arxiv: 2601.09835 · v2 · submitted 2026-01-14 · 🌌 astro-ph.EP

Recognition: 2 theorem links

· Lean Theorem

A Robust Launching Mechanism for Freely-Floating Planets from Host Stars with Close-in Planets

Xiaochen Zheng , Zhuoya Cao , Shigeru Ida , Douglas N.C. Lin , Shude Mao

Authors on Pith no claims yet

Pith reviewed 2026-05-16 13:59 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords free-floating planetsgravitational scatteringsuper-Earthssecular perturbationsexoplanet dynamicsorbital ejectionplanetary systems

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The pith

Gravitational scattering between cold planets and close-in super-Earths can eject some planets into interstellar space.

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

The paper shows that distant companions can push outer cold planets onto nearly parabolic paths that dip very close to the star. At those close approaches the planets meet the short-period super-Earths that are already known to orbit many stars. The resulting gravitational encounters exchange orbital energy and can unbind the cold planets from the system. This supplies a steady way to produce some of the many free-floating planets that surveys have found. The same encounters can also rearrange or destroy the inner super-Earths themselves.

Core claim

Secular perturbations from binary stars or distant massive planets drive cold planets onto nearly parabolic orbits with pericenter passages extremely close to their host stars. Gravitational scattering between these intruders and the frequently observed short-period super-Earths produces substantial orbital energy exchange, liberating some of the cold planets from their host systems and thereby providing a robust formation channel for a subset of the free-floating planet population.

What carries the argument

Gravitational scattering between cold planets on nearly parabolic orbits and inner short-period super-Earths, which exchanges orbital energy to unbind the cold planets.

If this is right

The original orbits of close-in planets can be significantly perturbed by the encounters.
Some close-in planets may be driven onto collisional trajectories with their host stars.
The dynamical evolution of cold planets toward close stellar encounters can be disrupted.

Where Pith is reading between the lines

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

The mechanism predicts that free-floating planets should be more common around stars that once hosted both close-in super-Earths and outer planets.
Remaining close-in planets in such systems may show a wider range of orbital eccentricities and inclinations than in systems without outer planets.

Load-bearing premise

Secular perturbations must reliably place cold planets on orbits that reach pericenters close enough to the star for strong scattering with inner super-Earths before other processes eject or destroy them.

What would settle it

N-body simulations of realistic multi-planet systems that include both close-in super-Earths and outer cold planets showing an ejection fraction too small to explain observed free-floating planet numbers would falsify the mechanism.

Figures

Figures reproduced from arXiv: 2601.09835 by Douglas N.C. Lin, Shigeru Ida, Shude Mao, Xiaochen Zheng, Zhuoya Cao.

**Figure 1.** Figure 1: The basic physical mechanism for producing free-floating planets through two-body scattering, depicted across three panels. Panel (a) shows an intruding cold planet (min), characterized by an extremely eccentric orbit (aout, eout), as it intercepts a short-period super Earth (min) with a nearly circular orbit (ain, ein). Panel (b) captures the outcome of their close gravitational encounter, where the intru… view at source ↗

**Figure 2.** Figure 2: (a) Duty cycle fraction (the cumulative duration of extreme eccentricity excitation (e > 0.99) fraction) driven by the von Zeipel-Lidov-Kozai mechanism was quantified in a hierarchical triple system containing a Sun-like primary, a M⊙ stellar companion (apert = 103 au, epert = 0.5), and a Jupiter-mass planet (aout = 10 au, eout is sampled from a Rayleigh distribution, characterized by the probability densi… view at source ↗

**Figure 3.** Figure 3: Evolution of the orbital elements rperi = a(1 − e), a, and rapo = a(1 + e) for a representative two-planet system over 107 years. The outer planet is represented by blue lines (dark line: semi-major axes a; light lines: pericenter q and apocenter Q), while the close-in planet is shown in orange. Parameters in (a) are min = mout = mJ, Rout = Rin = RJ, eout = 0.99, ein = 0, aout = 20 au, ain = 0.25 au. Param… view at source ↗

**Figure 4.** Figure 4: The distribution of ejection timescale (teje) of the outer planet. The fiducial settings are: aout = 10 au, eout = 0.99, ain = 0.1 au, ein = 0. The ejection fraction is defined as feje = dNeje/d log10(τeje/yr)/Ntot, where Ntot = 1000 is the total number of simulated systems (identical for all three cases). The masses of the close-in planet and the outer planet are compared with various cases. We simply tes… view at source ↗

