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White-dwarf formation kicks eject planets from roughly half of long-period multi-planet systems, creating a few-percent subpopulation of free-floating planets that stay warm and near their former hosts for millions of years.

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2026-07-12 07:55 UTC pith:L7BXX2TC

load-bearing objection Solid first quantification of WD-kick FFP yield plus a clean thermal-kinematic signature, but the 'half of all systems' Galactic claim rests on an optimistic extrapolation from a tiny biased sample. the 2 major comments →

arxiv 2607.02653 v1 pith:L7BXX2TC submitted 2026-07-02 astro-ph.EP astro-ph.GAastro-ph.SR

Contribution of White Dwarf Formation Kicks to the Free-Floating Planet Population

Alexander P. Stephan , Keivan G. Stassun This is my paper
classification astro-ph.EP astro-ph.GAastro-ph.SR
keywords free-floating planetswhite-dwarf kicksplanetary system dynamicsAGB mass lossorbital instabilitymicrolensing
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper shows that the mild recoil kick a white dwarf receives when it forms can unbind only about one percent of known planets by itself, yet it rearranges the orbits of multi-planet systems so thoroughly that dynamical instabilities arise in more than forty percent of known long-period cases. Numerical integrations of the fifty-three systems that survive the paper's selection cuts find that nearly half eject at least one planet within a few million years. Because the kicks are weak, the newly free-floating planets drift away slowly (roughly 0.75 pc per Myr) and remain heated for millions of years by residual heat from the host's earlier asymptotic-giant-branch luminosity. The result is a distinct, observationally identifiable minority of free-floating planets that can still be associated with young white dwarfs, a signature relevant to the forthcoming Roman microlensing survey.

Core claim

White-dwarf formation kicks, drawn from the Maxwellian velocity distribution measured by El-Badry & Rix, directly unbind only ~1 % of known planets but drive orbital instabilities in ≳40 % of known long-period multi-planet systems (numerically ~47 % of the 53 systems examined), leading to planet ejection in roughly half of all such systems and thereby contributing a distinct free-floating-planet subpopulation of a few percent of the Galactic total.

What carries the argument

The combination of the observed Maxwellian kick-velocity distribution with the Petrovich stability criterion (and direct REBOUND n-body checks) applied after stellar mass loss, which converts a modest instantaneous velocity perturbation into long-term orbital chaos and ejection.

Load-bearing premise

That the short-period-biased sample of only fifty-three multi-planet systems around white-dwarf progenitors can be scaled up to claim that at least half of all white dwarfs that once hosted planets will have ejected free-floating planets.

What would settle it

A statistically complete census of multi-planet systems around white-dwarf progenitors with outer semi-major axes beyond ~10 AU, followed by direct n-body integration of those systems under the El-Badry & Rix kick distribution, would show whether the instability fraction remains near 50 % or falls substantially.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper examines whether the mild recoil kicks (~0.75 km/s peak) experienced by white dwarfs at the end of the AGB phase can unbind planets and thereby contribute free-floating planets (FFPs). Using the Maxwellian kick distribution of El-Badry & Rix (2018), analytic separation fractions (Eqs. 1–4) are derived and validated numerically; direct unbinding is found to affect only ~1% of the known exoplanet sample. For multi-planet systems the authors apply the Petrovich (2015) stability criterion and 5-Myr REBOUND integrations to the 53 known multi-planet systems around MS hosts ≥1 M☉ that survive AGB engulfment, recovering instability/ejection fractions of ~41% (analytic) and ~47% (numerical). They therefore argue that WD kicks eject planets from roughly half of all such systems, producing a few-percent contribution to the Galactic FFP population. Additional predictions are that the ejected planets remain spatially associated with their former hosts for several Myr and retain elevated temperatures from AGB heating, making them observationally distinguishable near young WDs and relevant for the Roman Galactic Exoplanet Survey.

