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Disc Fragmentation. III. The need for a new paradigm for formation of planets within close binary systems

T0 review · 4 major / 7 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read Gas giants in tight binaries can form by disc fragmentation before the companion star exists, with survival depending sharply on planet mass.

desk verdict Serious hypothesis paper with a new quantitative survival map for planets in tight binaries; the central mass-dependent trend is real in the simulations but rests on an untested accretion/migration split from the authors' own unpublished papers. read the letter →

arxiv 2603.02395 v2 pith:RJINJ5LN submitted 2026-03-02 astro-ph.EP astro-ph.SR

Luyao Zhang , Sergei Nayakshin , Clement Baruteau , Philippe Thebault , Eduard I. Vorobyov This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords planetformationclosebinariesdiscfragmentationgravitationalinstabilityfree-floatingplanetsS-typecircumstellardiscsplanetarymigration
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

Standard planet-formation models assume planets form after their host stars in stable discs, but close binaries truncate discs to only a few au, making classical formation nearly impossible. This paper argues that planet formation and binary formation are simultaneous outcomes of gravitational fragmentation in massive circumstellar discs. As the disc grows, it hatches planetary-mass fragments that migrate inward, while a dominant 'oligarch' fragment accretes in a runaway to become the secondary star, ejecting many low-mass planets. Simulations show that planets above roughly 1–3 Jupiter masses tend to survive as bound 'S-type' planets near the primary, while planets below about 0.1 Jupiter masses are usually ejected as free-floating planets. This offers a natural explanation for the observed scarcity of small planets in tight binaries and predicts that free-floating planets have a steeper mass function than bound planets in binaries.

What carries the argument

The central mechanism is the 'oligarch fragment'—a fragment with mass ≳10 Jupiter masses that accretes gas in a runaway regime and becomes the secondary star. The argument runs on a race: in gravitationally unstable discs, type I migration speed scales roughly as planet mass, so massive planets reach the inner disc quickly, while low-mass planets lag behind and are caught by the oligarch. The Holman–Wiegert stability criterion marks the region where planetary orbits are unstable to ejection.

What would settle it

Measure the mass function of free-floating planets from microlensing surveys and compare it with the mass function of bound planets in tight binaries; if free-floating planets are not more bottom-heavy than bound planets, ejection of low-mass planets by the growing secondary is ruled out as the dominant channel.

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Extended reading notes

Core claim

On the paper's own terms, disc fragmentation can result in the formation of S-type planets in tight binary systems, provided the planets form before the secondary star is born. The branching ratio between survival as an S-type planet and ejection as a free-floating planet is strongly planet-mass dependent: the most massive planets tend to survive because they migrate inward fastest, reaching safe orbits close to the primary before the growing secondary can destabilize them, whereas low-mass planets migrate slowly and are typically ejected.

Load-bearing premise

The model assumes that fragments less than a few Jupiter masses migrate inward much faster than they accrete gas, while heavier fragments accrete in a runaway regime; if low-mass fragments actually accreted gas substantially, the mass-dependent survival trend would not follow.

Editorial extensions

If this is right

  • Explains why dozens of gas giants exist in tight binaries even though the discs are truncated to only a few au.
  • Explains the observed deficiency of low-mass planets (≲0.1 Jupiter masses) in tight binaries compared with gas giants.
  • Predicts that free-floating planets produced by this channel have a steeper (more bottom-heavy) mass function than bound planets in binaries.
  • Provides a formation path for systems such as HD 87646, HD 72892, and HD 41004 without requiring planet formation inside the present, very small circumprimary disc.
  • Suggests that hot Jupiter formation in close binaries is suppressed but not impossible, while wider binaries may promote it through a related fragmentation mechanism.

