Solar-System Abundances of $p$-Nuclides Probe Collective Neutrino Oscillations in Supernovae

Alexander Friedland; Amol V. Patwardhan; Derek J. Li; Giuseppe Lucente; Ian Padilla-Gay; Payel Mukhopadhyay

REVIEW 3 major objections 5 minor 1 cited by

Solar-System Abundances of $p$-Nuclides Probe Collective Neutrino Oscillations in Supernovae

T0 review · 3 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read Collective neutrino oscillations starting within ~10 km of the proto-neutron star surface can explain the solar abundances of key proton-rich nuclides like molybdenum, ruthenium, and niobium-92.

desk verdict A careful and genuinely new mapping of νp-process yields to the flavor-conversion radius, whose central claim is plausible but rests on an idealized equilibration prescription and a fitted radius. read the letter →

arxiv 2607.15392 v1 pith:IKJM4KW4 submitted 2026-07-16 hep-ph astro-ph.HEastro-ph.SRnucl-th

Alexander Friedland , Derek J. Li , Giuseppe Lucente , Payel Mukhopadhyay , Ian Padilla-Gay , Amol V. Patwardhan This is my paper · ORCID

classification hep-phastro-ph.HEastro-ph.SRnucl-th

keywords p-nuclidesνp-processcollectiveneutrinooscillationsfastcore-collapsesupernovaeproto-neutronstarnucleosynthesissolarabundances

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

Collective neutrino oscillations in core-collapse supernovae have not yet been directly observed, but this paper claims they leave a specific fingerprint in the solar-system abundances of proton-rich nuclides. Using a 20-solar-mass supernova model and a self-consistent calculation of the neutrino-driven outflow, the authors show that without flavor mixing the νp-process underproduces 92,94Mo, 96,98Ru, and 92Nb by about an order of magnitude. If mixing begins within roughly 10 km of the proto-neutron star surface—modeled as complete instantaneous flavor equilibration—the yields jump by up to two orders of magnitude and match meteoritic values. The paper concludes that these p-nuclide abundances are a probe of the onset radius of collective oscillations, and that the required near-surface conversion points to the fast collective oscillation mechanism.

What carries the argument

The central object is a conversion-radius prescription: flavor equilibration is modeled as happening instantaneously and completely at a radius r_mix = R_PNS + Δr_mix, after which every neutrino flavor shares the same spectrum, f'_νe = f'_νx = (f_νe + 2 f_νx)/3 and similarly for antineutrinos. This gives a one-parameter family of scenarios. What makes the parameter meaningful is the self-consistent treatment: for each Δr_mix, the hydrodynamics of the neutrino-driven outflow is re-solved (since the extra heating can switch the outflow from subsonic to supersonic), and the resulting trajectories are run through a nuclear reaction network to get yields. The outputs are time-averaged yields and

What would settle it

Run a multi-dimensional core-collapse supernova simulation with multi-angle neutrino transport that resolves the fast flavor instability; if the resulting conversion begins beyond ~30 km from the proto-neutron star or achieves only partial flavor equilibration, the paper's central claim is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that collective neutrino flavor conversion starting within ~10 km of the proto-neutron star surface—and only such 'near' conversion—brings the νp-process yields of the p-nuclides 92,94Mo, 96,98Ru, and the long-lived radionuclide 92Nb into agreement with solar abundances. This is established by computing, for a benchmark 20 M☉ progenitor with a 1.93 M☉ proto-neutron star, the full time-dependent outflow for each assumed equilibration radius Δr_mix, and then post-processing the trajectories with a nuclear network. Near conversion raises the electron fraction toward 0.6 and increases heating enough to occasionally push the outflow into a supersonic regime, effects t

Load-bearing premise

The strongest assumption is that collective conversion can be treated as complete, instantaneous flavor equilibration at a single radius; if actual oscillations are less complete or spread over a range of radii, the computed yield enhancements and the inferred ~10 km onset could change.

