Gamma-ray emission from decays of boosted nuclei in protomagnetar jets

Nick Ekanger; Sean Heston; Shunsaku Horiuchi

REVIEW 3 major objections 6 minor 90 references

Gamma-ray emission from decays of boosted nuclei in protomagnetar jets

T0 review · 3 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read This paper argues that boosted, time-dilated gamma-ray lines from decaying nuclei in protomagnetar jets would be detectable from a Galactic supernova and from on-axis events out to about 35 Mpc.

desk verdict New idea, broken Doppler factor: the claimed tens-of-days line window is actually compressed to about a day for on-axis jets. read the letter →

arxiv 2502.07888 v2 pith:J4KMR2A6 submitted 2025-02-11 astro-ph.HE

Sean Heston , Nick Ekanger , Shunsaku Horiuchi This is my paper · ORCID

classification astro-ph.HE

keywords gamma-raylinesprotomagnetarjetsr-processnucleosynthesisrelativisticbeamingcore-collapsesupernovaeradioactivedecayINTEGRAL/SPIe-ASTROGAM

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 whether radioactive heavy nuclei synthesized in the relativistic jets of magnetorotational supernovae — explosions powered by protomagnetars, the rapidly spinning and highly magnetized newborn neutron stars — can be seen from Earth. It argues that they can: $\beta$-decay gamma rays from nuclei moving with bulk Lorentz factor $\Gamma=10$ have observed energies multiplied by the Doppler factor (about 20 for a jet pointed at us) and apparent half-lives stretched by time dilation, pushing lines from hundreds of keV to tens of MeV and keeping them visible for tens of days. For a supernova at 10 kpc the predicted lines fall within the sensitivity of the current INTEGRAL/SPI instrument and the planned e-ASTROGAM mission, and for the fastest-spinning on-axis models the signal would remain detectable out to about 35 Mpc. Measuring several decay lines together with the integrated luminosity over roughly ten days would distinguish engine models and reveal properties such as the protomagnetar's spin and magnetic field.

What carries the argument

The load-bearing object is the boosted $\beta$-decay line: a nuclear transition with rest-frame energy $E_\gamma$ and half-life $\tau_{1/2}$ seen from a jet with bulk Lorentz factor $\Gamma=10$, so the observed energy is $\delta E_\gamma$ and the observed decay constant is $\Gamma\lambda$. The calculation chains together the protomagnetar wind model for mass loss, temperature, and density; a nuclear reaction network for the abundances; a decay database for half-lives, intensities, and line energies; the jet optical depth for the escape factor $e^{-\tau}$; and the beamed luminosity $L=\delta^3\sum_i (dN_{i,\gamma}/dt)E_{i,\gamma}$. Time dilation is what stretches the signal over tens of days, and the $\delta^3$ beaming is what lets on-axis models be seen at extragalactic distances.

What would settle it

Watch a Galactic core-collapse supernova that shows evidence of an on-axis relativistic jet: if no narrow lines appear at the Doppler-boosted energies of magnesium-28 (about 0.6 MeV), scandium-47 (about 3.2 MeV), zinc-72 (about 2.9 MeV), or krypton-85 (about 3.0 MeV) during the first thirty days at INTEGRAL/SPI or e-ASTROGAM sensitivity, the detectability claim fails. Equivalently, a radiation-transport calculation showing that nuclei with Lorentz factor 10 are photodisintegrated in the jet's photon field before decaying would remove the signal at its source.

Watch

Extended reading notes

Core claim

The paper's central claim is that a magnetorotational core-collapse supernova with a jet pointed near our line of sight produces a recognizable, long-lived gamma-ray line signal from the decays of unstable nuclei made inside the jet. Using wind trajectories for four protomagnetar models with dipole fields between $5\times10^{14}$ and $10^{16}$ G and spin periods of 1.5-3.5 ms, the authors compute r-process (rapid-neutron-capture) abundances with a nuclear reaction network, then propagate parent and daughter $\beta$-decay photons through the expanding jet once it becomes optically thin. The observed line energies are Doppler-boosted by a factor of about $\delta\approx20$ for an on-axis jet with $\Gamma=10$, and the decay times are dilated by $\Gamma$, so lines from isotopes such as magnesium-28, scandium-47, zinc-72, and krypton-85 remain above detector sensitivity at 10 kpc for up to tens of days. When 10% of nuclei are accelerated to a nonthermal power law, the decays blend into a continuum that extends to much higher energies and is detectable by ground-based gamma-ray observatories at 10 kpc. The result is a new multimessenger probe: the line spectrum and roughly ten-day light curve carry information about the ejected mass and isotopic yields, which depend on the engine's spin and magnetic field.

