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Properties of Free Floating Planets Ejected through Planet-Planet Scattering

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Pith's one-line read Planet-planet scattering can eject 40-80% of a planetary system's planets, and matching the observed free-floating planet count requires that 5-10 planets form around each star.

desk verdict Systematic N-body parameter study of scattering-ejected FFPs, useful, but the headline '5-10 planets per star' is not what their own Eq. (3) computes. read the letter →

arxiv 2501.13166 v1 pith:J4TB7IBU submitted 2025-01-22 astro-ph.EP astro-ph.GAastro-ph.SR

Hareesh Gautham Bhaskar , Hagai Perets This is my paper · ORCID
classification astro-ph.EPastro-ph.GAastro-ph.SR
keywords exoplanetsfree-floatingplanetsplanet-planetscatteringN-bodysimulationsejectionfractionmicrolensingplanetarydynamics
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 uses N-body simulations of planetary systems to quantify how many planets get ejected through planet-planet scattering and what the ejected planets look like. The authors find that 40-80% of planets are ejected over a billion-year evolution, with most ejections happening within 1e8-1e9 years, and that ejected planets typically leave with excess speeds of 2-6 km/s. They also find that all planets are equally likely to be ejected regardless of starting position, and that lighter planets are ejected while heavier planets remain bound. Comparing the simulated ejection fractions with the observed census of free-floating planets, they conclude that on average 5-10 planets must form around each star, implying scattering can account for a substantial fraction of observed free-floating planets.

What carries the argument

The argument is carried by ensemble N-body simulations using the MERCURIUS integrator in the REBOUND package. Each run places 3-10 Jupiter-mass or log-uniform-mass planets on near-circular, near-coplanar orbits and follows them for up to 1e9 years, removing planets as ejected when they reach a prescribed distance D that is varied between 1e2 and 1e5 AU. The key output is the ejection fraction f_eject, which feeds the population equation N_free/N_stars = sum_Np f_giant f_unstable f_eject, together with the observed free-floating planet abundance and the assumed fraction of unstable systems.

What would settle it

Measure the intrinsic fraction of planetary systems that experience scattering instability, for example from the fraction of systems showing high-eccentricity or high-inclination architectures; if that fraction is well below 50%, the required formation rate of 5-10 planets per star would exceed the 8-10 planets that core-accretion models typically allow. Alternatively, if future microlensing surveys find a free-floating planet abundance significantly below the 1.8 per star adopted from Sumi et al. (2011), the inference weakens.

Watch

Extended reading notes

Core claim

The central claim is that planet-planet scattering alone can produce a large share of the observed free-floating planets. In ensembles of N-body systems with 3-10 planets on initially near-circular, coplanar orbits, the fraction of planets ejected over 1e9 years ranges from about 40% to 80%, increasing with the number of planets initially present. Ejections occur predominantly within 1e8-1e9 years, and the mean excess velocity of ejected planets is 2-6 km/s relative to the host star, depending most strongly on the semi-major axis of the innermost planet. Systems with unequal-mass planets eject fewer planets and show a clear mass segregation: lighter planets are preferentially ejected while heavier planets stay bound. When these ejection fractions are inserted into the accounting equation used for the observed free-floating planet population, with the fraction of unstable systems set to either 0.5 or 1, the authors conclude that 5-10 planets must form per star, a number within reach of current formation models.

Load-bearing premise

The 5-10 planets-per-star conclusion assumes that either half or all planetary systems undergo the kind of instability simulated here, a fraction the paper explicitly states is unconstrained.

Editorial extensions

If this is right

  • If scattering is the dominant ejection channel, a large share of observed free-floating planets, especially low-mass ones, are ejected members of formerly more-populous planetary systems.
  • The required 5-10 planets per star implies that observed exoplanet multiplicities are depleted remnants of initially richer systems, so planet formation must routinely build systems more massive than those seen today.
  • Ejected planets should arrive in the field with excess velocities of 2-6 km/s, mostly within about 30 degrees of their original system's plane, providing a kinematic signature for future surveys.
  • Bound planets left after scattering have broad eccentricity and inclination distributions, consistent with the observed eccentric exoplanet population and reinforcing scattering as a driver of those architectures.