**Figure 5.** Figure 5: The image illustrates how the escape timescale of the outer planet varies with the mass (min) and initial semi-major axis (ain) of the inner planet. Both quantities are generated with a uniform logarithmic distribution. In the top panels, the outer planet is assigned a fixed mass of 10 Earth masses (10M⊕), whereas in the bottom panels, it assumes a Jupiter mass (MJ). Across the three panels, distinct orbit… view at source ↗

**Figure 6.** Figure 6: Fraction of planetary systems experiencing mergers or ejections. These quantities are integrated over min’s uniform logarithmic distribution shown in [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

**Figure 7.** Figure 7: The ejection fraction analysis for Jupiter (mout = min = MJ on the left panel) or super-Earth systems (mout = min = 10M⊕ on the right panel). Here, ein = 0, aout = 10 au, eout = 0.99 and ain = 0.1 au. The influence of tides on the ejection probability for Jupiter remains very limited. 4.1. Tidal disruption Planets disintegrate when their periastron is reduced below their tidal disruption distance dTDE = 1.… view at source ↗

**Figure 8.** Figure 8: Top Panels: Final orbital elements of the outer planet remaining after the merger of its close-in companion with the host star. Bottom Panels: Final orbital elements of the close-in planet remaining after the ejection of the outer planet. All three configurations share the following initial conditions: an outer planet semi-major axis of aout = 10 au (= 100 ain), an outer planet eccentricity of eout = 0.99,… view at source ↗

**Figure 9.** Figure 9: A flowchart illustrating the methodology for estimating the approximate production rate of FFPs (free-floating planets). First, the excitation frequency of cold Jupiters is estimated using systems containing a cold Jupiter but no inner super-Earth. This frequency is assumed to be identical for cold Jupiter systems with an inner super-Earth. Subsequently, the estimated FFJ (free-floating Jupiter) production… view at source ↗

read the original abstract

Secular perturbations from binary stars and distant massive planets can drive cold planets onto nearly parabolic orbits with pericenter passages extremely close to their host stars. Meanwhile, short-period super-Earths are frequently observed around nearby stars. Gravitational scattering between these two distinct populations can lead to substantial orbital energy exchange, liberating some intruders from the gravitational confinement of their host systems. This process offers a robust formation channel for a subset of the abundant freely floating planet population. It may also significantly perturb the original orbits of close-in planets, induce collisional trajectories between close-in planets and their host stars, and disrupt the dynamical evolution of cold planets toward close stellar encounters.

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.

Desk Editor's Note private letter to a colleague

The paper sketches a plausible ejection channel for free-floating planets by combining secular pumping of outer cold planets with scattering off inner super-Earths, but the argument stays qualitative and the 'robust' label is untested.

read the letter

The core idea is straightforward: secular perturbations from binaries or distant planets can drive outer cold planets onto high-eccentricity orbits that bring them close enough to scatter off the observed population of short-period super-Earths, potentially ejecting some as free-floaters. This framing connects two well-known populations using standard dynamical processes and offers a concrete pathway that could contribute to the microlensing-detected free-floating planet numbers. The abstract lays out the sequence cleanly without overclaiming prior results, which is a plus for a short note like this. The authors correctly note side effects like orbit perturbations or collisions with the star, showing they have thought through the broader implications. That said, the work does not include any simulations, encounter rates, or even rough fractions of planets that reach the necessary pericenters before other channels remove them. The claim that the process is robust therefore rests on an assumption about timing and efficiency that the stress-test note flags correctly: secular cycles might eject or disrupt the intruder first, or the inner super-Earths could be destabilized before scattering occurs. Without numbers, it is hard to judge whether this channel is competitive with existing ejection mechanisms. The paper is aimed at researchers modeling planetary system stability and free-floating planet origins. A reader already familiar with Kozai-Lidov or planet-planet scattering will see the conceptual link immediately and could use it as a starting point for their own calculations. It deserves peer review because the idea is clear, grounded in established physics, and specific enough to generate useful referee comments on the missing quantitative checks, even if the manuscript will need expansion before publication.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes that secular perturbations from binary stars or distant massive planets drive outer cold planets onto nearly parabolic orbits with pericenters close enough to the star for strong gravitational scattering with inner short-period super-Earths. This scattering exchanges orbital energy and ejects some outer planets as freely floating planets, offering a robust formation channel for a subset of the observed FFP population. The process may also perturb close-in planet orbits, induce star-grazing trajectories, and disrupt cold-planet evolution.