Load-bearing premise

The heavy nuclei synthesized in the jet must survive photodisintegration and spallation long enough to decay after the jet becomes transparent; the paper assumes this survival, relying on unpublished work for thermal nuclei and stating the accelerated-nucleus case as an assumption.

Editorial extensions

If this is right

A Galactic magnetorotational supernova with an on-axis jet would show boosted gamma-ray lines from hundreds of keV to tens of MeV for tens of days, with the fastest-spinning models detectable out to about 35 Mpc.
Measuring several lines together with the roughly ten-day light curve would break degeneracies between ejected mass, isotope yields, and viewing geometry, constraining the protomagnetar's spin and dipole field.
Off-axis jets are hard to detect even at the Galactic Center, with critical viewing angles ranging from about 25 to 70 degrees across the four models, so a null detection by itself would not rule out the engine.
If about 10% of nuclei undergo nonthermal acceleration, a power-law continuum from boosted decays becomes detectable by ground-based gamma-ray observatories at 10 kpc and could extend to water-Cherenkov and air-shower instruments for fast-spinning on-axis models.
The same decays release roughly $10^{51}$ boosted neutrinos spread over days, potentially giving tens to a hundred events at Hyper-Kamiokande, separated in time from the ordinary ten-second supernova neutrino burst.

Reading between the lines

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

Beyond the paper, the same boosted-decay mechanism should apply to any relativistic outflow that synthesizes heavy nuclei; compact binary merger ejecta are mostly subrelativistic, but a relativistic component would inherit the same line boost and time dilation.
A concrete archival test would be to search past gamma-ray observations of nearby core-collapse supernovae for transient line groups in the 0.1-10 MeV range at the energies predicted by a single Doppler factor, which would appear or not depending on jet orientation and engine parameters.
If both the line signal and the nonthermal continuum are detected, their ratio would measure the accelerated fraction, turning the signal into a diagnostic of particle acceleration inside protomagnetar jets.
A null detection in a well-observed nearby event would not cleanly exclude the model, because off-axis geometry, low ejected mass, and nuclei destruction all suppress the signal; the paper leaves that degeneracy open.

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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

Colleague,

The core idea is genuinely new: nobody has computed the gamma-ray line signal from beta-decaying r-process nuclei boosted in a protomagnetar jet. The paper builds a transparent forward model from nucleosynthesis yields to detector sensitivities, is honest about its assumptions, and explicitly labels the nonthermal continuum an upper limit. That is real work, and the abundance tables, decay chains, and optical depth treatment are laid out carefully.

But there is a load-bearing error in the relativity that runs through the whole paper. For an on-axis jet, observed times are Doppler-compressed, not dilated: dt_obs = dt'/δ, with δ = 1/[Γ(1-β)] ≈ 2Γ for Γ=10. A nucleus with rest half-life τ is observed to have half-life τ/δ, roughly twenty times shorter, not longer. The abstract says time dilation lets the lines last to later times; Eq. (9) defines λ' = Γλ, which makes the decay faster; and the figures show lines surviving out to 30 days, which would require slower decay. Those three cannot all be right. With the correct Doppler factor δ≈20, the favorable isotopes in Table III (rest half-lives ~0.2–9 days) have observed half-lives of ~0.01–0.5 days. The emission is still beamed and bright, but it arrives as a burst of hours to about a day, not tens of days. The detection horizons and critical angles in Sec. IVB change qualitatively.

The other soft spots are secondary but real. Nuclei survival is asserted with an unpublished citation, and the paper concedes it 'must assume nuclei survival'; the entire signal is conditional on that. The input choices (Ye=0.45, κ=0.1, Γ=10) are hand-picked, but in a first exploration that is not a flaw as long as the numbers are read as illustrative. The reliance on Ref. [44] is not circular; that is a published nucleosynthesis calculation.

My take: the idea deserves a serious referee, but the current version is not publishable with this kinematic error. The authors should correct the Doppler factor, recompute the light curves and sensitivities, and reframe the prediction as a short, bright, beamed burst. If they do, the observable window may still be interesting, but the 'tens of days' discovery narrative will not survive.

