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REVIEW 2 major objections 5 minor 293 references

The Dynamics of Planetary Ejection

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Planetary ejection is a common, near-universal stage of planetary system evolution, and the observed census of free-floating planets is best explained by scattering, binary instabilities, and cluster flybys rather than by in-situ formation.

desk verdict A useful, honest review that consolidates ejection mechanisms and gives observers a comparative table; the central claim is conditional but explicitly flagged. read the letter →

arxiv 2608.00173 v2 pith:BGP3PPUG submitted 2026-07-31 astro-ph.EP astro-ph.SR

Malena Rice , William DeRocco , Sean N. Raymond This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords free-floatingplanetsplanetaryejectionplanet-planetscatteringbinarystarinstabilitiesstellarflybyspost-main-sequenceevolutiongravitationalmicrolensingexoplanetdynamics
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

Free-floating planets are common—roughly twenty per star in the completeness-corrected microlensing census—and this review argues that most of the low-mass ones are not born isolated but are planets ejected from their birth systems. It organizes the ejection process into four dynamical channels: planet-planet scattering, instabilities in binary and multi-star systems, flybys in dense stellar environments, and post-main-sequence stellar mass loss. Each channel leaves distinguishable signatures in the masses, velocities, and environments of the ejected planets, and the review's synthesis concludes that scattering, embedded-cluster encounters, and binary instabilities are the likely predominant producers. If that synthesis is right, the present-day planetary census records a history of violence: eccentric giant planets, tightly packed systems, and the rarity of resonant chains are all vestiges of past ejections.

What carries the argument

The carrying structure is a set of quantitative diagnostics, one per ejection channel, that convert a scenario into a testable prediction. The Safronov number $\Theta \equiv v_{\rm esc,p}^2/v_{\rm esc,*}^2$—the square of the ratio of a planet's surface escape velocity to the local escape velocity from its host star—decides whether close encounters end in collision or ejection. The angular momentum deficit (AMD) measures how far a planetary system is from circular, coplanar orbits and sets the threshold for secular chaos and orbit crossings. For binaries, empirical stability boundaries give the outermost stable orbit for a circumstellar planet and the innermost stable orbit for a circumbinary planet, while the mass-loss index $\Psi$ separates adiabatic from impulsive ejection during stellar evolution. Each channel also predicts an excess-velocity distribution, so measured FFP velocities can fingerprint the responsible mechanism.

What would settle it

Imaging the lens fields of a few dozen low-mass microlensing FFP candidates several years after the events, or searching archival precovery images, and finding host stars for a substantial fraction would show that many free-floating planets are actually bound, undercutting the census anchor. Conversely, a velocity sample from parallax measurements that clustered at 8–12 km/s rather than the 2–6 km/s predicted by planet-planet scattering would point to circumbinary or cluster mechanisms as dominant.

Watch

Extended reading notes

Core claim

This paper's central claim is that planetary ejection is not a rare accident but a standard phase of planetary system evolution: wherever planets form, some are later lost. The abstract states it directly, saying that the ubiquity of free-floating planets suggests that planetary ejection is common, and the summary sharpens it: planet-planet scattering, embedded cluster encounters, and binary instabilities are likely predominant in FFP production. The load-bearing evidence is the completeness-corrected microlensing census of roughly 20 free-floating planets per star for masses 0.33–6660 Earth masses, together with the direct-imaging limit that in-situ formation tapers off below about 3–5 Jupiter masses. The paper argues that the four reviewed mechanisms can account for all candidate FFPs, while acknowledging that some apparent FFPs may be wide-orbit bound planets rather than truly unbound ones.

Load-bearing premise

The load-bearing premise is that most microlensing free-floating planet candidates are truly unbound, so the inferred twenty per star is a real ejection count rather than a count of planets still orbiting faint host stars on very wide orbits.

Editorial extensions

If this is right

  • If the completeness-corrected census is real, the ejected mass budget of about 80 Earth masses per star implies that protoplanetary disks must be heavier than the classic minimum-mass nebula, or the observed FFPs cannot all be explained by core accretion.
  • Present-day giant-planet systems should carry vestiges of past ejection: high eccentricities, packed spacings near the stability limit, and a dearth of mean-motion resonances.
  • Upcoming microlensing surveys are projected to find hundreds of FFPs, and parallax-measured velocities could separate ejection channels by their typical speeds.
  • Directly imaged super-Jovian FFPs in star-forming regions are consistent with in-situ collapse, while low-mass microlensing FFPs are not, making the low-mass objects the crucial test bed for ejection models.
  • A fraction of apparent FFPs may be wide-orbit bound planets, so host-star follow-up of microlensing events will decide how much of the census is truly unbound.