Reading between the lines

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

  • If this model holds, some hot Jupiters in binaries are effectively 'siblings' of the secondary star, having formed in the same fragmenting disc rather than by core accretion after binary formation.
  • A testable extension would be to run the same simulations with a gas-accretion prescription for low-mass fragments that depends on local disc conditions, instead of neglecting accretion below a few Jupiter masses; this would directly stress the central assumption.
  • The model implies that binary formation itself acts as a mass filter on the planet population, which could be probed statistically by comparing the super-Earth-to-super-Jupiter ratio among free-floating planets and among bound planets in tight binaries.
  • The proposed mechanism may also shape the brown-dwarf-to-planet ratio in binaries, since the oligarch channel preferentially forms massive secondaries while lighter fragments are dispersed.
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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

4 major / 7 minor

Summary. This paper proposes that planets in close binary systems form by gravitational fragmentation of a massive circumstellar disc before the secondary star is born. The authors use 2D FARGO-ADSG simulations: in §4 they present a proof-of-concept run in which the disc fragments ab initio, a planetary fragment migrates inward and survives as an S-type planet, and a more massive 'oligarch' fragment accretes to become the secondary; in §5 they present a 28-run grid in which a secondary seed and a single planet are injected into a non-fragmenting, gravito-turbulent disc. They report that planets with Mp ≳ 1–3 MJ preferentially survive as S-type planets in the resulting tight binary, while lower-mass planets are ejected as FFPs or left as wide P-type planets. They argue this explains the observed deficiency of low-mass planets in tight binaries and predicts that FFPs have a steeper mass function than bound planets in binaries.

Significance. If the result holds, the paper offers a novel and observationally motivated route to form planets in binaries with separations ≲20 au, a regime where core accretion faces severe difficulties. The §4 ab initio run, albeit selected post hoc, demonstrates that the proposed sequence is dynamically possible, and the §5.2 grid is a clean, clearly described parameter study. The authors are also commendably explicit about their assumptions and limitations. The falsifiable predictions — a deficiency of low-mass S-type planets and a steep FFP mass function — are a useful contribution. However, the central mass-dependent survival trend rests on assumptions (iv)–(v) of §2, which are not tested or independently justified within this manuscript, and the statistical basis of the trend is thin (one realization per grid cell).

