Dynamical formation of long-period exoplanets systems in evolving binary stars

Diogo Belloni; Eder Martioli; Ernesto Vieira; Isabel J. Lima; Rafael R. Sousa; Rosana A. N. Ara\'ujo; Silvia M. Giuliatti Winter

REVIEW 5 major objections 5 minor 269 references

Dynamical formation of long-period exoplanets systems in evolving binary stars

T0 review · 5 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Long-period giant exoplanets can be produced by the coupled action of a binary companion and the host star's post-main-sequence mass loss, which pushes survivors outward and concentrates them inside roughly 50 au.

desk verdict The evolved-vs-control experiment is the right design and the direction is robust, but the headline claim rests on one binary architecture and the statistics are under-documented. read the letter →

arxiv 2607.19118 v1 pith:LP3MTDQ4 submitted 2026-07-21 astro-ph.EP

Isabel J. Lima , Rafael R. Sousa , Silvia M. Giuliatti Winter , Diogo Belloni , Ernesto Vieira , Rosana A. N. Araújo , Eder Martioli This is my paper · ORCID

classification astro-ph.EP

keywords long-periodexoplanetswidebinarystarspost-main-sequencestellarevolutionplanetarydynamicswhitedwarfsystemsplanetejectionN-bodysimulationsgiantplanets

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 is trying to establish that long-period giant exoplanets — planets on orbits wider than about 5 au, a population that is hard to detect and sparse in current surveys — can be produced dynamically as their host star ages. Using N-body simulations of a wide binary in which the 2-solar-mass primary evolves from the main sequence to a white dwarf, it shows that post-main-sequence mass loss destabilizes multi-planet systems, raising ejection rates in every configuration tested. The survivors are pushed outward: Jupiter-like planets end up mostly between 15 and 30 au, Saturn-like planets between 20 and 40 au, and lower-mass planets out to about 50 au. Comparing with an evolved single star, the paper finds that the binary companion makes the instability worse and concentrates the surviving planets inside roughly 50 au. If correct, this gives a formation route for wide-orbit giants that does not require in situ formation or planet-planet scattering alone.

What carries the argument

The mechanism that carries the argument is adiabatic orbital expansion caused by stellar mass loss, combined with secular perturbations from the secondary star. As the primary sheds most of its envelope, the gravitational potential weakens and every orbit — binary and planetary — widens by the same inverse-mass scaling; the binary separation grows from 100 to 202 au, and a single Jupiter analog drifts from 5 to about 13 au. In multi-planet systems this expansion changes period ratios and eccentricity structure that had protected the resonant 3:2 chain, re-triggering close encounters and ejections. The secondary star's continued perturbations make the instability stronger and, in the evolved

What would settle it

Rerun the same ensemble with binary separations of 50 au and 300 au and with planets initially spaced at 10–20 Hill radii; if the ejection-rate boost and the 15–50 au survivor distribution do not persist, the mechanism is specific to the chosen architecture. Observationally, a survey of giant planets around white dwarfs in wide binaries that finds no concentration in the 15–50 au range would falsify the predicted pile-up.

Watch

Extended reading notes

Core claim

The central discovery is that post-main-sequence mass loss is not a passive background in wide binaries: it destabilizes multi-planet systems that would otherwise remain stable. In a simulated binary with a 2-solar-mass primary evolving to a white dwarf and a 0.8-solar-mass companion at 100 au, a Jupiter-Saturn pair at 5 and 6.55 au in 3:2 resonance plus ice-giant-mass planets shows higher ejection rates when stellar evolution is included (0.44 vs 0.12 in the simplest system). Survivors end up on wider orbits — Jupiter-like planets mostly 15–30 au, Saturn-like 20–40 au, lower-mass planets out to ~50 au — and the binary companion concentrates these survivors within ~50 au, whereas an evolved

Load-bearing premise

The quantitative conclusions rest on a single hand-picked starting point — a 2 and 0.8 solar-mass binary at 100 au with circular orbit, and a planetary system packed with Jupiter at 5 au, Saturn at 6.55 au in 3:2 resonance, and additional planets at 5–10 Hill radii — and are not demonstrated to survive variation of those initial conditions.