Reading between the lines

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

  • The velocity-prediction table acts as a ready-made classification scheme: if Roman-era parallaxes yield a bimodal FFP velocity distribution, the peaks can be mapped directly onto ejection mechanisms—a test the paper describes but does not itself run.
  • The review's relative rates assume planets form in unstable regions such as circumbinary zones and wide binary orbits; if future disk surveys show that planet formation avoids these zones, the binary and tidal channels would shrink dramatically.
  • The same machinery applied to moons and planetesimals suggests that interstellar objects should share the velocity fingerprints of FFPs, so a joint census of interstellar objects and FFPs could test the universality of the ejection picture.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This review synthesizes the dynamical mechanisms by which planets can be liberated from their host stars, organized into four channels: planet-planet scattering (Section 2), instabilities in binary and multi-star systems (Section 3), stellar and substellar flybys (Section 4), and post-main-sequence stellar evolution (Section 5). The paper develops the relevant analytic tools (Safronov number, angular momentum deficit, variable-mass two-body equations, impulse approximation), surveys the solar-system and extrasolar evidence for each channel, and compiles a comparative table (Table 1) listing the percentage of stars susceptible to each mechanism, the associated ejection efficiencies, the typical ejected planet masses, and predicted excess velocities. The central claims are that planetary ejection is common, that the four mechanisms can account for the completeness-corrected microlensing census of roughly 20 free-floating planets per star (Sumi et al. 2023, Eq. 14), and that planet-planet scattering, embedded-cluster encounters, and binary instabilities are likely the predominant FFP production channels. Section 6.1 transparently lists the assumptions behind Table 1 and explicitly acknowledges that apparent microlensing FFPs may include wide-orbit bound planets; however, the Abstract and Section 7 state the conclusions without carrying that conditionality through.

Significance. If the central claim holds, this is a valuable consolidation of a dispersed literature: it unifies four research communities around common quantitative diagnostics (velocity distributions, mass-function features, environmental signatures), updates the earlier Safronov-number analysis with the current exoplanet census (Figures 3 and 4), and offers falsifiable forecasts, including velocity peaks near 2 to 3 km/s for scattering, 8 to 12 km/s for circumbinary and globular-cluster channels, a predicted mass-function trough near 0.8 Earth masses, and a roughly factor-of-ten expansion of the FFP sample with Roman. The analytic kernels (Eqs. 6 to 9, 10, 25 to 30, and 36) are standard and correctly stated; I verified that the stated integral of Eq. (14) over 0.3 to 13 Jupiter masses indeed gives about 0.09 FFPs per star and that the 14.2 AU accretion-limit example from Eq. (7) checks out. The synthesis is not circular: the cited population-level results, including several co-authored by the present authors, are independent N-body simulations with stated initial conditions rather than free parameters fitted here, and the paper does not invent new entities.