Recommendation: send it out, but tell the referee to check the time transformation first.

Referee Report

3 major / 6 minor

Summary. The paper proposes that unstable nuclei synthesized in protomagnetar jets can produce detectable gamma-ray line emission, with line energies boosted and decay timescales altered by the jet's bulk Lorentz factor. The authors construct a toy jet model for four protomagnetar parameter sets, compute the optical depth for gamma-ray escape, predict line light curves and spectra, and compare them with INTEGRAL/SPI and e-ASTROGAM sensitivities. They also consider a nonthermal accelerated-nuclei population and predict a continuum extending to very high energies. The headline results are that boosted decay lines are detectable from a 10 kpc Galactic supernova for up to tens of days, and for on-axis jets out to ~35 Mpc.

Significance. If the predictions were correct, this would be a genuinely new multimessenger channel linking r-process nucleosynthesis in protomagnetar jets to gamma-ray line observations, with potentially falsifiable signatures and the ability to discriminate engine parameters. The forward-modeling approach is transparent, the use of published nuclear data and detector sensitivities is careful, and the authors are appropriately explicit about many input choices. However, the central quantitative claim is compromised by an error in the relativistic transformation of decay rates, and the survival of the synthesized nuclei is asserted rather than demonstrated. After correction, the main conclusions regarding the duration and horizon of detectability will likely change substantially.

major comments (3)

[Eq. (9), Sec. IVA, Abstract] The treatment of relativistic decay rates is inconsistent with special relativity. For an on-axis jet (θ_view = 0), the Doppler factor is δ = 1/[Γ(1−β)] ≈ 2Γ = 20 for Γ = 10, and the observed half-life is τ_obs = τ_rest/δ, i.e., Doppler-compressed, not dilated. Equation (9) defines λ'_i ≡ Γ_bulk λ_i, which makes the decay faster by a factor Γ rather than slower; even ignoring the factor of ~2, the sign is wrong. The abstract and Sec. IVA claim that lines 'can also be seen until later times due to time dilation of the rest-frame half-lives,' but under the standard transformation the favorable isotopes in Table III (rest half-lives 4.6 hours to 8.7 days) would have observed half-lives of order 0.01–0.5 days. Consequently, the predicted line fluxes at t = 10 and 30 days in Figs. 5–7, the 'tens of days' detection window, and the extragalactic horizons quoted in Sec. IVB are not supported. The calculation should be redone with λ_obs = δ λ_rest, and the δ factor should appear consistently in Eq. (11); the detectability at early times after the jet becomes optically thin should be reassessed.
[Sec. IIIB and Sec. V] The survival of the synthesized nuclei is a precondition for the entire signal, but it is not demonstrated. In Sec. IIIB the statement that 'thermal nuclei are typically not photodisintegrated' is supported only by unpublished work (Ekanger et al. 2025, to be published), and in Sec. V the authors write that 'we must assume nuclei survival' for the nonthermal population, with no quantitative treatment. Since photodisintegration would eliminate the line and continuum signals, the detectability claims should be explicitly conditional on survival; for the nonthermal continuum the results are already labeled an upper limit, but the thermal line signal is presented as a firm prediction despite resting on the same unverified premise. The authors should either provide a published reference with the survival calculation or a self-contained estimate, or clearly frame all predictions as conditional on the survival assumption.
[Sec. IIC and Sec. VI] The opacity treatment uses a constant κ = 0.1 cm^2 g^-1 taken from Ref. [47], which the authors note was computed for Ye = 0.4 while the jet model uses Ye = 0.45. The optical depth determines the time at which the jet becomes transparent and therefore the peak time and overall normalization of the light curves. The sensitivity of the results to this choice is only discussed qualitatively in Sec. VI ('if the opacity is 1 g^-1 cm^2, for example, the lines are largely unchanged at ten days'). Since the detectability at t ≥ 1 day for the Pi = 1.5 ms models depends on τ falling below unity on that timescale, a quantitative exploration of κ (e.g., 0.01, 0.1, and 1 cm^2 g^-1) should be shown to establish the robustness of the predicted escape times.

minor comments (6)