Reading between the lines

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

  • If 5-10 planets form per star, the star-formation channel for free-floating planets may be less dominant than sometimes assumed, and formation models that cap planet yields near 8-10 would be stretched, motivating models that build more planets.
  • The near-planar ejection pattern suggests that wide-separation free-floating planets in young clusters should show a preferred orientation correlated with the cluster's angular momentum if they were scattered out, a prediction distinct from the core-collapse formation channel.
  • The mass-segregation result implies that the mass function of free-floating planets from microlensing should be bottom-heavy relative to the initial planet mass function, and comparing the two could directly test the scattering origin.
  • Extending the simulations to include the galactic tide or stellar flybys in dense cluster environments would likely convert some bound wide-orbit planets into free-floating planets, potentially raising the scattering contribution in star-forming regions beyond the present estimate.
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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. The manuscript presents an ensemble of N-body simulations of planet-planet scattering in systems with 3-10 giant planets, varying planet masses, radii, initial spacing, inner semi-major axis, and the distance at which planets are deemed ejected. The main results are that 40-80% of planets are ejected over timescales up to ~1e9 years, with mean excess speeds of 2-6 km/s, that ejection probability is roughly independent of initial orbital radius, that bound planets tend to be more massive than ejected planets, and that the ejection fraction is insensitive to the adopted ejection distance. The authors then combine their ejection fractions with the observed free-floating planet census to infer that 5-10 planets must form per star.

Significance. The parameter study is systematic and useful, and the long integration time (1e9 yr) is a strength compared to earlier work. The simulations are standard and the output quantities (ejection fractions, timescales, velocity distributions) are likely robust. The paper explicitly uses a forward-modeling approach without fitting parameters to the observed FFP count, so the inference is not circular. However, the headline '5-10 planets per star' is not supported by the paper's own Eq. (3), and the v_inf definition in Eq. (1) is missing a factor of 2. These issues affect the quantitative conclusions, particularly the observational comparison.

major comments (2)
  1. [Section 4.1, Eq. (3) and the abstract/conclusion] The paper defines f^Np_giant,crit as the critical fraction of systems that must contain Np planets, but then interprets the result as 'on average 5-10 planets should form around each star.' The per-star average number of planets formed is Np times f^Np_giant,crit. With the paper's nominal values (N_free/N_stars = 1.8, f_unstable = 1, f_eject ~ 0.7-0.8 for Np = 5-10), this average is approximately 2.3-2.6 planets per star, and even for f_unstable = 0.5 and Np = 10 it is about 4.5. Thus the stated conclusion is not what Eq. (3) yields; the text conflates the required initial multiplicity in unstable systems with the per-star average. The authors should correct the wording and the derived numbers, or explicitly state the assumed interpretation.
  2. [Section 2, Eq. (1)] The excess speed is defined as v_inf = sqrt(v^2 - G*ms/D), but the correct expression from energy conservation is v_inf = sqrt(v^2 - 2*G*ms/D). The missing factor of 2 is not negligible for small ejection distances; for D = 100 AU, the term G*ms/D is of the same order as the kinetic energy, so the reported excess velocities for those runs are overestimated. While the fiducial D = 10^5 AU makes the correction tiny, the definition is incorrect and should be fixed, and the D-dependence results in Section 3.6 should be re-examined.
minor comments (5)
  1. [Throughout] There are several typos: 'raii' in Section 3.5, 'systen' in Section 3.2, 'corelation' in Section 4.2, and 'galatic' in Section 3.6; a careful proofread is needed.
  2. [Section 3.1, Figure 2] The mean excess speed is given as 2.1 km/sec in the caption of Figure 2 but 2.2 km/sec in the text of Section 3.1; please harmonize the numbers.
  3. [References] The references Veras & Raymond (2012a) and (2012b) appear to refer to the same paper (MNRAS 421, L117); please use a single citation for both the introduction and Section 4.1.
  4. [Section 4.1] The nominal observational value is taken from Sumi et al. (2011); more recent microlensing constraints (e.g., Mroz et al. 2019; Sumi et al. 2023) give different estimates and could be used to bracket the uncertainty in the observational normalization.
  5. [Sections 3.2 and 4.1, Figures 3 and 14] The text in Section 3.2 reports an ejection fraction of 70% for N = 10, while Section 4.1 quotes 80% for Np = 10 at 10^9 years; please clarify which ensemble the figure is based on and ensure the values are consistent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: ejection properties are direct N-body simulation outputs, and the FFP comparison is an algebraic inversion with externally sourced observations, not a fitted parameter recycled as a prediction.