major comments (4)
  1. [§2, Assumptions (iv)–(v); §5.1, Fig. 6] The central mass-dependent survival trend is substantially imposed by the input assumptions. In §5.1, the 0.3, 1, and 3 MJ planets are explicitly not allowed to accrete gas, while the 10 and 12 MJ objects grow to ~0.1 Msun. The paper explains the trend by t_mig ∝ Mp^-1, but if a low-mass fragment accreted gas and became a few-MJ object before the secondary's migration, it would also migrate rapidly and could survive. The authors cite Nayakshin (2017b) and Papers I–II for this split, but those are not available to the reader (Papers I and II are listed as 'subm. to MNRAS'), and no sensitivity test of the accretion treatment is performed here. Since the observational interpretation (§6.3–6.4) depends directly on this split, the authors should either include runs with gas accretion enabled for low-mass fragments or provide a quantitative justification for neglecting it in these discs.
  2. [§4 and §5.2; Fig. 8] The paper's quantitative claims rest on very limited statistics. The §4 run was 'selected' as the one that produced the tightest binary and an S-type planet, which is a post hoc selection from 'a few such simulations' (the authors state the outcomes are 'quite stochastic' in §3). The §5.2 grid has 28 cells but only one realization per (Mp, Rp) pair. Given the acknowledged stochasticity of planet–secondary encounters, the statement that the branching ratio between S-type survival and FFP ejection is 'strongly planet-mass dependent' (§6.1) would be more convincing with at least a few repeat runs for representative cells (e.g., Rp30_Mp0.1 and Rp30_Mp1.0) or with a quantitative measure of run-to-run variance.
  3. [Abstract and §5.2] The abstract claims that 'survival depends strongly on formation time and mass', but formation time is not varied in the §5.2 grid: the planet and the secondary are injected simultaneously at t = 14 kyr. The only evidence for a formation-time effect comes from the single §4 case (P1 injected at 2.1 kyr, S1 at 3.9 kyr) and the Appendix A mass variations, which do not change injection times. To support the abstract claim, the grid should include a subset of runs in which the planet is injected earlier than the secondary, allowing the planet to migrate inward before the oligarch becomes massive.
  4. [§4, §5.2, §6.1; inner boundary artifacts] The simulations place the inner boundary at R_in = 0.5 au (§4) or 1 au (§5), and the paper repeatedly notes that the final positions of S-type planets are influenced by open-boundary artifacts near R_in. The simulated binary separation is ~14–15 au, not the tightest observed systems such as DMPP-3 (a_bin ≈ 1.2 au) or KOI-1257 (a_bin ≈ 5.3 au), which the paper invokes in §6.2. The authors state that smaller secondary masses would produce tighter binaries but would require a smaller R_in. This means the regime most relevant to the most extreme observed systems is not actually simulated. I request either a subset of runs with a smaller inner boundary (to follow planets to <1 au) or a clearly stated argument for how the current results extrapolate to a_bin ≲ 5 au.
minor comments (7)
  1. [Throughout] The terms 'S-type' and 'P-type' are used without explicit definitions in the text. Please define them at first use (e.g., S-type = planet orbiting one binary component; P-type = circumbinary).
  2. [§1] Typo: 'Assumng' should be 'Assuming'.
  3. [§4, Fig. 2 and Table 1] The paper refers to 'P1', 'S1', and 'P2' before Table 1 is introduced; please ensure the reader can identify these objects at first mention.
  4. [§5.2] In Fig. 8, the caption says 'Blue dots represent the P1 with purple bars indicating eccentricity' — this reads as a typo; presumably it should be 'represent the planets'.
  5. [§6.4] The sentence 'per Mdwarf star' should be 'per M-dwarf star'.
  6. [References] The papers 'Calovic et al. 2025, subm.' and 'Nayakshin et al. 2025, subm.' are load-bearing for assumptions (iv)–(v). If they are not yet published, please provide the arXiv IDs or otherwise make them available to the reader.
  7. [§5.1] The sentence 'Mp = 0.3 MJ planet (or any of the less massive planets that we experimented with)' refers to experiments not shown; the text would benefit from a brief statement about the mass range tested.

Circularity Check

0 steps flagged · score 2.0 of 10

No constructional circularity: survival outcomes are simulated, but key mass-dependent accretion inputs are imported from the authors' own unpublished Papers I/II.

full rationale

The paper's central claim is that a fragmenting circumprimary disc can produce S-type planets in tight binaries and that survival versus ejection is mass dependent. This is the output of explicit FARGO-ADSG simulations (§4 proof-of-concept, §5.2 grid), not a fit or an equation restatement. The mass-dependent trend is explained dynamically: type I migration is faster for more massive planets, so they reach the inner region before the oligarch/secondary destabilizes them; low-mass planets migrate slowly and are ejected. This causal chain is not equivalent to the inputs by construction. The load-bearing inputs (iv) and (v) — that low-mass fragments do not accrete gas while ≳10 M_J fragments undergo runaway accretion — are assumptions taken from the same authors' unpublished Papers I/II and Nayakshin (2017b), and the low-accretion prescription is not independently tested in this paper. If those assumptions are wrong, the conclusions could change, but that is a scientific risk and not a circular reduction. The paper itself qualifies its result as 'under the assumptions spelled out in §2' and acknowledges numerical boundary artefacts and the need for future work. No specific circular step (e.g., Eq X = Eq Y by construction, or a fitted parameter renamed as a prediction) can be exhibited. Score 2 reflects the presence of load-bearing self-citations; the derivation itself is not circular.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The model rests on a set of explicit idealized initial conditions and on self-cited assumptions about fragment migration and accretion. No free parameters are fitted to the observed planet population, but the central survival trend is essentially selected by the assumed mass-dependent migration rates and by the chosen injection masses/radii.