Editorial extensions

If this is right

If the paper is correct, a supernova that hosts fast collective oscillations within ~10 km of the proto-neutron star will be an efficient producer of Mo, Ru, and Nb-92, while a supernova where conversion starts farther out will not reach solar levels.
The observed solar p-nuclide pattern becomes a spatial diagnostic: near conversion (≲30 km) boosts yields by 10–60×, far conversion (≳40 km) by only 2–3×.
The long-lived radionuclide 92Nb, with its broadened production window and up to 100-fold enhancement, provides a separate, time-resolved check on the νp-process that earlier studies had used to argue against it.
Hydrodynamic feedback is essential: ignoring the oscillation-induced heating and possible transonic transition would change the yields and could mask the radius dependence the paper reports.

Reading between the lines

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

The inferred ≤10 km onset is a proxy: the paper compares it with typical fast vs slow collective oscillation scales, but does not simulate the conversion dynamics itself. A future calculation that predicts an onset radius from first principles could strengthen or break the identification.
If near-surface conversion is indeed responsible, then the solar inventory of p-nuclides would be direct evidence that neutrino flavor mixing occurs in supernovae, linking nuclear astrophysics to neutrino physics in a way that is testable with a Galactic supernova neutrino burst.
A testable extension: run the same mixing-radius mapping with partial conversion or spectral-swap prescriptions rather than full equilibration. The yields of 92,94Mo relative to 96,98Ru may distinguish these microphysical models, since the harder mixed-antineutrino spectrum affects the neutron production differently.
The near-criticality of the outflow suggests that the mechanism is sensitive to progenitor structure and PNS mass; scanning these parameters could identify which supernovae contribute the solar p-nuclides and which do not.

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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

You should know two things about this one. First, it is the first study to recompute the neutrino-driven outflow self-consistently for each flavor-conversion radius and feed that into a full nucleosynthesis network, so the radial dependence they map is not something you can get from earlier work. Second, the headline claim — that near-PNS conversion is required to match solar p-nuclide abundances — is conditional on an idealized instantaneous full-equilibration model, and the paper says so in a footnote. The interpreters should not run ahead of the calculation.

What they do well is real. They take a modern Garching 20 M_sun simulation, build a steady-state GR hydro model with time-dependent boundary conditions, and run SkyNet with careful microphysics: weak magnetism and recoil, medium-enhanced triple-alpha, updated 92Nb decay. They explore a second, mildly supersonic 18.6 M_sun model, which is a sensible robustness check. The qualitative behavior — near conversion boosts yields, far conversion only gives a factor of a few — survives across both models. The hydro feedback is nontrivial: extra heating can push the outflow transonic and clip the production window, which is exactly the kind of coupling earlier papers missed.

The soft spots are the ones the stress-test flags, and they are real but not disqualifying. The sharp radius r_mix with complete flavor equilibration (SM C, Eq. S7) is a limiting case. Partial conversion, spectral splits, or lepton-flavor-number conservation could change the magnitude of the boost and shift the inferred radius threshold. The paper's rebuttal — that any substantial νx-to-νe transfer drives Y_e toward ~0.6 — addresses the asymptotic electron fraction but not the hydrodynamics timing or the neutron-production far effect. So the 'and only then' in the Conclusions is stronger than what the calculation actually shows. Also, the radius where oscillations start is effectively fitted to observations, and the identification of that radius with fast collective oscillations is imported from the FCO literature, not derived here. Spectral moments are frozen at 3.5 s and most curves lack error bars, though the 92Nb analysis at least includes meteoritic uncertainties.

None of this makes the paper unserious. The authors are upfront about the approximation and flag the need for future work. The qualitative finding should survive better flavor-conversion input; the quantitative threshold may not.

This deserves a serious referee. Send it to review. The right referee will push for a partial-conversion sensitivity study and a clearer separation between what is computed and what is inferred. I would cite it for the self-consistent radial mapping, but I would not yet cite it as evidence that fast oscillations are the mechanism.