Editorial extensions

If this is right

Systems that are dynamically stable on the main sequence do not necessarily stay stable: when stellar evolution is included, only one of the nine configurations retained a fully stable system, versus 151 in the non-evolving controls.
Ejection, not merger, dominates the instability: merge rates stay at 1–2%, while ejection rates rise substantially, so the typical outcome of mass-loss-triggered instability is a lost planet, not a collision.
Surviving Jupiter-like planets should be found at 15–50 au with low-to-moderate eccentricity (below about 0.3), filling the currently under-sampled long-period giant region.
Lower-mass planets (super-Earth and ice-giant analogs) are the most vulnerable; their survival rate is lowest and their final orbits are the broadest, so evolved binary systems should be preferentially depleted in these planets.
The binary companion, not the mass loss alone, sets the final confinement: an evolved single star leaves survivors scattered to distances up to about 4,000 au, while the evolved binary keeps them inside about 50 au.

Reading between the lines

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

Because only one binary architecture (2 and 0.8 solar masses, 100 au, circular) is simulated, the specific 50 au confinement radius is not yet a robust prediction for the whole wide-binary population; varying binary separation and eccentricity in the same setup could either confirm or erase it.
The same adiabatic-expansion logic implies that planets initially inside a few au — not included here — would also be carried outward, but they would first have to survive the red-giant envelope; systems with close-in giants might therefore show a signature of engulfment rather than outward migration.
A testable extension: direct-imaging surveys of white dwarfs in wide binaries should find a pile-up of giant planets at 15–50 au with moderate eccentricities; if such surveys instead find planets at much wider separations, the initial condition of 5–10 Hill-radii packing would need revision.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Read it. Short version: the core experiment is sound and the evolved-vs-control comparison is the right way to isolate mass-loss effects, but the paper overstates what one binary architecture can establish, and the reporting of the rates is too thin to take them at face value.

What's new: this is a legitimate extension of Baronett et al. (2022) and Xing et al. (2025) to S-type multi-planet systems around a wide evolving binary. The individual ingredients—stellar mass loss expands orbits, a companion destabilizes the system—are known, but the quantitative survivor distributions across nine planet configurations and the secondary-star concentration result are new. I buy the direction: ejection rates rise when the primary loses mass, surviving Jupiter-likes move out to 15–50 au, and the companion adds a clear destabilizing effect. The qualitative comparison with observed long-period giants is appropriate at this stage.

Soft spots, in rough order of importance. First, one binary point. All simulations use a single architecture: 100 au, e=0, 2+0.8 Msun. The abstract's "direct consequence" and the Sec. 4.3 claim that the secondary concentrates survivors within 50 au are population-level statements derived from one point in binary-parameter space. S-type stability zones depend strongly on separation, eccentricity, and mass ratio; without at least a small grid, the general claim is underdetermined. This is a generalization gap, not an internal contradiction—the evolved-vs-control design is fine, but it is not yet a population study. Second, the statistics are under-reported. Table 3 has no error bars; the total of 8,400 planets implies 100 realizations per tag, but that is never stated. Early-ejected planets are excluded before 100 timesteps, which would bias absolute rates; the bias partly cancels in the evolved-vs-control comparison because early dynamics are identical, but it should be documented. Third, the analytical check in Fig. 3 uses Eq. 1, which is written for a circumbinary planet. For an S-type planet orbiting the primary, the relevant mass is M1, not M1+M2, so the claimed agreement is suspect. This is not load-bearing, but it is sloppy and should be fixed.

Bottom line: the central result holds up in direction and the paper deserves a serious referee. I would not desk-reject; I would ask for a binary-parameter variation, transparent sample sizes and error bars, and softer causal language. No code or data are provided, which also needs to be addressed in this day and age.

Referee Report

5 major / 5 minor

Summary. The manuscript couples a MESA stellar-evolution track of a 2 Msun primary (with a 0.8 Msun companion at 100 au, e=0, Z=0.02) to REBOUND N-body integrations of S-type multi-planet systems, and compares them with non-evolving controls. It reports that stellar evolution raises planetary ejection rates for all nine initial planet configurations, broadens the surviving semi-major-axis distributions of Jupiter/Saturn-like planets to roughly 15-50 au, and, from an additional set of 1,000 single-star vs binary simulations for the 19-60 configuration, that the secondary star makes systems more unstable and concentrates survivors within about 50 au. The paper concludes that long-period giant exoplanets may be a direct consequence of the coupled effects of binary dynamics and post-main-sequence stellar mass loss.