Significance. If the yield estimates hold, the work identifies a previously under-appreciated late-time channel for FFP production that is distinct from the usual young-system scattering or in-situ formation routes. The combination of slow ejection speeds and long-lived AGB heating supplies concrete, falsifiable observational markers (warm FFPs within a few pc of young WDs) that can be tested with Roman microlensing and infrared surveys. Strengths include the use of an external empirical kick distribution, an external stability criterion, public stellar-evolution tracks (SSE), and direct n-body cross-checks on the 53 systems; no free parameters are tuned to produce the claimed fractions. The few-percent Galactic estimate is therefore an order-of-magnitude product of independent ingredients rather than a fitted result, and the paper correctly flags the short-period bias of the input sample.

major comments (2)
  1. Section 3 (final two paragraphs) and the abstract claim that WD kicks lead to planet ejection in 'roughly half of all such systems' and thereby a few percent of Galactic FFPs. This rests on treating the ~47% (25/53) REBOUND ejection rate (and the ~41% Petrovich rate) obtained from the short-period-biased sample of 53 multi-planet systems as representative of the true population. The manuscript itself notes that the sample is 'mostly a reflection of the current observational biases' favoring short periods and that longer-period multi-planet systems are expected to be common, yet no occurrence-rate prior, completeness correction, or population-synthesis calculation is supplied to quantify how incompleteness for a ≳ 10 AU systems affects the half-system yield. If the true wide multi-planet fraction is substantially lower, or if many wide systems remain stable after the kick, both the 'half'
  2. Section 2.2 and Table 1: the Petrovich (2015) criterion (Eq. 5) and the orbit-crossing metric are applied to neighboring pairs and are only partially validated by the 5-Myr REBOUND runs. Mutual inclinations, secular resonances, and systems with more than two planets are acknowledged as caveats but are not systematically explored. Because the central claim is that instabilities (rather than direct unbinding) dominate the FFP yield, a short suite of integrations that sample mutual inclinations and three-planet architectures would strengthen the load-bearing numerical result that ~half of the systems eject planets.
minor comments (5)
  1. Figure 2 caption and surrounding text: clarify that the SMAs shown are the main-sequence values (pre-mass-loss) while the kick is applied after AGB expansion; the distinction is stated but easy to miss when reading the figure alone.
  2. Equation 6 and Figure 6: the cooling model is order-of-magnitude only (η ~ 0.01–0.03). A brief note on the sensitivity of the 8–20 Myr temperatures to η and to the precise AGB luminosity history would help readers assess how robust the 'warm FFP' prediction is.
  3. Table 1: the uncertainty is quoted as '~1%' for all entries; a short statement of how that figure was obtained (number of Monte-Carlo draws) would improve reproducibility.
  4. Introduction and Section 5: a few additional references to recent microlensing FFP occurrence-rate papers would better situate the 'few percent' claim relative to current observational constraints.
  5. Minor typographical issues: 'F ormation' and 'F ree-Floating' in the title line of the draft, and occasional missing spaces after periods in the abstract.

Circularity Check

0 steps flagged

No significant circularity: FFP fractions are computed from the external El-Badry & Rix kick distribution plus an observed exoplanet sample, using independent stability criteria and public codes; self-citations are non-load-bearing.

full rationale

The paper's derivation chain is self-contained and non-circular. The kick velocity distribution (Maxwellian with σ_kick ≈ 0.5 km s^{-1}) is taken as an external empirical input from El-Badry & Rix (2018). Direct unbinding fractions follow analytically from that distribution plus orbital mechanics (Eqs. 1–4) applied to catalogued SMAs; no free parameter is fitted to the target FFP yield. Instability fractions (≁41 % by Petrovich 2015 criterion; ≁47 % by REBOUND n-body on the 53 systems that survive the stated cuts) are likewise computed from the same external kick plus an external stability criterion and public codes (SSE, REBOUND). The subsequent order-of-magnitude Galactic estimate multiplies these fractions by independent literature numbers for the number of WDs and the overall FFP population; it is not forced by construction. Self-citations (Shariat et al., Stephan et al.) appear only as supporting references that prior work has already shown kicks can alter orbits; they do not supply the numerical results or uniqueness claims used here. The optimistic extrapolation from the short-period-biased sample of 53 systems to “half of all WDs” is an explicit incompleteness caveat, not a circular redefinition. No self-definitional loop, fitted-input-as-prediction, uniqueness theorem imported from the authors, or ansatz smuggled via citation is present.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 0 invented entities

