{"id":"89e218ab-5fdb-419e-a302-e10bae96a2f4","arxiv_id":"1908.06953","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":11,"one_line_summary":"Structured gamma-ray burst jets can emit far more neutrinos off-axis than uniform-jet scaling predicts, with GRB 170817A as the test case.","lead":"The authors derive how much high-energy neutrino emission a gamma-ray burst produces when observed from the side, for jets with internal structure rather than a uniform cone. They apply the result to the neutron-star merger event GRB 170817A and find sideways neutrino emission can be much larger than simple scalings suggested.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Off-axis neutrino enhancement hinges on applying the afterglow-inferred jet profile and an ad hoc low-Gamma efficiency model to the prompt phase; alternative prompt structures may erase it.","rationale":"The reader's weakest assumption identifies the same load-bearing point: the afterglow-derived jet model is transferred to the prompt internal-shock phase, and the internal photon spectrum is treated with ad hoc peak models. My reading of the derivation supports the reader's verdict: Eqs. (1)-(20) are a standard and correct account of relativistic Doppler boosts and the p-gamma opacity treatment, and the paper is explicit that the approximate scaling relation Eq. (23) is only valid for mildly varying internal spectra, which is why the GRB 170817A predictions use the exact expression Eq. (20). The main numerical claim is therefore not a consequence of the approximation but of the adopted prompt-jet physics. In particular, the 10-20 degree tail with Gamma of order a few is what produces the off-axis enhancement; this tail is only weakly constrained by the afterglow data, and its neutrino yield is amplified by the quadratic dependence on the local energy and the steep inverse-Gamma scaling in the optically thin regime. The paper acknowledges the tension between model (a) and the observed on-axis peak distribution and introduces model (b) to mitigate it, but it does not test how the final off-axis fluence changes under plausible variations of the jet profile, the dissipation efficiency, or the photon target model. Because the predictions lie far below current neutrino limits, the scientific value of the paper is the relative enhancement, and that relative enhancement is conditional on the prompt jet structure. Since the reader's verdict is already CONDITIONAL with this same concern, no adjustment to the verdict is needed.","tokens_in":18646,"tokens_out":15566,"duration_ms":158525,"concrete_test":"Recompute the off-axis muon-neutrino fluence at theta_v=15 degrees for the GRB 170817A model of Section 5.2 with the prompt jet structure replaced by the alternative afterglow-inferred structures of Lazzati et al. (2018), Troja et al. (2018), and Lamb et al. (2019), keeping all other model choices fixed, and also vary eta_infinity in Eq. (A6) between 0.05 and 0.5. If the 0.1-10 TeV off-axis fluence changes by more than an order of magnitude or falls below the top-hat jet off-axis expectation, the claimed enhancement is not robust to the prompt-jet assumptions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central numerical result, that the off-axis neutrino fluence of GRB 170817A at 15 degrees is comparable to the on-axis prediction in the TeV range and orders of magnitude above the off-axis uniform-jet expectation, is dominated by emission from the mildly relativistic tail at jet angles of about 10-20 degrees (Fig. 3, Fig. 4). In this tail the p-gamma opacity is low, and Eq. (28) together with Eq. (27) implies a neutrino energy density that scales roughly as eta_IC(theta*)^2 (dE*/dOmega)^2 / Gamma(theta*)^5. This makes the claimed enhancement highly sensitive to the prompt-phase jet structure and to the internal-shock efficiency model of Eq. (A6) with eta_infinity=0.2. The paper adopts the afterglow-derived structured jet of Ghirlanda et al. (2019) without propagating its parameter uncertainties and without testing alternative afterglow fits, even though nothing guarantees that the same angular profile of kinetic energy and Lorentz factor holds at the internal-shock dissipation radius of the prompt emission. The paper itself notes that the constant co-moving peak model (a) predicts an on-axis peak photon energy of about 20 MeV, in tension with the observed GRB peak distribution, and introduces model (b) ad hoc. If the true prompt jet is wider, has a slower or steeper tail, or has a different low-Gamma efficiency, the margins shown in Fig. 4 can shrink or disappear. The concern is not about the Doppler-integral formalism, which is standard, but about the input physics that makes the GRB 170817A illustration interesting.