Significance. If the conclusions were robust, the paper would provide a concrete late-stage dynamical pathway for forming long-period giant planets and make a falsifiable prediction about the orbital architecture of survivors around white dwarfs in wide binaries. The design has real strengths: it uses independent, standard tools (MESA tracks and REBOUND/IAS15), isolates the effect of stellar evolution by comparing evolved and non-evolved controls, and does not fit any quantity to the observed sample shown in Fig. 10. The direction of the evolved-vs-control effect (higher ejection, outward broadening) is internally consistent. However, the population-level claim rests on a single binary architecture and one prescribed initial planet packing, and several statistical and methodological details are not reported. The quantitative central claim is therefore not yet established at the level claimed in the abstract.

major comments (5)

[Sec. 2, Table 1; Sec. 4.3, Fig. 9] All simulations use a single binary configuration: a=100 au, e=0, M1=2 Msun, M2=0.8 Msun, Z=0.02 (Table 1), and the nine planet configurations in Table 2 also share the same initial binary. The abstract and Sec. 4.3 conclude that long-period giants may be a 'direct consequence' of binary dynamics plus mass loss and that the secondary 'concentrated the survivors within 50 au'. With one point in binary-parameter space, these population-level statements are underdetermined; the S-type stability boundary and the amplitude of the companion's secular perturbations depend strongly on a_bin, e_bin and mass ratio (Holman & Wiegert 1999). A grid over a_bin (e.g., 30-1000 au) and e_bin, or at least an explicit argument that 100 au/e=0 is representative of the relevant wide-binary population, is needed before the conclusion can be stated in this form.
[Sec. 3.3, Table 2; Sec. 4.2, Table 3] The nine configurations vary only the number and mass of low-mass 'other' planets. Jupiter-like and Saturn-like planets are always initialized at 5.0 au and 6.55 au in the same 3:2 mean-motion resonance, with e=0. Since the paper's headline population is long-period giant planets, the instability rates and final-a distributions of Jupiter/Saturn-like planets are sensitive to this chosen spacing and resonance. Without varying the giant-planet architecture (period ratios, presence of the 3:2 resonance, number of giants), the quantitative conclusions, especially the 'direct consequence' claim, are conditional on one packing prescription.
[Table 3; Sec. 4.2] The ejection and merge rates are quoted without error bars or sample sizes. Summing the implied planet counts per configuration (3, 4, 6, 6, 6, 11, 11, 16, 21 planets) gives 84 planets per realization, so the stated total of 8,400 corresponds to 100 realizations per tag, but this is never stated. With N=100, the uncertainty on a rate of 0.5 is about ±0.05, so differences such as 0.88 vs 0.83 for 19-60 are not statistically distinguishable. Please report N, confidence intervals or raw counts, and the test used to support the claim of a consistent trend across all configurations.
[Eq. (1), Fig. 3; Sec. 3.2] Equation (1) uses the total binary masses and is the standard adiabatic expression for a circumbinary test particle. The simulated planets are on S-type orbits around the primary; at lowest order the adiabatic response to primary mass loss is a_f ≈ a_i M1,i/M1,f, with the companion entering as a perturbing potential rather than as part of the central mass. The factor of ~2.6 in Fig. 3 (5 au to 13 au) lies between the primary-only (3.45) and total-mass (2.03) predictions, so the claimed agreement with the magenta curve is not self-evident. Please derive the applicable S-type expression or show explicitly why Eq. (1) applies; otherwise the validation of the interpolation method in Fig. 3 is not justified.
[Captions to Figs. 4 and 5; Sec. 4.1] The manuscript states that planets ejected before a 100-timestep are 'excluded from the simulations' and not shown. Because the initial configurations are deliberately compact and unstable, this cut could remove a substantial fraction of the sample before the evolved/control comparison begins, and the ejection rates in Table 3 and survivor counts in Sec. 4.2 are then not defined over the full initial ensemble. Please quantify how many planets are removed by this criterion and verify that the evolved-control differences are not driven by it. Since the two branches are nearly identical in the first ~100 timesteps, any early-ejection asymmetry in the random draws could bias the comparison.

minor comments (5)

[Table 3, row 2-45] The entry '0.56−0.28 0.01' appears to have a corrupted separator; it is unclear whether the intended evolved/non-evolved ejection rates are 0.56/0.28 and what the corresponding merge rates are. Please reformat.
[Abstract; Sec. 1] The repeated 'Although' at the start of consecutive sentences and the phrase 'we propose that their formation pathways are robust' should be rewritten for clarity. The term 'long-period' is defined as a≥5 au in the introduction but used inconsistently elsewhere.
[Sec. 3.2] The sentence 'The winds and this planetary nebulae originating from the evolution of the primary are not considered here' has a grammar error, and it should be clarified whether the planetary-nebula mass-loss episode is included in the MESA track or removed by the envelope cut-off.
[Sec. 4.2.1; Fig. 6] The text refers to 'simulations with 10 and 20 bodies' and 'with 2 and 3 exoplanets survived with masses of 15 M⊕'; these do not map cleanly to the tags in Table 2. Please align the nomenclature with the simulation tags.
[Footnote 4; Fig. 10] The footnote conflates the NASA Exoplanet Archive (exoplanetarchive.ipac.caltech.edu) with exoplanet.eu. Please provide the correct catalog and a version/data reference for the observed sample used in Fig. 10.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: evolved-binary outcomes are genuine N-body outputs against non-evolved controls.

