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REVIEW 3 major objections 5 minor 61 references

Fine-Tuned Supernova or Failed Explosion? Decoding the Origins of the G3425 Binary

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The nearly circular orbit of G3425 points to a failed supernova and a 4 to 4.4 solar-mass black hole.

desk verdict A clean dynamical case against a normal SN for G3425, but the 'most likely failed SN' conclusion skips the prior on rates and the kick distribution. read the letter →

arxiv 2506.20386 v1 pith:HKOKF4YX submitted 2025-06-25 astro-ph.SR astro-ph.HE

Zsolt Regaly , Viktoria Frohlich , Jozsef Vinko This is my paper · ORCID
classification astro-ph.SRastro-ph.HE
keywords G3425mass-gapblackholefailedsupernovavariable-masstwo-bodyproblembinaryeccentricitystripped-envelopenatalkickwideevolution
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 asks how the wide binary G3425—a red giant with a massive unseen companion on a nearly circular orbit—came to be, since a supernova that removes most of the primary's mass should normally leave the companion on a wider, more eccentric orbit or unbind it entirely. Applying the variable-mass two-body problem, it finds that ordinary type II supernovae cannot produce the observed eccentricity of $0.05 \pm 0.01$, and that a stripped-envelope SN Ib/c can do so only if the explosion happened within a few degrees of the companion's apocenter, a fine-tuning with probability at most about 10 percent. A failed supernova, which ejects essentially no mass and leaves a black hole, requires no such fine-tuning because the binary simply inherits its pre-explosion orbit. The paper therefore concludes that the unseen component is most probably a mass-gap black hole with mass between about 4 and 4.4 solar masses, and that the same reasoning can be applied to any wide, nearly circular binary with a dark companion.

What carries the argument

The carrying object is the analytical solution of the instantaneous variable-mass two-body problem: closed-form expressions for the post-explosion semi-major axis $a_1$ and eccentricity $e_1$ in terms of the initial total mass $\mu_0$, the post-explosion total mass $\mu_1$, the initial eccentricity $e_0$, and the true anomaly $\nu_0$ (the companion's angular position along its ellipse). The critical identity is the apocenter circularization condition, $e_0=(\mu_0-\mu_1)/\mu_0$, which converts a measured near-zero eccentricity into a constraint on how much mass the primary lost and where the companion was when it exploded. A numerical homologous-envelope expansion model, with ejecta speeds of $6{,}000$-$30{,}000$ km s$^{-1}$, checks the instantaneous approximation and also tracks the growth of the semi-major axis and possible mass loss from the secondary. Together these tools map each supernova type onto an allowed region of progenitor mass and orbital phase, which is what separates the fine-tuned SN Ib/c channel from the unconstrained failed-SN channel.

What would settle it

Measure the unseen component's mass directly by combining radial velocities and astrometry; if it comes out below about 4 solar masses or above 4.4, or if the system's space velocity shows a natal kick of more than a few km/s relative to the local stellar population, the failed-supernova no-kick explanation is ruled out. A statistically robust census showing that failed supernovae make up only a few percent of core collapses would also overturn the likelihood ranking.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the nearly circular orbit of G3425 selects a failed supernova as the formation channel. For instantaneous mass loss from the primary, the post-explosion eccentricity $e_1$ is a function of the initial eccentricity $e_0$, the pre- and post-explosion total masses $\mu_0$ and $\mu_1$, and the companion's true anomaly $\nu_0$ at the moment of explosion. Circularization ($e_1 = 0$) at apocenter requires $e_0 = (\mu_0-\mu_1)/\mu_0$. Type II progenitors (8-30 $M_\odot$) would need high initial eccentricities whose pericenters fall inside the $\sim 500\,R_\odot$ progenitor envelope, so the companion would be engulfed; SN Ib/c progenitors (5-10 $M_\odot$) match the observed $e = 0.05\pm0.01$ only when $\nu_0 \approx 180^\circ \pm 5^\circ$ to $\pm15^\circ$, which carries at most a $\sim 10\%$ probability. Failed supernovae, by contrast, eject no mass, so the remnant inherits the pre-explosion orbit unchanged; the only requirements are a progenitor mass in the range $3.48$-$4.4\,M_\odot$ and an initial eccentricity already equal to the observed one. This is why the paper proposes a mass-gap black hole of $4$-$4.4\,M_\odot$ as the most probable identity of the unseen component.