major comments (2)
  1. [Section 6.1 / Table 1] The text states that the piecewise power-law IMF of Kroupa (2001) yields 63%, 29%, and 8% of stars in the mass bins 0.075-0.225, 0.225-0.675, and >0.675 solar masses, respectively, and these fractions feed the derived '9% of stars' (p-type) and '10% of stars' (s-type) binary-instability susceptibilities listed in Table 1. Direct integration of the standard Kroupa slopes (alpha = 1.3 for 0.08-0.5 solar masses and alpha = 2.3 above 0.5 solar masses), normalized over 0.075-120 solar masses, gives approximately 50/35/16 for these same bins, and I could not reproduce the quoted 63/29/8 regardless of whether the substellar (0.01-0.075 solar masses) regime is included. Please recompute the star-count fractions from the cited IMF and state the normalization convention and mass range explicitly, or cite the source from which the 63/29/8 values were taken; the affected Table 1 entries should then be regenerated.
  2. [Section 6.1; Abstract; Section 7] Section 6.1 transparently acknowledges that 'apparent FFPs observed through microlensing are not necessarily unbound' and cites Hadden and Wu (2025) predicting that roughly half of Neptune-mass apparent FFPs may reside on wide bound orbits, yet this ambiguity is not propagated to the load-bearing inference: the Abstract and the first bullet of Section 7 assert that the low-mass FFP census 'implies a high rate of planetary ejection' without the condition, and the cross-check in Section 2.4.1 (roughly one giant planet ejected per instability) together with the 'can account for all candidate FFPs' statement in Section 6.1 treat the Sumi et al. (2023) normalization of Eq. (14) as an unbound census. Because the required ejection efficiency scales linearly with the assumed unbound fraction, I recommend adding a one-sentence sensitivity analysis (for example, noting that a 50% bound-orbit fraction halves the required efficiency while leaving the qualitative ranking intact) and inserting the conditionality into the Abstract or Section 7 where the central claim is stated.
minor comments (5)
  1. [Section 5.4] In the sentence 'for e0 = 0 and the limiting case cos f0 -> 0, more than half of the stellar mass must be lost instantaneously to eject a planet,' the qualifier 'cos f0 -> 0' is unnecessary and potentially confusing: for e0 = 0, Equation 36 reduces to beta < 1/2 for every value of f0, so the limiting-case phrase should be removed or reworded.
  2. [Table 1 / Section 6.1] The '% stars' entries for evolved open clusters (10%), globular clusters (0.5%), AGB-phase evolution (5%), and Type II supernovae (0.1-1%) are not derived anywhere in Section 6.1, which supplies stated assumptions only for the binary and cluster-encounter rows; please add a sentence or footnote tracing each of these percentages to its source or to an explicitly stated stellar-population model.
  3. [References] P. Mroz, A. Udalski, J. Skowron, et al. (2017, Nature 548, 183) appears twice as an identical entry in the reference list; please deduplicate, and verify that the in-text citations in Sections 1 and 6.2 refer to the same paper or, if not, disambiguate them with distinct years or identifiers.
  4. [Section 6.2] The sentence 'Roughly a dozen microlensing FFP candidates have been reported to date that are attributed to low-mass (super-Earth-mass or below) planets' is followed by a list of fourteen citations; please reconcile the 'roughly a dozen' count with the length of the list, or clarify which of the cited events are considered low-mass candidates.
  5. [Section 1] The phrase 'at of order ≈20 FFPs' in the first section combines 'of order' with 'approximately' and reads awkwardly; consider revising to 'of order 20 FFPs' or 'approximately 20 FFPs'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; the synthesis rests on external microlensing data and independent N-body simulations, with self-citations that are not load-bearing.

full rationale

This paper is a review and synthesis rather than a derivation-from-principles paper. The load-bearing empirical anchor is the completeness-corrected microlensing FFP census of Sumi et al. (2023), which is external to the authors; the mechanism-by-mechanism yields cited for Table 1 are published N-body simulations with stated initial conditions (Holman & Wiegert 1999; Kaib et al. 2013; Coleman & DeRocco 2025; etc.), not parameters fitted here. The paper's own calculation in Section 2.4.1 (Eqs. 13-14) is a consistency check: it asks what ejection yield would be needed to match the observed FFP mass function, rather than 'predicting' that yield from a fitted input. The explicitly acknowledged ambiguities (Section 6.1: 'apparent FFPs observed through microlensing are not necessarily unbound' and direct collapse as an in-situ alternative) are empirical caveats, not circular reductions. Self-citations to works co-authored by Raymond and DeRocco are frequent, but they are real, independently testable simulation results and standard analytic formulas; under the review rules these do not raise the circularity score. No equation in the paper is equivalent to its own input by construction, no fitted parameter is renamed as a prediction, and no uniqueness claim is imported from the authors' prior work. Score 1 reflects the presence of self-citations while affirming that none are load-bearing.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new free parameters or invented entities. It adopts several domain assumptions from the literature, the most important being the completeness-corrected FFP census and the occurrence of planet formation in unstable regions; both are explicitly flagged as uncertain in the text.