full rationale

No specific circular step is present. The stellar mass-loss history comes from MESA (Section 2, Table 1) and is interpolated into REBOUND (Section 3.1); the reported ejection/merge rates (Table 3) and final a/e/i distributions (Figs. 6-8) are outputs of the N-body integrations, not quantities fitted to the observed exoplanet catalog used in Fig. 10, which is only a qualitative comparison. Equation (1) is a known adiabatic mass-loss scaling used as a consistency check for the N-body orbital expansion (Section 3.2), not as the source of the paper's main conclusions. The self-citations to Belloni et al. (2024) for the MESA setup (Section 2) state explicit modeling assumptions; they do not supply the central claim, and the key comparisons are controlled (evolved vs non-evolved; binary vs single-star in Section 4.3). The manuscript's own limitation that "Exoplanets ejected before a 100-timestep are excluded from the simulation and it is not shown here" (Figs. 4 and 5 captions) affects evolved and control arms equally, since significant mass loss begins only near t≈1.37 Gyr, so it is a completeness caveat rather than a circular step. The main weakness is external validity: only one binary architecture (a=100 au, e=0, 2+0.8 M_sun) is explored, so the population-level "direct consequence" and "within 50 au" statements are underdetermined, but that is a generalization gap, not internal circularity.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

All listed parameters are hand-set inputs; none are fitted to the observational data in Fig. 10. The central claims are conditional on these choices.

free parameters (7)

Primary initial mass = 2 M_sun
Sets the evolutionary clock and the amount of mass lost (final ~0.58 M_sun).
Secondary mass = 0.8 M_sun
Controls the perturbation strength; no variation across runs.
Binary initial separation and eccentricity = 100 au, e=0
Wide-binary regime; final a grows to 202 au. Single configuration only.
Metallicity = Z=0.02
Solar composition; affects MESA track and mass-loss timing.
Reimers/Blocker wind efficiencies = 0.1 and 0.02
Calibrated from literature, not from this system; sets AGB mass-loss rate.
Initial planet architecture = Jupiter at 5 au, Saturn at 6.55 au 3:2 MMR; additional planets at 5-10 Hill radii; masses per Table 2
The packing of the initial system is the main driver of early instability; results are conditional on these choices.
Planet removal radius = 1 au; e>1
Defines 'lost'; no tidal model or WD engulfment radius used.

assumptions (6)

domain assumption Newtonian point-mass N-body dynamics (IAS15) with no tides or spin evolution captures the relevant orbital evolution.
REBOUND treats stars/planets as point masses; tidal interactions, stellar spin, and non-gravitational effects are neglected. Sec 3.
domain assumption Stellar mass loss is slow and isotropic; the planet's mass is unchanged and Eq. 1 gives the expected orbital response.
Used in Sec 3.2 and in the interpretation of orbital expansion; during AGB thermal pulses the mass loss is episodic, and wind accretion onto the secondary is approximated, not resolved.
ad hoc to paper Planets are fully formed at t=0 with specified masses and orbits; no gas disk or planet formation is modeled.
Abstract/Conclusions claim 'formation pathways are robust', but the simulations skip planet formation and begin after disk dissipation (Sec 3.3).
ad hoc to paper The single MESA binary track (2 M_sun + 0.8 M_sun, 100 au, Z=0.02, e=0) is representative of wide binaries hosting long-period planets.
No variation of binary separation, eccentricity, mass ratio, or metallicity; Sec 4.3 generalizes from this one configuration to a population statement.
domain assumption Removing planets with a<1 au or e>1 is a valid proxy for planet loss.
Section 3 states planets are removed under these conditions. For a final WD radius ~0.013 R_sun, 1 au is not an engulfment radius, and eccentric orbits can be temporarily hyperbolic in osculating elements; this choice may misclassify some survivors.
ad hoc to paper Eq. 1 (a_f=a_i(M1,i+M2,i)/(M1,f+M2,f)) applies to an S-type planet around the primary.
Sec 3.2 uses this P-type scaling. It predicts 10.1 au for a 5 au planet given stated masses, while the N-body run reaches ~13 au; the claimed alignment is not quantitative.