Referee Report

3 major / 5 minor

Summary. This Letter argues that the solar-system abundances of the p-nuclides 92,94Mo, 96,98Ru and of the extinct radionuclide 92Nb can diagnose the radius at which collective neutrino oscillations begin in core-collapse supernovae. Using a 20 M_sun Garching progenitor with a 1.93 M_sun PNS, the authors model the νp-process by recomputing the neutrino-driven outflow hydrodynamics for each oscillation scenario and post-processing tracer trajectories with SkyNet. Flavor conversion is prescribed as complete instantaneous flavor equilibration at radius R_PNS + Δr_mix (SM C, Eq. S7), with Δr_mix scanned from 1 to 3000 km. They find that near conversions (Δr_mix ≲ 10 km) enhance p-nuclide yields by up to two orders of magnitude and bring the isotopes into agreement with meteoritic solar thresholds, whereas far conversions are insufficient. The authors conclude that the observed p-nuclide pattern indicates fast collective oscillations occurring close to the PNS surface.

Significance. If correct, this would provide a new astrophysical probe of collective neutrino oscillations and connect an otherwise elusive quantum phenomenon to a long-standing nucleosynthesis puzzle. The paper has real strengths: it uses public, modern supernova simulations, a detailed GR steady-state outflow model, an open nuclear reaction network with important corrections (medium-enhanced triple-α, 92Nb decay), and it systematically scans the mixing radius in two progenitor models. The inclusion of hydrodynamic feedback, especially the near-critical transonic transition, is a clear improvement over earlier νp-process studies. The principal caveat is that all quantitative yield results and the inferred radius threshold rest on the idealized complete-instantaneous-equilibration prescription of SM C, Eq. (S7); the sharp 'and only then' conclusion would be substantially strengthened by a partial-conversion sensitivity study.

major comments (3)

[SM C, Eq. (S7); Fig. 3; Conclusions] The central quantitative map of ⟨Y_A⟩ versus Δr_mix is computed under complete instantaneous flavor equilibration, f'_νe = (f_νe + 2 f_νx)/3 and analogously for antineutrinos. As the authors note in footnote 90, this is an approximate limiting case and lepton-flavor-number conservation constrains full equilibration. All yield enhancements in Fig. 3, the heating-rate boost in SM C (Fig. S4), and the inferred threshold Δr_mix ≲ 10 km scale with the degree of ν_x → ν_e transfer. No sensitivity study is presented for partial conversion, spectral swaps, or flavor-equilibration efficiency. The Conclusions claim that solar agreement is achieved 'when oscillations occur close to the PNS surface, and only then' is therefore not yet established for realistic FCO outcomes. Please add a conversion-efficiency parameter (e.g., ε ∈ [0,1] interpolating between no mixing and full equipartition) or equiva
[Abstract; Discussion; Conclusions; Refs. [21-25]] The abstract's 'indicating fast collective oscillations' and the Discussion's assignment of near conversion to FCO (and far conversion to SCO) rely on identifying the scanned free parameter Δr_mix with the FCO radius obtained from cited literature. The calculation itself does not derive an oscillation radius; Δr_mix is a scanned parameter, and the best-match radius is selected a posteriori. This is not internally inconsistent, but the claim as worded is stronger than the evidence. Either show that FCO in this specific 20 M_sun model is expected to begin within ~10 km, or explicitly flag this as an external identification and temper the wording to 'consistent with FCO'.
[SM B; Table S1; Eq. (S10); Fig. 3] Spectral moments are frozen at their t = 3.5 s values for all launch times t_launch ∈ [1,10] s (Table S1 and Eqs. S4-S5). The paper states that the moments vary only mildly during the first ~5 s, but the time-averaged yields in Eq. (S10) integrate over the whole window, and the near-conversion result is sensitive to the balance between the Y_e boost and transonic clipping. Since production rates (Fig. 2) extend to late times, a quantitative test with time-dependent spectral parameters, or at least an estimate of the resulting yield uncertainty, is needed to confirm the robustness of the Δr_mix threshold.

minor comments (5)