[Sec. IVB text near Fig. 5] In the paragraph below Fig. 5, '47S' should be '47Sc' (the table and figures correctly list 47Sc).
[Sec. VI] The sentence referring to off-axis viewing states 'θview ∼90%'; this should read 'θview ∼90°'.
[Sec. VI] The phrase '0.1g^{-1} cm^2' in the opacity discussion should be written as '0.1 cm^2 g^{-1}' for consistency with Sec. IIC.
[Sec. IVA] The text states 'Γbulk = 10 ⇒ δ∼20' but Eq. (9) uses λ' = Γ_bulk λ; the relationship between δ, Γ, and the decay-rate transformation should be stated explicitly and used consistently, since the current inconsistency is central to the main error.
[Sec. IIIA, Fig. 3] The abundance cutoff Y = 10^-8 is introduced without a sensitivity study; because it directly determines which isotopes appear in Table III, the impact of varying this threshold should be quantified.
[References] Reference [83] contains a corrupted author string ('Christopher A. aSkyNetnd Pols'); this should be corrected to the proper citation of Hurley, Tout, and Pols.

Circularity Check

1 steps flagged · score 4.0 of 10

Core detectability is a forward model, but the survival of synthesized nuclei — a necessary premise for every predicted line — rests solely on an unpublished self-citation.

self citation load bearing [Sec. IIIB (Survival of heavy nuclei); also Sec. V (Nonthermal Nuclei)]
"Thermal nuclei are typically not photodisintegrated regardless of whether the ambient photon field is thermal or nonthermal [Ekanger et al. 2025 (to be published)]. ... In this case, we must assume nuclei survival, which can occur if photons are also nonthermal, but we do not investigate the process in detail in this work."

The entire gamma-ray line signal requires that synthesized nuclei survive photodisintegration while traveling through the jet; if they are destroyed, the predicted lines, light curves, and detection horizons vanish. The only support offered for this necessary premise is an unpublished manuscript by the same group ('Ekanger et al. 2025 (to be published)'), and the paper explicitly declines to model or verify the process. The claim is therefore not derived from the present equations and not independently checkable; it is imported from an in-preparation self-citation whose assumptions are not stated. This is load-bearing because every thermal line flux in Sec. IV, the light curves in Fig. 4, and the distance horizons in Sec. IVB presuppose survival. The other main input, Ref.

full rationale

The derivation of the gamma-ray signals is a genuine forward model: abundances from the published nucleosynthesis calculation of Ref. [44] are combined with NUDAT decay data, a specified jet geometry, optical depth, and detector sensitivities to produce line fluxes and light curves. No parameter is fitted to the gamma-ray observations being predicted, and the detection claims do not reduce to the inputs by definition. The one load-bearing support gap that resembles circularity is the survival of nuclei: the paper asserts, on the basis of an unpublished same-group manuscript, that thermal nuclei are not photodisintegrated, and then states that for the nonthermal case survival 'must be assumed' and is not investigated. Because every predicted signal presupposes survival, this self-citation is material rather than cosmetic. Separately, the manuscript contains an internal inconsistency between its stated 'time dilation' and Eq. (9)'s λ' = Γλ, which would compress rather than dilate half-lives; that is a serious correctness risk, but it is not a circularity and does not affect this score.

Assumptions & free parameters 9 free parameters · 9 assumptions · 0 invented entities

The detectability claim depends on a chain of model inputs, several of which are chosen by hand or taken from prior or unpublished work by the same group. The paper is transparent about most of them, but the strongest result is conditional on these choices.

free parameters (9)

Electron fraction Y_e = 0.45
Chosen to ensure synthesis of unstable heavy nuclei; authors state outflows with Y_e >= 0.5 do not produce much beyond iron (Sec. IIB, VI).
Bulk Lorentz factor Gamma_bulk = 10
Assumed constant for all jet models; sets Doppler factor, line energy boost, and time dilation (Sec. IIB).
Gamma-ray opacity kappa = 0.1 cm^2 g^-1
Constant ejecta opacity taken from 'blue kilonova' models at Y_e = 0.4 and extrapolated to Y_e = 0.45 (Sec. IIC).
Jet opening angle theta_op = 1/Gamma_bulk
Assumed relation; affects ejecta density and CSM mass swept (Sec. IIC).
Abundance cutoff = Y = 10^-8
Abundances below this threshold are ignored in computing detectable signals (Fig. 3).
Thermal fraction f = 0.9
Assumes 10% of nuclei undergo nonthermal acceleration; the choice is motivated by cosmic-ray injection literature but not derived (Eq. 13).
Nonthermal spectral index = -2
Power-law index for accelerated nuclei, adopted following Ref. [37] (Eq. 14).
CSM constant density = 10^-25 g cm^-3
Assumed low-density environment outside the progenitor; sets late afterglow timing of 10^3 days in Case 1/Ibc (Sec. IID).
Pre-SN mass-loss parameters = D* = 1, R* = 10^13 cm (IIn); D* = 10^-5, R* = 3 x 10^11 cm (Ibc)
Two representative CSM shell profiles from Ref. [49]; the IIn case gives early afterglow at about 1 day (Sec. IID).