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper derives a general relation between the internal emissivity of a relativistic, axisymmetric structured jet and the observed photon or neutrino fluence at an arbitrary viewing angle, using the standard D^3 Doppler transformation and a thin-shell geometry (Eqs. 1-20). It introduces a jet scaling factor Njet and an average Doppler factor Djet, leading to a revised off-axis scaling relation for particle fluences (Eq. 23) that reduces to the naive (D_off/D_on)^3 scaling only for top-hat jets at large viewing angle. The formalism is then applied to neutrino production from p-gamma interactions in internal shocks, with a numerical illustration for GRB 170817A using the structured jet profile inferred from afterglow fits by Ghirlanda et al. (2019). The central numerical result is that the predicted off-axis neutrino fluence at theta_v = 15 degrees is comparable to the on-axis prediction in the TeV range and orders of magnitude above the expectation from an off-axis observation of a uniform jet, because low-opacity regions at jet angles of about 10-20 degrees contribute strongly.","tokens_in":18990,"tokens_out":10409,"duration_ms":96585,"significance":"If the derivation is accepted, the paper provides a clean and useful generalization of the standard on-axis uniform-jet neutrino fluence calculation, and it clarifies why structured jets can produce neutrino angular distributions that are much broader than the gamma-ray angular distribution. The exact expression (20), the reduction of the approximate scaling relation (23) to known limits, and the explicit identification of the assumptions behind the approximation are genuine strengths. The application to GRB 170817A is a concrete and in principle falsifiable model prediction, although the predicted fluence is currently orders of magnitude below the available ANTARES, Auger, and IceCube upper limits shown in Fig. 4. The main weakness is not the Lorentz-transformation formalism, which is standard and internally consistent, but the dependence of the numerical result on unquantified input assumptions about the prompt-phase jet structure and the internal photon target spectrum.","major_comments":[{"comment":"The headline claim that the off-axis neutrino fluence at theta_v = 15 degrees is comparable to the on-axis prediction in the TeV range and orders of magnitude above the uniform-jet expectation is driven by low-opacity emission from jet angles of about 10-20 degrees (Fig. 3). In this regime Eq. (29) gives dE_nu/dOmega proportional to Gamma^{-5} (dE_IC/dOmega)^2, so the result is extremely sensitive to the Lorentz-factor and energy profiles adopted from the afterglow fit of Ghirlanda et al. (2019) and to the internal-shock efficiency model of Eq. (A6) with eta_infinity = 0.2. The afterglow fit constrains the external forward shock, not the prompt internal-shock dissipation radius, and the manuscript neither propagates the fit uncertainties nor tests alternative structured-jet profiles such as those of Lazzati et al. (2018), Troja et al. (2018), Margutti et al. (2018), and Lamb et al. (2019). A quantitative variation of s1, s2, Delta-theta, and Gamma-hat within the allowed ranges is needed to determine whether the claimed enhancement is a robust prediction or an artifact of the chosen prompt-jet model.","section":"§5.2, Fig. 4; Eqs. (16), (17), (29), (A6)"},{"comment":"The neutrino fluence calculation requires the internal photon target spectrum, which is fixed by one of two ad hoc peak-energy models. The paper itself states that model (a) implies an on-axis photon peak of about 20 MeV, in tension with the Fermi-GBM GRB peak-energy distribution, and model (b) is introduced phenomenologically; Fig. 4 shows that the two models change the on-axis neutrino fluence by up to two orders of magnitude at EeV energies. The conclusion that the off-axis and on-axis fluences are 'similar in the TeV range' should therefore be accompanied by a demonstration that this comparison is insensitive