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Free Floating or Merely Detached?

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read About half of the reported free-floating Neptunes are actually 'detached' planets still bound to their host stars.

desk verdict A credible N-body case for a real population of detached Neptunes that masquerade as free-floating, but the 'about half' headline is an upper bound dressed as a central value. read the letter →

arxiv 2507.08968 v1 pith:RL6RZRCW submitted 2025-07-11 astro-ph.EP astro-ph.GA

Sam Hadden , Yanqin Wu This is my paper
classification astro-ph.EPastro-ph.GA
keywords free-floatingplanetsmicrolensingplanet-planetscatteringdetachedNeptune-massangularmomentumdeficitSafronovnumberexoplanetdynamics
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

The paper argues that many of the 'free-floating planets' found by microlensing surveys are not truly unbound. N-body simulations of unstable multi-planet systems show that planet-planet scattering around Neptune-mass planets ejects planets only slowly and typically leaves one to three 'detached' planets stranded on orbits 10-100 times their original semi-major axes. These detached planets lie far outside the host star's Einstein radius, so their stars are invisible in lensing events and the planets are misclassified as free-floating. Using observed occurrence rates of bound Neptune- and Jupiter-class planets around M-dwarfs, the authors estimate that about half of the reported free-floating Neptunes are merely detached. If correct, the true population of unbound Neptune-mass planets is roughly half the current quoted value.

What carries the argument

The argument is carried by the Safronov number, $\Theta = v_{\rm esc}^2/(2 V_{\rm orb}^2)$, which separates ejection-dominated encounters ($\Theta \gg 1$) from collision-dominated ones ($\Theta \ll 1$), showing that Neptune-mass planets outside roughly 2.4 AU around an M-dwarf can eject, and by the angular momentum deficit (AMD) with the AMD-stability criterion. After orbit-crossing, systems undergo diffusive AMD growth followed by an 'AMD cooling' phase in which detached planets torque each other until the remaining planets are AMD-stable, which is why one to three detached planets survive. The quantitative backbone is the ejection timescale $T_{\rm ej} \sim 2.9\times10^7 (m_p/m_{\rm Nep})^{-1.64} P_{1,0}$, which makes Neptune-mass ejections take billions of years and leaves the scattering incomplete in old systems.

What would settle it

A high-angular-resolution imaging campaign of a sample of microlensing events currently classified as free-floating Neptunes: if host stars are detected at roughly 0.1 arcsecond separation for about half the events, the detached-planet claim is confirmed; if essentially no host stars are found, the central claim is falsified.

Watch

Extended reading notes

Core claim

The central discovery is that scattering does not simply eject planets; it also creates a previously under-appreciated class of 'detached' planets. In simulations of five equal-mass planets and of one Jupiter with ten Neptunes, an instability typically resolves into one tightly bound inner planet plus one to three detached planets orbiting at tens to hundreds of AU. These detached planets are shielded from further scattering because mutual secular torques raise their pericenters, and they remain bound for the duration of the integration. Since they orbit at 10-100 times the initial semi-major axis (median about 30 times), they lie far beyond the Einstein radius and would appear as free-floating in microlensing surveys. Combining the simulated detached yield with the observed occurrence of ~0.35 bound Neptunes and ~0.06 Jovians per M-dwarf, and assuming all such systems undergo scattering, the paper estimates ~0.9 detached Neptunes per star, about half of the reported ~2 free-floating Neptunes per star.

Load-bearing premise

The 'about half' estimate assumes that all known planetary systems with bound Neptune- or Jupiter-class planets are 'mobilized in scattering', meaning each one undergoes the full dynamical instability simulated here and contributes the computed yield of detached planets.

Editorial extensions

If this is right

  • If correct, microlensing-based estimates of free-floating Neptune occurrence drop from about 2 to roughly 1 per star, with the missing planets present as wide-orbit companions.
  • Detached planets at ~300 AU (for an initial orbit at 10 AU) would show host stars ~0.1 arcseconds away, detectable by high-contrast imaging or by the star's own lensing signal.
  • The scattering scenario predicts that systems with wide-orbit Neptunes should typically have a single inner planet, and that inner planets can be driven to very small pericenters with observable consequences.
  • The mass function of true free-floating planets should be skewed toward lower masses than the bound population, a trend consistent with current data but requiring larger samples to confirm.