free parameters (8)
  • Mass deposition rate and radius (Mdot_dep, R_dep) = 3e-5 Msun/yr at 100 au (§4); 1e-5 Msun/yr at 50 au (§5)
    Chosen by hand to make the disc fragment (§4) or remain gravito-turbulent (§5); sets the growth/fragmentation timescale.
  • Initial surface density profile (Σ0, Rcut, R0) = Σ0 = 2.5e-6 or 5e-5 Msun/au^2; Rcut = 150 or 100 au; R0 = 100 au
    Initial disc mass and distribution are model inputs selected to achieve the desired disc state.
  • Infall specific angular momentum factor j_dep = 0.7 (G M* R)^(1/2)
    Ad hoc factor chosen to mimic cloud collapse; authors say it affects location/timing of fragmentation but not main results.
  • Planet mass grid and injection radii (Mp, Rp) = Mp = 0.1, 0.3, 1, 3 MJ; Rp = 10, 20, 30, 40, 50, 75, 90 au
    The central mass-dependence result is defined by these chosen masses and radii.
  • Oligarch initial mass and radius = Ms = 12 MJ at 60 au (§5); Ms = 5 MJ at 16 au (§4)
    The secondary seed mass and location determine binary separation and ejection efficiency.
  • Secondary accretion efficiency f_acc = 0.1
    Sets the rate at which the secondary consumes gas in its Hill sphere; authors note it changes secondary mass but not conclusions.
  • Gravitational softening parameter ε_s = 0.5 H
    Softening length for sink particles; affects close encounters and scattering outcomes.
  • Disc viscosity and equation-of-state parameters (α, γ) = α = 0; γ = 1.4
    Idealized choices; artificial viscosity is relied on to capture GI turbulence, and a fixed adiabatic index is used.
assumptions (6)
  • domain assumption A single protostar forms first and is surrounded by a massive circumstellar disc that continues to gain mass from the parent cloud for ~0.1-0.3 Myr.
    Section 2(i); standard picture of cloud collapse and disc growth, adopted as the starting point.
  • domain assumption Disc fragmentation occurs at radii of tens to hundreds of au and produces a broad mass spectrum of gaseous fragments.
    Section 2(iii), following Rafikov 2005, Clarke 2009, etc.; external established result.
  • ad hoc to paper Low-mass fragments (< a few MJ) migrate inward much faster than they accrete gas, so gas accretion on them is neglected.
    Section 2(iv); taken from Papers I/II and Nayakshin 2017b. This is the load-bearing migration/accretion assumption behind the survival trend.
  • ad hoc to paper Fragments with mass ≳10 MJ accrete gas in a runaway regime and become the secondary star (the 'oligarch').
    Section 2(v); based on the same self-cited simulation program; central to binary formation in the model.
  • ad hoc to paper Most fragments formed by disc fragmentation are low-mass (planetary), while oligarchs are rarer and more massive because they form at larger radii where the Toomre mass is larger or via mergers.
    Section 2(vi); needed to have both planets and a secondary present in the same disc.
  • domain assumption Type I migration in gravito-turbulent discs makes more massive planets migrate inward faster (t_mig ∝ M_p^{-1}).
    Section 5.1 and Fig. 6; standard type I migration result (Baruteau et al. 2011), but it largely forces the mass-dependent survival outcome.

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Cite this review

Pith. "Pith review of Disc Fragmentation. III. The need for a new paradigm for formation of planets within close binary systems." pith.science (2026). https://pith.science/paper/RJINJ5LN

@misc{pith2026260302395,
  author       = {Pith},
  title        = {Pith review of: Disc Fragmentation. III. The need for a new paradigm for formation of planets within close binary systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RJINJ5LN}},
  note         = {Machine review of arXiv:2603.02395}
}
abstract