to the target-spectrum model, or the claim should be explicitly hedged as applying only under one of the adopted spectral assumptions.","section":"§5.1, Eqs. (32)-(33), Fig. 4"},{"comment":"The approximate scaling relation (23) is derived under the assumption that the relative emission spectrum n'(theta*, epsilon')/u'(theta*) is nearly angle-independent, and the paper correctly notes in Section 4 that this condition can fail in structured jets with strong local variations of magnetic fields and photon densities. Since the paper recommends the exact expression (20) for such cases, the numerical neutrino results should state explicitly whether they are obtained from Eq. (20) or from the approximate Eq. (23), particularly because the approximate relation is one of the paper's stated main results and is presented without this caveat in the conclusions.","section":"§4, Eq. (23)"}],"minor_comments":[{"comment":"The sentence 'For low-opacity (tau_pgamma >> 1) regions' should read 'tau_pgamma << 1'; the opposite inequality is used in the same paragraph and in Fig. 3.","section":"§5.2"},{"comment":"There is a typo in 'GRB 170717A'; it should be 'GRB 170817A'.","section":"§5.2"},{"comment":"The reference to 'the thick green line in Fig. 4' appears to be a mis-reference: the angular distributions of neutrino emissivity are shown in Fig. 3, whereas Fig. 4 shows fluence spectra.","section":"§5.2"},{"comment":"The conclusion states that the average Doppler factor is 'defined by Eq. (23)', but Djet is defined in Eq. (22); this should be corrected.","section":"§6"},{"comment":"The name 'Thompson scattering' appears in a few places; it should be 'Thomson scattering'.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The formalism in Sections 2 and 3 is sound and likely useful to the community, so the paper should not be rejected. The decision hinges on whether the authors can convert the numerical illustration for GRB 170817A into a robustness-tested prediction, or alternatively soften the abstract and conclusions to clearly label the enhancement as model-dependent. I would encourage the editor to request the parameter scans and the explicit distinction between exact and approximate calculations as part of the revision; without those, the central quantitative claim is not yet supported at the level claimed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Markus,\n\nThe thing to know: the lasting value is the formalism and the scaling relation, not the GRB 170817A neutrino number. The derivation from emissivity to fluence for arbitrary viewing angles and jet structures (Eqs. 1-22) is standard in outline—building on Salafia, Granot, and others—but it is done cleanly and it fixes a real gap. The improved scaling relation Eq. (23) shows when the naive D^3 rescaling used earlier is wrong: it only works for top-hat jets at large viewing angle. The paper's Eq. (29) is the more interesting result: in low-opacity regions the neutrino energy scales as (1/Gamma^5)(dE_IC/dOmega)^2, making off-axis structured jets far more emissive in neutrinos than uniform jets. That qualitative point is solid.\n\nThe authors are honest that Eq. (23) requires a mildly varying spectrum across the shell, and for the GRB 170817A application they use the exact expression (20), so that concern does not bite. They also normalize to the observed gamma-ray fluence, so there is no circularity in the neutrino prediction.\n\nThe soft spots are where the stress-test lands. The quantitative claim that the 15-degree off-axis fluence is comparable to on-axis in the TeV range is driven by emission from the jet tail at theta* ~ 10-20 degrees, where the p-gamma opacity is low. The calculation adopts the Ghirlanda et al. (2019) afterglow-fit jet profile and the Appendix-A efficiency model (eta_infinity=0.2) without propagating parameter uncertainties or testing alternative afterglow fits. Nothing guarantees that the angular profile of kinetic energy and Lorentz factor at the internal-shock radius is the same as the late-time afterglow structure. If the true prompt jet is wider, slower, or has a different low-Gamma efficiency, the enhancement can shrink. That is a genuine uncertainty, not a fatal flaw—the authors flag the model dependence, and the predicted fluence sits orders of magnitude below current limits anyway, so the result is a fair illustration rather than a testable prediction.