Reading between the lines

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

  • If even a substantial fraction of bound-Neptune systems never undergo instability, the detached yield of ~0.9 per star would be an upper limit, so measuring the instability fraction is the clearest way to tighten the estimate.
  • The same scattering logic applied to lower-mass planets predicts very long ejection times and Safronov numbers below unity, so truly free-floating super-Earths are more likely to have been ejected by higher-mass planets than by their own kind.
  • A natural extension is to search for detached planets around stars with known inner super-Earths; the paper's suggestion that cold Jupiters protect inner systems implies a testable anti-correlation between outer instability and inner compactness.
  • Future microlensing surveys with higher cadence and adaptive-optics follow-up could directly measure the detached fraction by detecting host stars near FFP events, providing a clean test of the scattering origin.
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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

3 major / 6 minor

Summary. The paper uses N-body simulations (REBOUND/ias15) of unstable multi-planet systems—five equal-mass planets at 1, 3, 10, and 30 Neptune masses, plus one Jupiter interacting with ten Neptunes—to study whether planet-planet scattering can explain the observed population of free-floating Neptune-mass planets. It finds that Neptune-mass scatterers eject planets slowly, often requiring more than a gigayear, and that scattering leaves one inner planet plus one to three 'detached' planets on orbits 10–100 times the original semimajor axis, which would appear as free-floating planets in microlensing surveys. Combining detached yields with observed bound-planet occurrence rates (Eq. 10), the paper estimates about 0.9 detached Neptunes per star, or about half of the reported free-floating Neptune rate, and discusses implications for AMD stability and inner planetary systems.

Significance. If the quantitative estimate held, this would be an important correction to microlensing free-floating-planet statistics: roughly half of the reported Neptune-mass FFPs would be bound but detached, with testable signatures such as a host star at ~0.1 arcsec and rare double-lensing events. The dynamical findings are well supported: the integrations use a standard integrator with energy-error checks, the ensembles are scale-free, and the AMD stability criterion provides a physical explanation of the final configurations. The paper is also transparent about missing physics in Section 4.3. The main weakness is that the headline number rests on occurrence-rate assumptions that are not calibrated; the central dynamical result is robust, but the 'about half' estimate requires substantial qualification.

major comments (3)
  1. [Section 4.2, Eq. (10)] Equation (10) treats the observed per-star planet occurrence rates (0.35 Neptunes and 0.06 Jupiters per star) as if they were rates of scattering systems, and the text explicitly assumes 'all known planetary systems are mobilized in scattering.' This is a strong assumption: if only a fraction of bound-planet systems actually undergo dynamical instability, or if some of the 0.35 Neptunes are members of multi-planet systems (which the paper itself argues is likely in Section 4.1), the number of systems producing detached planets is smaller and the ~0.9 per star estimate is an upper bound rather than a central value. The authors should replace the point estimate with N_detached = 2 f_N (0.35) + 3 f_J (0.06) for the fraction of mobilized systems f_N and f_J, or explicitly label Eq. (10) as a conditional upper bound.
  2. [Sections 3 and 4.3] The detached yields of 2 per system for the equal-mass ensembles and 3 for the 1J+10N ensemble come from point-mass integrations that ignore collisions and stellar engulfment. Figure 7 shows that inner planets in most simulated systems approach within a stellar radius for the Neptune-mass ensembles, and Section 4.3 states that these effects are not captured and that 'we are at no position to predict the actual dynamics.' Because Eq. (10) multiplies these yields by observed occurrence rates, the headline estimate inherits this idealization. The paper should either demonstrate that the detached-planet yields are insensitive to collisions and tidal capture (for example, by rerunning with a simple collision prescription) or present the estimate as an idealized limiting case with an explicit uncertainty.
  3. [Section 4.1 vs Section 4.2] There is an internal tension that the authors should resolve. Section 4.1 argues that the observed frequency of multi-planet microlensing systems makes the ejection hypothesis 'less tenable' because it is hard to retain two or more closely-spaced planets after a full-scale dynamical instability, yet Eq. (10) assumes every bound Neptune or Jupiter is the sole survivor of exactly one fully destabilized system. These two statements need to be reconciled; for instance, the authors could estimate the fraction of bound planets that can be retained as inner survivors after scattering and use that to correct Eq. (10) downward.
minor comments (6)
  1. [Section 4.1] The text contains a typo: 'typically onw planet' should read 'typically one planet.'
  2. [Figure 1 caption] The caption spells 'Sarfronov number' in the figure label; this should be 'Safronov number' for consistency with the text and Equation (3).
  3. [Section 3.2 and Figure 8] The typo 'percienter' should be 'pericenter' in the discussion of the 1J+10N evolution.
  4. [Section 2 and Eq. (4)] The notation 'mNep' is used as a mass unit in Equation (4) but is not explicitly defined as a unit; please write 'mNep = 1 Neptune mass' in the text before first use.
  5. [Section 4.2] The estimate of the rare double-lensing event rate, '0.35 × 10−4/π ∼ 10−5 per stellar lensing event,' would benefit from a brief derivation of the factor π and the Einstein-radius scaling, as the current one-line statement is difficult to follow.
  6. [Conclusions and Section 4.2] The claim that the 'about half' result is 'testable' could be strengthened by stating the concrete observable prediction, such as the expected fraction of FFP microlensing events that should show a faint stellar counterpart at ~0.1 arcsec, and how that fraction depends on the assumed host-star mass and distance.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central estimate combines independent microlensing occurrence rates with uncalibrated N-body yields; the 'about half' claim is a conditional model estimate, not a derived tautology.