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Cite this review

Pith. "Pith review of Dynamical formation of long-period exoplanets systems in evolving binary stars." pith.science (2026). https://pith.science/paper/LP3MTDQ4

@misc{pith2026260719118,
  author       = {Pith},
  title        = {Pith review of: Dynamical formation of long-period exoplanets systems in evolving binary stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LP3MTDQ4}},
  note         = {Machine review of arXiv:2607.19118}
}

read the original abstract

The dynamical formation and evolution of long-period giant exoplanets have not been well constrained due to the few observational parameters. In this study, we explore the dynamical effects in a multi-planetary system around one star of an evolving wide binary system. We used an interpolated result of a MESA stellar evolution inside REBOUND N-body integrations to perform simulations with a range of distinct planetary masses in a circumstellar configuration (S-type orbit), centered on a primary star that evolves from the main sequence star to a white dwarf. Control simulations without stellar evolution were performed to isolate the effects of mass loss. Although few exoplanets are currently known to possess long-period and moderate eccentricities, we investigated the evolution mechanisms of long-period gas giants within this specific regime. Although these exoplanets often remain undetected due to their wide orbits and long periods, we propose that their formation pathways are robust throughout the evolution of binary systems. We also simulated an evolved single star in a multi-planetary system and concluded that the secondary star made the exoplanets more unstable and concentrated the survivors within a semi-major axis of 50 au.

Figures

Figures reproduced from arXiv: 2607.19118 by the authors.

**Figure 1.** Evolution of the primary star obtained with the MESA code from the ZAMS to the white dwarf in the HR diagram. The track is color coded according to the mass. The mass loss starts being significant during the AGB phase, dropping to ∼ 0.58 M⊙. The orange line indicates the post-AGB phase to white dwarf. We allowed both stars in the binary to eventually synchronize with the orbit due to tidal interaction. The Roche-lo… view at source ↗

**Figure 2.** shows the masses of the two stars as a function of time, obtained from MESA simulations. The primary star has an initial mass and radius of 2 M⊙ and 1.65 R⊙, respectively, and evolves into a white dwarf with a final mass and radius of ∼ 0.58 M⊙ and ∼ 0.013 R⊙. The secondary star remains in the main sequence with a mass of 0.8 M⊙ and a radius of ∼ 0.7 R⊙. The initial semi-major axis of the binary system is 100 au, … view at source ↗

**Figure 3.** Time evolution of the orbital elements in a binary system hosting a Jupiter-like planet initially placed at 5 au. The blue lines correspond to the N-body simulation data, the black dashed line represents the MESA-predicted orbit of the secondary star. The inclination and eccentricity of the secondary are initially set to zero. Top: Semi-major axis evolution (in au) for the secondary star and the Jupiter-like plane… view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Temporal evolution of the planet’s periapsis (q), semi-major axes (a), and apoapsis (Q) plotted together for each planet in evolved binary simulations. The inclination and eccentricity of the secondary are set to zero. Panels (a), (b), (c), and (d) show the simulations…

**Figure 5.** Figure 5: Temporal evolution of the planet’s periapsis (q), semi-major axes (a), and apoapsis (Q) plotted together for each planet in non-evolved binary simulations corresponding to the same simulations in [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 6.** Figure 6: Cumulative normalized distributions of the semi-major axis for surviving Jupiter-like, Saturn-like, and other planets simulated for different planetary systems (see [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: Cumulative normalized distributions of eccentricity for Jupiter-like, Saturn-like, and other planets simulated for different planetary systems (see [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

**Figure 8.** Figure 8: Cumulative normalized distributions of inclination for Jupiter-like, Saturn-like, and other planets simulated for different planetary systems (see [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

**Figure 9.** Figure 9: Histograms showing the distributions of the semi-major axis of the surviving exoplanets. The color red represents Jupiter-like planet, the color blue represents Saturn-like planet, and color gray represents other planets with masses similar to Neptune and Uranus. Panel…

**Figure 10.** Figure 10: Currently known exoplanets plotted as a function of semi-major axis and planetary mass. The color coding indicates the orbital eccentricity. Circle symbols indicate exoplanets in single stars with no white dwarf stars, the pentagram symbols indicate exoplanets in bina…

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Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.

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