Load-bearing premise

The scenario ranking assumes, without an explicit prior, that failed supernovae are not intrinsically much rarer than normal core-collapse supernovae and that the black hole received no natal kick; if either assumption fails, the fine-tuned stripped-envelope supernova channel becomes competitively probable.

Editorial extensions

If this is right

  • If the identification holds, G3425 becomes a directly measured example of a roughly 4 solar-mass black hole produced by a failed supernova, anchoring the low-mass end of black-hole birth masses.
  • Because the apocenter timing needed for an SN Ib/c is a roughly 10 percent geometric fine-tune while a failed SN needs none, wide nearly circular binaries with unseen companions can be used to estimate how often core collapses fail.
  • Type II supernova progenitors are excluded as formation channels for such systems even without observing the explosion, since their required initial eccentricities would place the companion inside the progenitor envelope.
  • The same analytic condition, $e_0=(\mu_0-\mu_1)/\mu_0$, can be applied to any other wide, nearly circular post-supernova binary to recover its pre-explosion eccentricity and progenitor mass.

Reading between the lines

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

  • If failed supernovae turn out to be intrinsically rare, the likelihood ranking could invert: a roughly 10 percent apocenter coincidence in an SN Ib/c might be more probable than a rare failed event, so the mass-gap conclusion should be re-tested with measured failed-SN statistics.
  • A natal kick of even a few km/s would break the no-mass-loss inheritance; a precise space-velocity measurement of G3425 relative to its local stellar population could therefore rule the failed-SN scenario in or out.
  • A systematic search for wide, nearly circular binaries with dark companions could test the paper's prediction that most such systems host low-mass black holes rather than neutron stars.
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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

3 major / 5 minor

Summary. The paper studies the formation of the wide binary G3425 (P ≈ 877 d, e = 0.05 ± 0.01), whose unseen component has a mass of 2.9–4.4 M☉, by modeling the orbital response to the supernova that formed it. Using an instantaneous mass-loss solution of the two-body problem (Appendix A) and a homologous-expansion numerical model (Appendix B), the authors show that any mass-losing SN channel can reproduce the near-circular remnant orbit only if the explosion occurred near apocenter. They argue that SN II channels are excluded because the required initial eccentricity (e0 ≳ 0.4) puts the secondary inside the 500–1500 R☉ progenitor at pericenter; that SN Ib/c is possible but requires a fine-tuned near-apocenter explosion, with a geometric probability ≲ 10% (Appendix C); and that a failed SN with no mass ejection requires no such fine-tuning. They conclude that the failed-SN channel is the most likely origin and that the unseen component is a mass-gap black hole of 4–4.4 M☉.

Significance. The dynamical core of the paper is worth publishing once corrected. The derivation in Appendix A is explicit and checkable; the eccentricity equation (2) and the circularization condition (3) are correct, and the numerical model is validated against the analytical solution at high ejecta velocity (Fig. 2). The tidal-circularization timescale estimate (Eq. 6, τe ≳ 26 Gyr) appropriately rules out post-explosion circularization, and the stated caveats (§2.3) show due care. The paper makes a falsifiable prediction — a low-mass BH in the 3.5–4.4 M☉ range on a wide, nearly circular orbit — and the method is genuinely applicable to other wide binaries with unseen companions. The circularity concern raised in review does not land: the observed eccentricity is an external input, not a fitted quantity. However, the scenario ranking in §3 rests on an implicit uniform prior over channel rates and an unmodeled kick distribution, and the printed semi-major-axis formula contains a load-bearing error (below); both require correction.