assumptions (9)

standard math Standard radioactive decay chain equations for parent and daughter, with time-dilated constants lambda' = Gamma * lambda (Eq. 9).
Uncontroversial physics; not a source of uncertainty.
domain assumption Protomagnetar wind and jet model of Refs. [29] and [44], with neutrino light curves from Ref. [46].
Provides mass-loss rate, entropy, expansion timescale, and r-process abundances; the present paper does not re-derive these.
domain assumption The jet is a uniform-density conical sector between R_bo and R_E,max with a constant velocity and Lorentz factor.
Used for optical depth and ejecta mass estimates (Sec. IIC).
domain assumption Initial composition is NSE at Y_e = 0.45; reaction rates from REACLIB via SkyNet.
Determines the abundance distribution of unstable nuclei (Sec. IIIA).
ad hoc to paper Thermal nuclei survive photodisintegration in the jet; accelerated nuclei survival is assumed.
Cited to an unpublished paper; authors state the process is not investigated in detail (Sec. IIIB, V).
domain assumption Opacity is constant at 0.1 cm^2 g^-1 and there is no photon downscattering after the jet becomes optically thin.
Simplifies Eq. (10); authors note opacity may be higher (Sec. IIC, VI).
domain assumption At each decay, only first-generation beta-plus/minus gamma rays and daughter gamma rays are included; isomeric transitions are ignored.
Could add comparable signals but are omitted due to lack of spin-state tracking (Sec. IVA, VI).
domain assumption The afterglow begins when the swept-up CSM mass equals the jet mass.
Used to compute afterglow timing in Table II (Sec. IID).
ad hoc to paper Nonthermal accelerated nuclei follow dN/dGamma proportional to Gamma^-2 exp(-Gamma/Gamma_max).
Chosen by analogy with cosmic-ray spectra (Eq. 14); not derived from the jet dissipation model.

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Cite this review

Pith. "Pith review of Gamma-ray emission from decays of boosted nuclei in protomagnetar jets." pith.science (2026). https://pith.science/paper/J4KMR2A6

@misc{pith2026250207888,
  author       = {Pith},
  title        = {Pith review of: Gamma-ray emission from decays of boosted nuclei in protomagnetar jets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J4KMR2A6}},
  note         = {Machine review of arXiv:2502.07888}
}

abstract

We examine the detectability of $\gamma$-ray emission originating from the radioactive decays of unstable nuclei that are synthesized in relativistic outflows launched in magnetorotational core-collapse supernovae. The observed lines have enhanced energies due to the Lorentz boosted nuclei and can also be seen until later times due to time dilation of the rest-frame half-lives. We find that instruments like \textit{e-ASTROGAM} and \textit{INTEGRAL/SPI} are sensitive to these boosted line emissions from hundreds of keV to tens of MeV at a distance of 10 kpc over timescales of tens of days. For favorable viewing angles, these decays can be detected to extragalactic distances for rapidly spinning protomagnetar models. On the other hand, detection for off-axis jets is challenging, even for a supernova at the Galactic Center. Measuring multiple decay lines in addition to the integrated luminosity over $\sim10$ days postbounce would allow for the ability to distinguish between models and shed light on central engine properties like magnetic field and spin.

Figures

Figures reproduced from arXiv: 2502.07888 by the authors.

**Figure 2.** FIG. 2. Optical depth ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. Abundances for the PM models used in this work. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: FIG. 4. Light curves of decay lines for the four different mod [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. Line emission from the decays of thermal nuclei, for the case of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: FIG. 6. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: FIG. 7. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: FIG. 8. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

Discussion (0). Continue with ORCID to comment.

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