assumptions (4)
  • domain assumption The Sumi et al. (2023) microlensing FFP mass function is correct and represents truly unbound planets.
    Load-bearing for the conclusion that ejection is common; the paper itself flags the bound-vs-unbound ambiguity in Section 6.1.
  • domain assumption Planets form and migrate into the unstable regions of parameter space at rates sufficient to populate them.
    Raised in Section 3.4 ('Do planets form or arrive in unstable regions in the first place?'); the paper treats it as an open question.
  • standard math The isotropic variable-mass two-body equations (Eqs. 26-30) are valid for the mass-loss regimes considered.
    Taken from Omarov (1962), Hadjidemetriou (1963), and Veras et al. (2011); the paper notes anisotropic corrections scale as sqrt(a) but does not include them.
  • domain assumption Cited numerical simulation results for ejection rates and velocities (e.g., Holman & Wiegert 1999; Kaib et al. 2013; Coleman & DeRocco 2025) are reliable.
    The review's synthesis inherits the correctness of its cited simulations, which are not reproduced here.

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Cite this review

Pith. "Pith review of The Dynamics of Planetary Ejection." pith.science (2026). https://pith.science/paper/BGP3PPUG

@misc{pith2026260800173,
  author       = {Pith},
  title        = {Pith review of: The Dynamics of Planetary Ejection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BGP3PPUG}},
  note         = {Machine review of arXiv:2608.00173}
}
read the original abstract

The ubiquity of free-floating planets inferred from microlensing and direct imaging surveys suggests that planetary ejection---a process in which planets initially born encircling a stellar host become gravitationally unbound---is common. Four overarching mechanisms have been proposed to induce planetary ejection: close approaches of neighboring planets, instabilities in binary or multi-star systems, stellar and planetary flybys, and post-main-sequence stellar evolution. Here we review the mechanisms underlying planetary ejection, as well as predictions derived from each. Current and upcoming microlensing surveys offer the potential to test existing models and distinguish between potential planetary ejection mechanisms, offering further insight into the demographic-level architectures of exoplanets across stellar environments.

Figures

Figures reproduced from arXiv: 2608.00173 by the authors.

Figure 1
Figure 1. Schematic overview of instability-inducing mechanisms through which planets may be ejected from a system. These mechanisms, each discussed throughout this work, include close approaches between neighboring planets (top left; Section 2), binary-induced instabilities (top center and right, and bottom left; Section 3), flyby encounters (bottom center; Section 4), and post-main-sequence orbital evolution (bottom right; … view at source ↗
Figure 2
Figure 2. Schematic depiction of the grazing-encounter sce￾nario considered in Section 2.1.1, through which the Safronov number, which is used to determine the likelihood of colli￾sions vs. ejections as the outcome of close encounters, is de￾rived. Here x is an initially large distance from which mass m, at initial velocity vi, approaches a planet with mass Mp and Rp with impact parameter b. The final velocity vf of mass m is… view at source ↗
Figure 3
Figure 3. Maximum Safronov number of known, bound planets shown as a function of semimajor axis (left) and eccentricity (right), as a scatter plot (bottom) and histogram (top). The histograms are each normalized to peak at 1 for a clearer comparison between samples. Only planets with measured, nonzero uncertainties in orbital eccentricity are included. Though these planets remain bound to their host systems, the elevated ecce… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Theoretical, piecewise mass-radius scalings across planetary mass regimes, alongside associated scalings of the Safronov number. The census of observed exoplanets with masses and radii (including uncertainties) reported in the NASA Exoplanet Archive PSCompPars table as…
Figure 5
Figure 5. Figure 5: Example thresholds for s−type and p−type bi￾nary instabilities for stellar binary mass ratio µb = 0.3, dis￾played as a function of the binary eccentricity and the ra￾tio between the planet and binary semimajor axis. Bound￾aries are drawn directly from M. J. Holman & P.…
Figure 6
Figure 6. Figure 6: Flyby rates Γ as a function of stellar density and velocity dispersion. Representative values for example stellar environments are shown alongside a reference line tracing the threshold for one flyby encounter per Gyr. Here we adopt the cross-section for flyby interact…
Figure 7
Figure 7. Figure 7: Planetary ejection regimes in the impulse approximation during a supernova explosion, shown for β = 0.8, 0.5, and 0.3 where β = µf /µi is the fractional stellar mass that remains after near-instantaneous mass loss. Here e0 and f0 are the initial orbital eccentricity an…
Figure 8
Figure 8. Figure 8: Log-normal binary separation distributions adopted from S. S. R. Offner et al. (2023) and derived from data drawn from D. Raghavan et al. (2010). The adopted limiting regimes for three categories of binary-driven instabilities are shown as the shaded background regions…

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