Central claim rests on one external empirical kick distribution, standard stellar-evolution and N-body tools, and two stability criteria; the only free parameters are those already fixed by prior observations. No new dynamical entities are invented.

free parameters (1)
  • σ_kick = ≈ 0.5 km s⁻¹
    Dispersion of the Maxwellian kick-velocity distribution taken from El-Badry & Rix (2018); peak velocity fixed at √2 σ_kick ≈ 0.75 km s⁻¹. All separation fractions and ejection velocities scale directly with this number.
axioms (3)
  • domain assumption WD kick occurs instantaneously at the end of the AGB phase and is isotropically random in direction.
    Stated explicitly in Sec. 2; the true mass-loss asymmetry may be gradual, which would alter the impulse approximation used in Eqs. 2–4.
  • domain assumption Violation of the Petrovich (2015) two-planet stability criterion (or orbit crossing) implies eventual planetary ejection on ≲ few-Myr timescales.
    Adopted in Sec. 2.2 and Table 1; partially validated by REBOUND runs but ignores mutual inclinations and higher-multiplicity secular resonances.
  • ad hoc to paper The known exoplanet sample after mass and period cuts is a conservative lower bound on the true wide-orbit multi-planet fraction around WD progenitors.
    Sec. 3 acknowledges severe short-period bias yet still extrapolates to “at least half of all WDs.”

pith-pipeline@v1.1.0-grok45 · 16053 in / 2566 out tokens · 27199 ms · 2026-07-12T07:55:30.828338+00:00 · methodology

0 comments
read the original abstract

Free-Floating Planets (FFPs) are a distinct class of exoplanets that do not orbit stars but are nevertheless found to be very common. A variety of formation mechanisms have been proposed as their origin, such as "star-like" direct collapse from gas and dust clouds or ejection from young planetary systems via dynamical instabilities. Here, another possible formation scenario is explored that would instead apply for old planetary systems, in the form of White Dwarf (WD) formation kicks. Observations over recent years have shown that WDs experience a mild recoil kick during their formation from Asymptotic Giant Branch (AGB) stars. Here we show that, while WD formation kicks directly unbind only $\sim1\%$ of the known planet and exoplanet population, they drive dynamical instabilities in $\gtrsim40\%$ of known long-period multi-planet systems, likely leading to planet ejection and FFP generation in roughly half of all such systems. We also show that FFPs generated via WD kicks will additionally have undergone significant and long-lasting heating via their host stars' enhanced AGB luminosities. Given the low ejection velocities due to the weakness of the WD kicks, such warmed FFPs can thus be associated with their former host stars for several Myr after formation. Therefore, WD formation kicks contribute a distinct, observationally identifiable FFP sub-population comprising a few percent of the Galaxy's FFPs, relevant for the results of the upcoming {\it Roman} Galactic Exoplanet Survey.

Figures

Figures reproduced from arXiv: 2607.02653 by Alexander P. Stephan, Keivan G. Stassun.

Figure 1
Figure 1. Figure 1: Schematic of the Evolution of a Planetary System due to Stellar Mass loss and WD Kicks. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Fraction of Kick-separated Planetary Or [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example Evolution of a 2-Planet System undergoing a WD Kick. Shown is the orbital evolution of the SMAs (upper frame) and eccentricities (lower frame) of a Jupiter-like (red lines) and Saturn-like (blue lines) planet orbiting a solar-type star, as modeled using REBOUND. The orbits are initially nearly coplanar and circular, and are dy￾namically stable. The orbits remain stable throughout the RGB mass loss … view at source ↗
Figure 4
Figure 4. Figure 4: Time Evolution of WD-FFP Projected Dis [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Time Evolution of Fraction of ejected FFPs [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

discussion (0)

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Reference graph

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