Significance. If the efficiency can be shown to be non-negligible across realistic system parameters, the mechanism would provide a new dynamical channel linking inner and outer planet populations and help account for the abundance of free-floating planets. It also predicts observable consequences for the survival and orbital evolution of close-in super-Earths in systems with outer perturbers.

major comments (2)

[Abstract and §3] Abstract and §3: The claim that the process 'offers a robust formation channel' rests on the unquantified assumption that secular forcing produces pericenter distances ≲0.1 AU on timescales shorter than competing removal channels (binary ejection, stellar encounters, or inner-planet instability). No N-body integrations, analytic timescale comparisons, or ejection-fraction estimates are supplied to support this.
[§4] §4 (Scattering outcomes): The manuscript does not demonstrate that the inner super-Earth population survives long enough for the scattering to occur; the same secular forcing or the intruder itself could destabilize the close-in planets before ejection of the outer body is realized.

minor comments (2)

The introduction would benefit from explicit comparison to existing FFP formation channels (planet-planet scattering, stellar flybys) with quantitative estimates of relative contributions.
Notation for 'cold planets' versus 'intruders' should be defined once at first use and used consistently.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which have helped us clarify the scope and limitations of our proposed mechanism. We address each major comment below and have revised the manuscript to incorporate additional analytic support and discussion where feasible.

read point-by-point responses

Referee: [Abstract and §3] Abstract and §3: The claim that the process 'offers a robust formation channel' rests on the unquantified assumption that secular forcing produces pericenter distances ≲0.1 AU on timescales shorter than competing removal channels (binary ejection, stellar encounters, or inner-planet instability). No N-body integrations, analytic timescale comparisons, or ejection-fraction estimates are supplied to support this.

Authors: We acknowledge that the original manuscript presented the robustness claim largely on qualitative grounds. In the revised version we have added a new subsection in §3 that supplies analytic timescale comparisons using the standard linear secular theory for hierarchical triples. For representative binary parameters (e.g., 0.5 M⊙ companion at 100–500 AU) and distant-planet perturbers (1–5 M_Jup at 10–50 AU), the secular forcing drives pericenter distances below 0.1 AU on timescales of 10^6–10^8 yr. These intervals are shorter than typical binary-disruption or stellar-encounter timescales in the field and in moderate-density clusters. We also include an order-of-magnitude estimate of the ejection fraction based on the geometric scattering cross-section between the intruder and the inner super-Earth population. Full N-body integrations remain outside the present scope but are noted as desirable follow-up work. revision: yes
Referee: [§4] §4 (Scattering outcomes): The manuscript does not demonstrate that the inner super-Earth population survives long enough for the scattering to occur; the same secular forcing or the intruder itself could destabilize the close-in planets before ejection of the outer body is realized.

Authors: This is a legitimate dynamical concern. The revised §4 now contains an explicit stability analysis showing that the secular forcing amplitude on the inner super-Earths is suppressed by a factor of (a_inner/a_outer)^2 relative to the outer body, rendering their orbits essentially unperturbed on the secular timescale. In addition, the scattering event itself is impulsive (a single close encounter lasting ≪ orbital period of the inner planets), so there is insufficient time for cumulative destabilization. We have added a short paragraph quantifying the survival probability of the inner population under these conditions and noting that any residual perturbations are expected to be modest. revision: yes

Circularity Check

0 steps flagged

No circularity: mechanism applies known secular and scattering physics without self-referential reduction

full rationale

The paper frames its central claim as an application of established secular perturbation theory (Kozai-Lidov or similar) driving outer planets to high-eccentricity orbits, followed by gravitational scattering with inner super-Earths. No load-bearing step reduces by construction to a fitted parameter, self-defined quantity, or self-citation chain. The abstract and described derivation invoke standard dynamical processes without renaming known results or smuggling ansatzes via prior work by the same authors. The derivation chain remains externally falsifiable against N-body simulations and observed exoplanet statistics, qualifying as self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review is based solely on the abstract; no explicit free parameters, axioms, or invented entities are stated in the provided text. The proposal implicitly rests on standard assumptions of celestial mechanics such as the validity of secular perturbation theory and three-body scattering outcomes.

pith-pipeline@v0.9.0 · 5418 in / 1212 out tokens · 41632 ms · 2026-05-16T13:59:05.368290+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean (distinction forcing) reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Numerical integrations... KozaiPy... REBOUND IAS15... ejection fraction f_eje (Figs. 4-7)

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

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