full rationale

The paper's central products—ejection fractions, excess velocities, timescales, and bound/ejected mass distributions—are direct outputs of N-body integrations with stated initial conditions (Section 2, Figures 1–14). No simulation parameter is fitted to the observed free-floating planet abundance. The comparison with observations in Section 4.1 uses an external census value (N_free/N_stars = 1.8 from Sumi et al. 2011) and external constraints on the fraction of systems with giant planets (Gould et al. 2010; Mayor et al. 2011). Equation (3) is an algebraic rearrangement of Equation (2), defining the critical fraction of systems that must contain Np planets; it is explicitly labeled as a required fraction, not a prediction, and it is not used to re-derive the simulated ejection fractions. The parameter f_unstable is honestly stated to be unconstrained and is bracketed by two assumed values (0.5 and 1.0), which is an input assumption rather than a circular step. Self-citations (Perets & Kouwenhoven 2012; Rozner & Perets 2023) appear only as alternative formation channels for wide-orbit planets and do not carry the load of the ejection-fraction result; there is no uniqueness theorem, fitted-input-renamed-as-prediction, or ansatz-smuggled-via-citation pattern. The abstract's '5-10 planets per star' wording is arguably an overstatement of the f_giant,crit fraction in Eq. (3) and may conflict with the paper's own f_total_giant < 0.5 constraint, but that is a quantitative/interpretation concern, not circularity: the inference does not assume what it purports to derive.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The paper uses a suite of N-body simulations with defined initial conditions; it does not introduce new physical entities. The main hand-chosen input in the population comparison is f_unstable, which the authors themselves mark as unconstrained. The conclusions also rest on assumptions about the representativeness of initial conditions and the adopted observational census.

free parameters (1)
  • f_unstable = 0.5 or 1.0
    The fraction of exosystems that become dynamically unstable is unconstrained and is chosen as 0.5 or 1.0 in Section 4.1 to compute the critical number of planets that must form; it directly scales the 5-10 planets per star conclusion.
assumptions (5)
  • domain assumption External perturbations such as stellar flybys and the galactic tide do not affect ejections before planets reach 1e5 AU.
    Invoked in Section 2 and Section 3.6 to define the ejection boundary; in denser environments, decoupling could occur at smaller distances and change FFP yields.
  • domain assumption The simulated initial conditions (near-circular, near-coplanar orbits with 3-10 planets, spacing 2-5 Hill radii, inner semi-major axis 1-10 AU) are representative of post-formation planetary systems.
    Section 2 setup; if real systems have significantly different architectures, the ejection fractions and velocities would differ.
  • domain assumption Sticky-sphere collisions with radii from the adopted mass-radius relation approximate real collisions; tidal effects may increase effective radii by up to a factor of 2.
    Section 2; the authors partially test this by running simulations with larger radii.
  • domain assumption The observed free-floating planet abundance (N_free/N_stars ~ 1.8) and the giant-planet occurrence limits from Gould et al. and Mayor et al. are adopted as external inputs.
    Section 4.1; if the observed FFP census is revised, the inferred 5-10 planets per star changes.
  • domain assumption The empirical instability timescale relation of Chatterjee et al. (2008) is used to guide expectations for simulation stopping times.
    Section 2; used to justify the 1e9 year maximum simulation time.

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Pith. "Pith review of Properties of Free Floating Planets Ejected through Planet-Planet Scattering." pith.science (2026). https://pith.science/paper/J4TB7IBU

@misc{pith2026250113166,
  author       = {Pith},
  title        = {Pith review of: Properties of Free Floating Planets Ejected through Planet-Planet Scattering},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J4TB7IBU}},
  note         = {Machine review of arXiv:2501.13166}
}
abstract

Multiple studies have shown that planet-planet scattering plays an important role in the dynamical evolution of planetary systems. For instance, it has been shown that planet-planet scattering can reproduce the eccentricity distribution of exoplanets. It can also contribute to the current census of free floating planets. In this work we run an ensemble of N-body simulations of planetary systems, and record the properties of planets which are ejected from the system. In our simulations we sample a wide range of orbital and physical properties of the planets. We find that in general $40-80\%$ of the planets are ejected from the system depending on the number of planets initially in the system. Most of the planets are ejected over a timescale of $\sim 10^8-10^9$ years. The ejected planets have a mean excess velocity in the range of 2-6 km/sec with respect to the host star. The excess velocities of the planets ejected from the system strongly depends on the semi-major axis of the inner most planet. We find that irrespective of their initial location in the planetary system, all planets are equally likely to be ejected from the system. Also, bound and ejected planets have distinct mass distributions, with bound planets being more massive than ejected planets. In addition, increasing the radii of the planets reduces the ejection fraction. The properties of the ejected planets do not strongly depend on the initial spacing between the planets. The timescale over which ejections happen does increase with the initial separation between the planets. We also find that the ejection fraction does not strongly depend on the distance from the host star beyond which the planets are considered unbound. Finally, we compared our results with observed populations of free floating planets. We conclude that on average 5-10 planets should form around each star to reproduce the observations.