full rationale

The paper's central quantitative step, Eq. (10), is not circular. The coefficients 2 and 3 are detached-planet yields measured from new N-body integrations, and the rates 0.35 and 0.06 are independently observed bound-planet occurrence rates from Zang et al. (2025). Nothing in the simulations is fitted to the Sumi et al. (2023) free-floating-planet rate, and the 'about half' statement is explicitly conditional: Section 4.2 says 'assuming that all known planetary systems are mobilized in scattering.' The self-citations (Lammers et al. 2024 for choosing initial separations that produce the desired instability-time window, and Hadden & Tremaine 2024 for test-particle scaling) are supporting context and do not carry the final claim; neither paper supplies the detached-planet yields. The authors themselves flag the main uncertainties, including that observed multiplicity 'makes the ejection hypothesis less tenable' (Section 4.1) and that inner-system collisions and engulfment are not modeled (Section 4.3). These are limitations and modeling assumptions, not circular reductions. The only notable self-citation is not load-bearing, so the score is 1 rather than 0.

Assumptions & free parameters 1 free parameters · 5 assumptions · 1 invented entities

The central estimate depends on simulation outcomes plus observed bound-planet occurrence rates. The most important hidden choices are the point-mass approximation, the assumption that all relevant systems undergo scattering, and the use of targeted initial conditions that discard non-destabilizing systems. The free-parameter ledger is short because the simulation yields are outputs rather than fitted inputs.

free parameters (1)
  • Ejection timescale power law (Tej) = 2.9 x 10^7 (mp/mNep)^-1.64 P1,0
    Eq. 4 is fit to the average time for the mean bound planet number to drop by one in the four equal-mass ensembles. No error bars are quoted, and the exponent differs from the test-particle Fokker-Planck scaling (m^-2), so it is an empirical fit rather than a derived law.
assumptions (5)
  • domain assumption Planets are treated as point masses with no physical extent; collisions between planets and with the star are ignored.
    Stated in Section 2. The simulations are scale-free and claimed to apply only where the Safronov number exceeds unity. Collisions would remove planets or the inner scatterer and could change the number of detached survivors; the authors acknowledge in Section 4.3 that these effects are not captured.
  • ad hoc to paper All known planetary systems are mobilized in scattering when estimating the detached planet rate.
    Section 4.2: 'assuming that all known planetary systems are mobilized in scattering.' This assumption is required to convert simulation yields (2 detached planets per Neptune system, 3 per Jovian system) into a per-star rate. If only a fraction of systems are unstable, the 'about half' estimate fails.
  • domain assumption The simulated initial conditions (five equal-mass planets, or one Jupiter plus ten Neptunes, on circular near-coplanar orbits) are representative of the real planetary systems that produce free-floating planets.
    Section 2 initial conditions. Real systems have mass distributions, eccentricities, inner planets, and varying multiplicity. The choice of equal-mass ensembles and targeted instability timescales may not represent the field population.
  • domain assumption Unstable systems evolve toward a final state with one inner planet plus one to three detached planets, and systems not yet converged at 10^8 orbits continue along this path.
    Section 3.1 and 3.2 conjecture this final state, supported by Juric and Tremaine (2008) and by AMD stability arguments. About 60% of the lowest-mass ensembles still have two detached planets at the end of the integration, so the yields used in Eq. 10 are partly extrapolated.
  • domain assumption The observed occurrence rates of bound Neptune and Jupiter planets around M-dwarfs are accurate and applicable to the same population as the free-floating planets.
    Eq. 10 uses 0.35 Neptunes per star and 0.06 Jovians per star from Zang et al. (2025) and Montet et al. (2014). If these rates are biased or the populations do not overlap with the FFP sample, the detached estimate changes.
invented entities (1)
  • Detached planet population independent evidence
    purpose: To explain a large fraction of reported free-floating Neptunes as bound wide-orbit planets rather than truly unbound objects.
    The paper names the orbital state 'detached' and supplies falsifiable handles: a host star should appear roughly 0.1 arcseconds from the lensing planet, and rare double-lensing events are predicted. This is a new classification of a known type of orbit, not a new fundamental object.