[Fig. 2; Fig. S7 captions] The captions appear to label both the upper and lower rows as 'Upper panels'; the lower panels should be labeled explicitly. In Fig. S7 the text also refers to panels a1, b1, c1, d1 but the caption does not define them consistently.
[Abstract; Comparison with solar abundances] The abstract says 'best match' without defining a fitting criterion. Please specify the criterion used (e.g., Δr_mix ≲ 10 km for all listed species to enter the co-production band) or soften the wording.
[Methods; Conclusions] The statement that agreement is reached 'without tuning any aspects of explosion' should acknowledge that Δr_mix is a free parameter that is scanned and then selected to match observations. This is a fair parametric study, but the word 'tuning' is misleading here.
[Footnote 90] The limitation of the full-equilibration prescription is important enough to appear in the main text rather than only in a footnote, especially because it is load-bearing for the central conclusion.
[SM D, Eq. (S13)] The 'solar abundance thresholds' in Fig. 3 are computed for the unmixed case only, as explained in SM D. This is conservative, but the caption could state this explicitly to avoid misreading.

Circularity Check

1 steps flagged · score 2.0 of 10

No structural circularity: the abundance agreement is a forward computation against independent meteoritic data, though the 'within ~10 km / and only then' claim is conditioned on a disclosed maximal-equilibration ansatz and the FCO attribution is imported from external literature.

other [Methods (main text); SM A; SM C Eq. (S7); footnote [90]]
"Following existing literature [75], we model flavor conversion as complete instantaneous equilibration at a distance Δrmix from the PNS surface. ... We vary Δrmix as a free parameter to quantify the νp-process's sensitivity to conversion location. [90] This prescription should be viewed as a representative, approximate limiting case, since flavor equilibration is constrained by lepton-flavor number conservation [110, 111]."

The headline claim—'best match within 10 km ... indicating fast collective oscillations' (Abstract) and 'and only then, the predicted abundances line up' (Conclusions)—is read off the Δrmix scan (Fig. 3), whose yield map is produced by the input prescription (Eq. S7): complete instantaneous flavor equilibration at the scanned radius, adopted from Ref. [75] rather than derived from FCO dynamics. This maximal ansatz is what makes near-conversion boosts large enough to clear the solar thresholds, so the exclusive 'and only then' statement is partly built from the assumed strongest-effect limit; footnote [90] and SM A ('which maximizes the effect of neutrino mixing') concede this and defer a partial-conversion study to [101]. The abundance computation is itself a genuine forward result against

full rationale

The paper's derivation chain is largely self-contained and does not reduce to its inputs. The load-bearing calculation maps yields ⟨Y_A⟩ to the flavor-mixing radius Δr_mix using (i) the Garching 20 M⊙ benchmark (external), (ii) the steady-state GR hydrodynamics framework of the authors' prior JCAP paper [81] with SkyNet reaction-network post-processing, and (iii) meteoritic solar abundances [100] with the standard overproduction-factor ≥ 10 criterion [79, 129]. No parameter is fitted to the solar data: the unmixed case underproduces the p-nuclides and the near-mixing cases clear the thresholds, so the agreement is computed content, not enforced. The self-citations ([80], [81], [82]) are methodological and numerical frameworks, not uniqueness theorems invoked to forbid alternatives; the hydrodynamics framework is code-based and independently published, so per the review rules it counts as real evidence rather than circular support. The identification of the near/far radius regimes with FCO/SCO is imported from external references [21–25], [35–38], not from the present authors, so there is no 'uniqueness imported from authors' or 'ansatz smuggled via self-citation' chain. The one partial concern is flagged by the paper itself: the flavor-conversion input is complete, instantaneous equilibration (SM C, Eq. S7), an ansatz adopted from Ref. [75] and described in footnote [90] as 'a representative, approximate limiting case' and in SM A as a prescription that 'maximizes the effect of neutrino mixing.' Because the magnitude of the yield boost—and hence the exclusive claim that abundances line up 'and only then'—is generated by this maximal-conversion assumption, the inferred ≤10 km constraint and the FCO indication are conditional on it. The paper's own robustness argument covers only the asymptotic Y_e (SM A), not the hydrodynamic-feedback thresholds under partial-conversion outcomes, and it defers a quantitative study of such outcomes to future work [101]. This is a disclosed modeling limitation bearing on the strength of the physical conclusion (a correctness/robustness risk), not a definitional reduction of the prediction to the input. Verdict: no significant circularity; score 2 reflects the mild, disclosed assumption-dependence of the headline claim.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central parameter is Δr_mix, the flavor equilibration radius, which is scanned and effectively fit to solar abundances. Other inputs (luminosity fits, spectral moments, PNS mass) are inherited from public supernova simulations. The key ad hoc assumption is instantaneous full flavor equilibration, which maximizes the oscillation effect and shapes the quantitative conclusion. No new particles or forces are invented.

