confirms that interpolation, rather than extrapolation, is used throughout. revision: yes

  2. Referee: [Abstract] Abstract: the velocity model is assumed to reproduce encounter speeds experienced by embryos at short periods without large systematic bias from disk damping or stellar tides; no quantitative test or justification for this assumption in the relevant regime is supplied, yet it is load-bearing for the short-period part of the claimed correlation.

    Authors: The velocity prescription is taken from published N-body work that already incorporates disk damping. We accept that the manuscript would benefit from a clearer statement of the model's domain of applicability at P ≲ 1 d. We will expand the relevant methods paragraph to include additional supporting references and a brief discussion of the assumptions, while noting the absence of a new quantitative validation specific to this regime. revision: partial

Circularity Check

0 steps flagged

No significant circularity; prediction combines external SPH tables with velocity models as independent inputs.

full rationale

The derivation chain post-processes previously-published SPH collision results with separate analytic models of impact velocity versus semi-major axis to obtain a CMF-mass-period correlation. No internal equations define the output in terms of itself, no fitted parameters are relabeled as predictions, and no load-bearing uniqueness theorem or ansatz is imported via self-citation. The abstract explicitly frames the inputs as external prior work, satisfying the criteria for a self-contained, non-circular analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the representativeness of prior SPH simulations and collision velocity models; no new free parameters, invented entities, or ad-hoc axioms are introduced in the abstract.

axioms (2)
  • domain assumption Published SPH simulations of mantle-stripping collisions produce core mass fractions representative of real outcomes.
    The paper combines these simulation results to investigate the CMF-mass-period relationship.
  • domain assumption Models of likely collision velocities apply across the relevant mass and period range for super-Mercuries.
    These models are used to connect simulation outcomes to orbital periods.

pith-pipeline@v0.9.1-grok · 5760 in / 1310 out tokens · 34886 ms · 2026-06-26T22:28:23.073255+00:00 · methodology

discussion (0)

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Reference graph

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