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Cite this review

Pith. "Pith review of Free Floating or Merely Detached?." pith.science (2026). https://pith.science/paper/RL6RZRCW

@misc{pith2026250708968,
  author       = {Pith},
  title        = {Pith review of: Free Floating or Merely Detached?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RL6RZRCW}},
  note         = {Machine review of arXiv:2507.08968}
}
read the original abstract

Microlensing surveys suggest the presence of a surprisingly large population of free-floating planets, with a rate of about two Neptunes per star. The origin of such objects is not known, neither do we know if they are truly unbound or are merely orbiting at large separations from their host stars. Here, we investigate planet-planet scattering as a possible origin through numerical simulations of unstable multi-planet systems. We find that planet ejection by scattering can be slow, often taking more than billions of years for Neptune-mass scatterers orbiting at a few AU and beyond. Moreover, this process invariably delivers planets to orbits of hundreds of AU that are protected from further scattering. We call these ``detached" planets. Under the scattering hypothesis, we estimate that about half of the reported ``free-floating" Neptunes are not free but merely ``detached".

Figures

Figures reproduced from arXiv: 2507.08968 by the authors.

Figure 1
Figure 1. Safronov number, Θ, as a function of semi– major axis for Earth-, Neptune-, and Jupiter-mass planets around a solar mass star. Close encounters among planets with Safronov numbers less than unity will generally lead to collisions, while to ejections in the opposite limit. We first integrate planetary systems of five equal-mass planets. This includes four ensembles, comprised of 101 numerical integrations each, with … view at source ↗
Figure 2
Figure 2. Example evolution of an unstable system with 5 one-Neptune-mass planets. Top: the semi-major axes of individual planets are plotted as solid lines. Orbits’ radial ex￾tents between pericenter and apocenter are indicated by the corresponding shaded regions. The black dashed line indi￾cates the semi-major axis of an orbit with the same binding energy as the initial five-planet system. Bottom: planets’ orbital inclinati… view at source ↗
Figure 3
Figure 3. Average number of bound planets as a function of time after first orbit-crossing, plotted in different colors for different ensembles. Results for all simulations and only those with energy errors |∆E/E| < 0.01 are shown with dashed and solid lines, respectively. Lower-mass ensembles take longer to eject planets. In all cases, more than one planet remains bound [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: Cumulative distributions of the ratios between systems’ total AMDs, Ctot, and their constituent detached planets’ critical AMDs, C ∗ i , the amount needed to cross orbit with the inner planet. Thick black lines show the cumula￾tive distributions of Ctot/C∗ i for all de…
Figure 6
Figure 6. Figure 6: Cumulative distributions for the mean projected distances, ⟨rproj⟩ = π 4 a [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Cumulative histogram of the minimum pericen￾ter distances reached by the innermost planets, measured in units of the initial semi-major axes of the innermost planets. Results for all simulations and only those with energy errors |∆E/E| < 0.01 are shown with dashed and …
Figure 9
Figure 9. Figure 9: Similar to Figs. 3-5 but for the 1J+10N ensemble. Left panel shows that, on average, the Jupiter is able to eject all but three Neptunes. In the middle panel, the average AMD for the 1J+10N systems (yellow) are compared against those in the 5 equal-mass ensemble (black…

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    A review of planetary ejection mechanisms and their predicted free-floating planet demographics, concluding that planet-planet scattering, cluster encounters, and binary instabilities likely dominate FFP production.

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.