major comments (3)
  1. [Eq. (1) and Eq. (A6), §2.1] Equating the pre- and post-explosion specific energies (Appendix A) yields a1/a0 = (μ1/μ0)/[1 + 2(μ1/μ0 − 1)(1 + e0 cos ν0)/(1 − e0²)]. The printed Eqs. (1)/(A6) instead contain 2e0(μ1/μ0 − 1)(1 + cos ν0)/(1 − e0²). The printed form is algebraically inconsistent with the rest of the paper: at apocenter it gives a1/a0 = μ1/μ0 < 1 for any mass loss (orbital shrinkage), whereas the circularization condition e1 = 0 of Eq. (3) requires a1 = r_apo = a0(1 + e0); the two equations can only agree if μ1 = μ0. The error is load-bearing for the SN II exclusion argued in §2.2 and §3: with the printed formula the required progenitor pericenters are ~3–5 AU (≈ 640–1100 R☉), outside the 500 R☉ SN II progenitor, so SN II would not be excluded; with the correct formula the pericenters are ~0.25–0.95 AU (≈ 54–200 R☉), inside the progenitor, and the exclusion stands. Because the dashed curves in Figure 2 are described as the analytical solution, the authors should verify which formula generated them, correct Eqs. (1)/(A6), and rerun the analytical–numerical comparison.
  2. [§3 and Appendix C] The statement that the failed-SN channel is 'the most likely scenario' and that the system 'highly probable[ly]' contains a mass-gap BH is a likelihood ranking, not a posterior. Appendix C computes a geometric factor P(ν0 ∈ 180° ± Δν | e0), and §3 multiplies this by nothing: the conclusion implicitly assumes a uniform prior over the intrinsic rates of failed SNe versus SNe Ib/c in the relevant mass range and assumes zero BH natal kick. The paper cites several low-kick BH systems (Vigna-Gómez et al. 2024, etc.), but those constrain individual objects, not the kick distribution; for this binary, the orbital speed is ~35–40 km s−1, so a kick of even a few km s−1 changes the eccentricity by Δe ~ 0.1–0.3, comparable to or larger than the observed 0.05, and would reintroduce a phase constraint into the failed-SN channel. A failed SN also loses some mass (neutrinos, residual ejecta), which the 'no mass loss' scenario ignores. To support the headline ranking, the authors should either combine published rate estimates (e.g., Adams et al. 2017; Gerke et al. 2015) with a kick sensitivity analysis, or state the conclusion as conditional on these assumptions.
  3. [Abstract and §3] The headline mass claim is internally inconsistent. The abstract states the BH mass is 'constrained between the theoretical minimum for failed supernova progenitors (4 M☉) and the observed upper limit (4.4 M☉)', while §2 defines the failed-SN scenario with M1 = M'1 = [3.48, 4.4] M☉ and §1 quotes 3.48 M☉ as the rotation-extended NS mass limit. The origin of the 4 M☉ lower bound is not derived or cited in the body. Either the failed-SN scenario allows remnant masses down to 3.48 M☉, in which case the abstract's interval [4, 4.4] is too narrow, or a specific theoretical minimum failed-SN progenitor mass must be introduced and justified.
minor comments (5)
  1. [Table 1 and §3] The text says the probability of being within 180°±5°, ±10°, and ±15° of apocenter is 'equally ≲10%', but the matching-solution entries in Table 1 are 10% (Δν=5°, e0=0.65), 12% (Δν=10°, e0=0.4), and 4% (Δν=15°, e0=0.2); these are not equal and the 12% entry exceeds the quoted cap.
  2. [Figure captions 1, 2, and 5] The figure captions contain garbled fragments (e.g., 'M1=8, M1=20, M1=20, M1=30, M1=5, M1=10, M1=5, M1=10, → → 1' and '6, 0000 and 30, 0000 km s−1'); these need to be cleaned before publication.
  3. [§2.1] The sentence 'This is highly unlikely for SN II progenitors but guaranteed for SN Ib/c progenitors, which range in size from 500−1500 R☉ and 1−10 R☉, respectively' is confusingly phrased, since the two size ranges are attached to the scenarios in the order listed but the clause reads as if they were attached to the preceding adjectives.
  4. [§2.2, fourth paragraph] The sentence beginning 'However, at lower ejecta velocity the final eccentricity is larger...' has an unmatched parenthesis and a garbled clause ('vmax = 6, 000 km s−1, square symbols), see panels'); rephrase.
  5. [Figure 3 caption] The caption does not identify the panels; since §3 refers to 'panel (b)' and 'panel (c)', the caption should explicitly map panels to progenitor masses or Δν values.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the orbital-response derivation is first-principles and anchored by the observed eccentricity; cited prior work by the authors is non-load-bearing.