free parameters (2)

Δr_mix (flavor equilibration radius offset) = ≤10 km (best match; scanned 1–3000 km)
Central free parameter. Yields and solar agreement are mapped against it; the conclusion that oscillations start within 10 km is this parameter's best-fit range, not a derived prediction.
front-shock velocity v_FS = 6000 km/s (benchmark), 7000 km/s (perturbed)
Sets the outer boundary confining pressure; adopted from Garching simulation conventions but chosen by hand. Perturbing it changes yield normalization but not the qualitative conclusions.

assumptions (6)

ad hoc to paper Complete instantaneous flavor equilibration at r_mix (Eq. S7).
The paper replaces neutrino spectra with fully equilibrated ones beyond a chosen radius, maximizing the oscillation effect. Footnote [90] concedes this is an approximate limiting case constrained by lepton-flavor conservation.
domain assumption Steady-state, spherically symmetric GR outflow with time-snapshots captures the neutrino-driven wind.
Hydrodynamics is solved as a boundary value problem with snapshots every 0.1 s (SM A); multi-dimensional and time-dependent transients are not included.
domain assumption The Garching 20 Msun / 1.93 Msun PNS simulation is representative of νp-process sites.
The authors use one benchmark model plus one perturbation; other progenitors, PNS masses, and equations of state could change the yields and the inferred radius constraint.
domain assumption Pinched Fermi-Dirac spectra with moments frozen at t=3.5 s accurately represent neutrino distributions.
Spectral parameters T_ν and η_ν are fixed from the simulation at t=3.5 s (SM B); time evolution of spectral shape is ignored.
domain assumption FCO occurs within ~10-30 km and SCO at 40-500 km from the PNS surface.
The interpretation of Δr_mix thresholds as distinguishing fast versus slow collective oscillations is imported from cited literature, not derived in this paper.
standard math SkyNet with REACLIB v2.2 plus medium-enhanced triple-alpha provides reliable nucleosynthesis.
The nuclear network and reaction rates are standard open-source tools; the paper modifies them as described in SM A.

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Pith. "Pith review of Solar-System Abundances of $p$-Nuclides Probe Collective Neutrino Oscillations in Supernovae." pith.science (2026). https://pith.science/paper/IKJM4KW4

@misc{pith2026260715392,
  author       = {Pith},
  title        = {Pith review of: Solar-System Abundances of $p$-Nuclides Probe Collective Neutrino Oscillations in Supernovae},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IKJM4KW4}},
  note         = {Machine review of arXiv:2607.15392}
}

abstract

Direct evidence for collective neutrino oscillations in core-collapse supernovae remains elusive. We show that this quantum phenomenon leaves a footprint on the abundance pattern of proton-rich nuclides in the solar system. Modeling the $\nu p$-process using a $20\,M_\odot$ progenitor, we map out the dependence of the total yields on the starting radius of the oscillations, self-consistently coupling hydrodynamics and nucleosynthesis. The oscillations boost key $p$-nuclides ($^{92,94}\text{Mo}$, $^{96,98}\text{Ru}$) and long-lived $^{92}\text{Nb}$ by up to two orders of magnitude, bringing their abundances into agreement with the observations. The best match is found when oscillations commence within $10\text{ km}$ of the proto-neutron star surface, indicating fast collective oscillations.

Figures

Figures reproduced from arXiv: 2607.15392 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Time-averaged yields [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Neutrino quantum kinetics for fast flavor conversion in a time-dependent environment
astro-ph.HE 2026-08 unverdicted novelty 6.0 of 10

Fast flavor conversion in a time-varying supernova background proceeds through three episodes and broadly agrees with static two-step model results.

Reference graph

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

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