Figures

Figures reproduced from arXiv: 2501.13166 by the authors.

Figure 1
Figure 1. The average number of collisions (red) and ejec￾tions (blue) as a function of time in our fiducial simula￾tions. We can see that most of the ejections happen in 108 years. Meanwhile collisions happen on much shorter timescales (∼ 106 years). On average ∼ 3 planets are ejected from the system as compared to 0.4 collisions. We use the fol￾lowing parameters to run the simulations: Np = 5, a0,init = 3 AU, ms = 1 M⊙, mj … view at source ↗
Figure 2
Figure 2. The left panel shows the distribution of excess velocities of ejected planets (with respect to their host stars) in our fiducial simulations. We can see that most of the ejected planets have excess speeds less than a 10 km/sec. We find the mean excess speed to be 2.1 km/sec. The right panel shows the distribution of ejection angle with respect to the initial angular momentum of the planetary system. The results for … view at source ↗
Figure 5
Figure 5. The distribution of planets which have either been ejected (left panel) or have collided (right) during the course of the simulation. The x-axis shows the planet index, and colors show the initial number of planets in the system. Planets with an index of 0 are initialized closest to their host stars, and those with index N−1 are on the widest orbits. We can see that collisions mostly happen in close-in planets, and … view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Dependence of the mean excess velocity with respect to the host star (y-axis) on the initial semi-major axis of the inner most planet, a0,init (x-axis). The colors show the number of planets initially in the system. We can see that the excess velocity decreases with th…
Figure 7
Figure 7. Figure 7: Dependence of excess velocity on the semi-major axis of the inner most planet. The colors show the semi￾major axis of the inner-most planets. The excess velocity decreases with the semi-major axis of the inner most planets. We use the following parameters to run the si…
Figure 8
Figure 8. Figure 8: The mass distribution of planets ejected (left panel) and planets which remain bound (right panel) to the host star. The colors show the number of planets initially in the system. We can see that heavier planets remain bound to host star, and the lighter planets are ej…
Figure 10
Figure 10. Figure 10: shows the number of planets ejected from the system as a function of time. The colors show the ejection distance. It should be noted that we remove planets from the simulations only when they reach a dis￾tance of 105 AU from the host star. Consequently, many of the pl…
Figure 11
Figure 11. Figure 11: The distribution of semi-major axes (left panel) and eccentricities (right panel) of planets which are eventu￾ally ejected from the system. The colors shows the time at which the distribution was calculated. We can see that the ejected planets initially have close-in …
Figure 13
Figure 13. Figure 13: The average number of planets ejected from the system as a function of time. The colors show the initial separation between the planets in terms of mutual Hill radii (K). We can see that total number of ejected planets does not strongly depend on K. Also, the timescal…
Figure 15
Figure 15. Figure 15: The critical fraction of stellar systems that must contain N planets to produce the observed number of free floating planets. The limits from observations are shown using the horizontal black lines. The results shown using the blue (red) line assume that all (50%) of …
Figure 16
Figure 16. Figure 16: The figure shows the cumulative distribution of eccentricity (left panel), semi-major axis (middle panel), and the inclination (right panel) of bound planets at the end of the simulation. The colors shows the initial number of planets in the system. We use the followi…
Figure 17
Figure 17. Figure 17: Orbital properties of planets which remain bound to the host star at the end of the simulation. The left panel shows semi-major axes (x-axis) vs eccentricities (y-axis), the middle panel shows the inclination (y-axis) vs semi-major axis (x-axis) and the right panel sh…

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Free Floating or Merely Detached?

    astro-ph.EP 2025-07 conditional novelty 6.0 of 10

    Planet-planet scattering can leave 'detached' planets at hundreds of AU, and these may account for about half of the free-floating Neptunes detected by microlensing.

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Reviewed August 10, 2026 · model on record in the stance chip above.