full rationale

The central dynamical derivation is not circular. Equations (1)-(2), derived in Appendix A from energy and angular-momentum conservation under instantaneous mass loss, take the observed eccentricity e=0.05±0.01 as an external boundary condition, not as a fitted parameter. The SN Ib/c apocenter likelihood in Appendix C is a standard Keplerian probability calculation from orbital mechanics, and its values are not imported from the conclusion. The homologous-expansion numerical model in Appendix B is explicitly constructed with its own density-profile and integration equations and is validated against the analytical solution, so the self-citations (Regály et al. 2022; Fröhlich et al. 2023) are not load-bearing. The failed-SN scenario is transparently defined as zero mass loss, so e1=e0 by construction; the paper explicitly states that 'no numerical calculation is performed' and does not present this identity as a prediction. The scenario ranking's main vulnerability is the unstated prior over intrinsic supernova rates and the neglect of a natal-kick distribution, which is a statistical modeling concern rather than a circularity. Therefore no circular step meets the quoted-equation evidentiary bar; the score of 2 reflects only the presence of minor, non-load-bearing self-citations in the model heritage.

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

The ledger lists the hand-chosen mass ranges and model assumptions that the scenario ranking depends on. No parameters were fitted to the G3425 data; instead, ranges were adopted from the literature, so the central claim is not the result of a fit. The implicit prior on failed vs successful supernova rates is the most consequential unstated assumption.

free parameters (6)
  • SN II progenitor mass = 8-30 Msun
    Adopted from core-collapse supernova literature (Smartt 2009; Sukhbold et al. 2016) to define the two SN II scenarios.
  • SN Ib/c progenitor mass = 5-10 Msun
    Adopted from stripped-envelope supernova literature (Woosley & Bloom 2006); used to generate Figure 3.
  • Minimum failed SN progenitor mass = 4 Msun
    Assumed theoretical lower bound for black hole formation by failed supernovae; sets the lower limit of the claimed mass-gap black hole mass.
  • Ejecta expansion velocity = 6000-30000 km/s
    Assumed range for supernova ejecta velocities; controls whether numerical and analytical models agree.
  • Envelope power-law index n = 7
    Assumed density profile exponent in the homologous expansion model (Appendix B).
  • Core radius fraction = 0.1 R
    Assumed inner constant-density core in the homologous expansion model.
assumptions (6)
  • standard math The SN mass loss is instantaneous and the secondary's position and velocity are unchanged during the event.
    Assumed in Appendix A for the analytical model; standard impulsive mass-loss approximation.
  • domain assumption The SN ejecta expands homologously and spherically with a power-law density profile (n=7).
    Used in the numerical model in Appendix B; the paper notes asymmetric ejection is not modeled.
  • domain assumption SN II progenitors have radii of 500-1500 Rsun and SN Ib/c progenitors have radii of 1-10 Rsun.
    From the literature; used to argue that SN II scenarios require the secondary to pass inside the progenitor envelope.
  • domain assumption No mass transfer or common envelope evolution occurred before the SN.
    Adopted from the discovery paper (W24) and used to assume the pre-SN orbit was wide and non-interacting.
  • domain assumption The failed SN scenario involves no mass loss and no natal kick, so the orbit is unchanged.
    Central to the conclusion that the failed SN needs no fine-tuning; a kick is not modeled.
  • ad hoc to paper The relative intrinsic rates of failed vs successful SNe are comparable (implicit).
    The likelihood ranking of scenarios relies on this unstated prior; no population synthesis is used.