Dozens of planets and brown dwarfs are known to orbit one component of tight stellar binaries ($a_{\rm bin} \lesssim 20$ au), despite circumstellar discs in such systems being truncated to radii of only $\sim (0.2-5)$ au. This presents a challenge to classical planet formation models, which assume planets form after their host stars within stable discs. We propose instead that planet formation and binary formation are concurrent outcomes of gravitational fragmentation in massive circumstellar discs. In this scenario, rapid disc growth driven by infall from the parent molecular cloud leads to fragmentation at radii of tens of au, producing planetary-mass objects that migrate inward. Continued disc growth produces a dominant "oligarch" fragment that undergoes accretion runaway to become the secondary star. During this process, dynamical interactions eject many lower-mass planets, producing free-floating planets (FFPs), while others survive if they migrate sufficiently close to the primary star before destabilisation. Using numerical simulations, we show that survival depends strongly on formation time and mass. Planets formed early and those with masses $> 1-3M_j$ are preferentially retained, whereas lower-mass planets ($<0.1M_j$) are typically ejected. This mechanism naturally explains why low-mass planets are more deficient in tight binaries than gas giants, and predicts that FFPs have a steeper mass function than bound planets within binaries.

Figures

Figures reproduced from arXiv: 2603.02395 by the authors.

Figure 1
Figure 1. Schematic illustration of the model. (a) Several planets (the smaller blue circles) and the secondary seed (”oligarch”, the larger brown circle) are born at ∼ 50 − 100 au disc of the circum￾primary disc. The innermost planet has migrated the deepest be￾cause it had been born first and/or it is more massive than the other planets. (b) The oligarch begins its rapid inward migration, while also gaining mass rapidly by … view at source ↗
Figure 2
Figure 2. The density for the disc at different times. White dots with black edges indicate the inserted objects. Panels: t = 2.1 kyr, the insertion of planet P1 in the clump; t = 3.2 kyr, P1 decouples from the disrupted clump and migrates inward; t = 3.9 kyr, the secondary S1 is inserted into a massive and dense clump that migrated to R ≈ 16 au, whereas low mass planet P2 is inserted in a dense filament. selected a particula… view at source ↗
Figure 3
Figure 3. Left: Time evolution of the secondary’s orbital radius and mass. The left y-axis shows the orbital radius (blue curve), while the right y-axis shows the secondary mass (red curve). Right: Orbital radii of the secondary and planets in the simulation. The grey shaded region indicates the radially unstable range according to the criterion of Holman & Wiegert (1999). The grey dotted line marks t = 3.9 kyr, when the seco… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Surface density field of the disc at t = 5.2 kyr. Note that the figure is centred on the secondary. The primary star is towards the top left corner of the figure, inside the (white) inner boundary region. The white dashed lines trace the trajectories of S1 and P2 in th…
Figure 5
Figure 5. Figure 5: The Toomre Q-parameter field for the relaxed disc at t = 14 kyr. gravitating discs (Baruteau et al. 2011; Malik et al. 2015), and therefore they migrate in a type-I like (Crida et al. 2006) regime. In this regime, the migration timescale scales approx￾imately as tmig ∝…
Figure 6
Figure 6. Figure 6: Left: Evolution of the orbital radius for the secondary object with masses Mp = 0.3, 1, 3, 10, 12 MJ. Right: Evolution of the object mass and radius in the mass-radius plane for the simulations shown on the left. The crosses on the solid curves mark the time of 19 kyr.…
Figure 7
Figure 7. Figure 7: The azimuthally averaged disc surface density for sim￾ulations with Mp = 1 MJ at t = 14, 16, 17, 19 kyr. suffiently massive to eject the planets. At the same time, by the time it gains sufficient mass to eject the outer planets, they are too far away from it to eject t…
Figure 8
Figure 8. Figure 8: Census of simulated planet-hosting binaries. The y-axis lists simulations labeled as ‘Rp(initial planet radius in au) Mp(initial planet mass in MJ)’. Blue dots represent the P1 with purple bars indicating eccentricity, while yellow dots represent the secondary companio…
Figure 9
Figure 9. Figure 9: Evolution of the orbital radius for three cases from [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

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Forward citations

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