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Cite this review

Pith. "Pith review of Fine-Tuned Supernova or Failed Explosion? Decoding the Origins of the G3425 Binary." pith.science (2026). https://pith.science/paper/HKOKF4YX

@misc{pith2026250620386,
  author       = {Pith},
  title        = {Pith review of: Fine-Tuned Supernova or Failed Explosion? Decoding the Origins of the G3425 Binary},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HKOKF4YX}},
  note         = {Machine review of arXiv:2506.20386}
}
read the original abstract

A binary system (G3425) consisting of a massive unseen component and a red giant star on a nearly circular orbit was recently discovered. The formation of such a system is puzzling because orbital stability generally breaks down due to the large mass loss from the system caused by the SN explosion while forming the unseen component. Analytical solutions of the variable-mass two-body problem suggest that the explosion should have occurred when the component was close to its apocenter to explain the near-circular remnant system. This provides a strong constraint on the total mass and orbital configuration of the progenitor system. The nearly circular orbit of G3425 rules out type II SN scenarios and allows only for a fine-tuned SN~Ib/c explosion to occur when the secondary was close to its apocenter. Such a scenario, although possible, is highly unlikely. However, the most likely scenario is a failed SN that produced a black hole, for which no additional constraints on the position of the secondary are needed. We propose that the unseen component of G3425 is a mass-gap black hole with a mass constrained between the theoretical minimum for failed supernova progenitors (4 MSun) and the observed upper limit (4.4 MSun). Our analysis can be applied to any wide binary system containing an unseen component on a nearly circular orbit.

Figures

Figures reproduced from arXiv: 2506.20386 by the authors.

Figure 1
Figure 1. Analytical modeling of the G3425 progenitor system. In panel (a), the analytical solutions for the initial eccentricity, e0, as a function of the progenitor mass, M1, are shown assuming zero final eccentricity (i.e., e1 = 0). Solid and dashed lines correspond to the minimum and maximum remnant–secondary pairs for a given SN scenario, respectively. Plausible progenitor solutions are in the shaded regions for each SN … view at source ↗
Figure 2
Figure 2. The final versus initial eccentricity and the growth of the semi-major axis of the secondary are illustrated, under the assumption of different unseen remnant masses. The left and right plots illustrate SN-II and SN Ib/c scenarios, respectively. Blue and magenta colors represent the heaviest (M′ 1 = 3.48 M⊙, M2 = 3.84 M⊙) and lightest (M′ 1 = 2.9 M⊙, M2 = 1.7 M⊙) SN II models, respectively. Orange and black colors r… view at source ↗
Figure 3
Figure 3. Plausible analytical solutions for the initial eccentricity of the system in SN Ib/c scenarios as a function of the mass of the unseen component. Three different positions of the secondary, ν0 = 180◦ , 180◦ ± 5 ◦ , 180◦ ± 15◦ were assumed. The distinct colors represent the three progenitor masses M1 = 5, 7.5, 10 M⊙. The solid and dotted border regions represent M2 = 1.7 and 3.83 M⊙, respectively. The critical mass b… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Ranges of initial eccentricity, e0, calculated according to Eq. (A11) on the M′ 1 − M2 plane assuming three different progenitor masses of M1 = 7.5, 14 and 25 M⊙. Plausible solutions for e0 at a given M′ 1, M2 are in the shaded regions. Using Eqs. (A6) and (A3) this ca…
Figure 5
Figure 5. Figure 5: The mass inside the secondary’s orbit, Min, as a function of time in the four core collapse SN scenarios. Three different progenitor masses are assumed in each scenario, as indicated by the colors in the legend. Solid and dashed lines correspond to expansion velocities…
Figure 6
Figure 6. Figure 6: Panel (a): Probability density functions given by Eq. (C23) for various eccentricities shown with different colors. Panel (b): Probability that the secondary is found at a given true anomaly range, as a function of orbital eccentricity. Bahramian, A., & Degenaar, N. 20…

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Pith tools

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