\n\nMinor points: the two ad hoc photon-peak models (a) and (b) are exactly that—the paper admits model (a) implies an on-axis peak at 20 MeV, in tension with observations. The off-axis result depends weakly on this choice, so it is a minor issue. The modified SOPHIA code is not released, so the cascade calculation is not independently reproducible; that is a small but real loss. The citation pattern is solid, with Salafia, Biehl, and Ghirlanda as the right anchors.\n\nWho this is for: GRB neutrino modelers and the multimessenger community doing kilonova and off-axis jet follow-up. It deserves a serious referee. My recommendation: send it out, and ask for a robustness section that varies the jet profile and efficiency parameters, plus code or numerical tables behind Fig. 4.","headline":"Clean Doppler-integral formalism and a useful scaling relation for off-axis structured jets, with an honest but model-dependent GRB 170817A application.","tokens_in":19587,"tokens_out":4808,"would_cite":true,"duration_ms":47130,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"For structured gamma-ray burst jets, neutrinos observed far off the jet axis can arrive at fluence comparable to an on-axis view, and far above the naive uniform-jet off-axis rescaling.","keywords":["gamma-ray bursts","high-energy neutrinos","structured jets","off-axis emission","internal shocks","proton-photon interactions","GRB 170817A","neutrino fluence"],"falsifier":"Recompute the off-axis neutrino fluence using Eq. (20) with a prompt-emission-constrained jet profile for GRB 170817A, of the kind fixed by the gamma-ray time structure and Doppler factor rather than by the afterglow fit; if the TeV fluence at $\\theta_v\\simeq 15^\\circ$ falls to within a factor of a few of the naive uniform-jet $D_{\\rm off}^3/D_{\\rm on}^3$ rescaling, the claimed enhancement rests on the afterglow-profile assumption and would not survive alternative prompt-jet structures.","tokens_in":18384,"feed_emoji":"🌌","tokens_out":9908,"duration_ms":96972,"temperature":0.7,"pith_summary":"The paper tries to establish that neutrino fluence from gamma-ray bursts cannot be treated with the usual on-axis uniform-jet formula when the jet is structured and the observer is off-axis. It derives an exact angular integral for the fluence of any particle species emitted by thin relativistic shells and packages it into a revised scaling relation using a jet factor and an average Doppler factor. Its central result is that in structured jets the neutrino emission has its own angular dependence, set by the proton-photon opacity, which is much broader and stronger at intermediate angles than the gamma-ray emission. Applied to GRB 170817A with an afterglow-inferred structured jet, the predicted off-axis neutrino fluence at about 15 degrees is similar to the on-axis prediction in the TeV range and orders of magnitude larger than the expected fluence from an off-axis uniform jet.","feed_headline":"Off-axis GRB neutrinos can rival on-axis brightness","feed_subtitle":"Structured jets break the naive uniform-jet rescaling, making off-axis neutrino fluence far larger.","key_machinery":"The machinery is the Doppler-boosted fluence integral for thin relativistic shells, $F = (1+z)/(4\\pi d_L^2)\\int d\\Omega_*\\, D^3(\\Omega_*)/\\Gamma(\\theta_*)\\, dE_*/d\\Omega_*$, from which the paper defines the jet scaling factor $N_{\\rm jet}$ and average Doppler factor $D_{\\rm jet}$ and derives the revised off-axis scaling $F_{\\rm off}(\\epsilon)\\simeq (N_{\\rm jet}(\\theta_v)/N_{\\rm jet}(0))\\, \\eta^{-2} F_{\\rm on}(\\epsilon/\\eta)$ with $\\eta = D_{\\rm jet}(\\theta_v)/D_{\\rm jet}(0)$. For neutrinos the load-bearing new ingredient is the proton-photon opacity $\\tau_{p\\gamma}(\\theta_*) \\propto \\Gamma^{-5}(\\theta_*)\\, dE_\\gamma^*/d\\Omega_*$, which gives the neutrino angular distribution a different, broader profile than the gamma-ray distribution. That opacity scaling, rather than geometry alone, produces the claimed off-axis enhancement.","core_discovery":"The central claim is that for a structured jet, the neutrino fluence is not obtained by rescaling an on-axis calculation with a single Doppler factor; one must integrate the Doppler-boosted emissivity over the jet and, for neutrinos, include an angular-dependent proton-photon opacity. In the low-opacity regime, the neutrino energy per solid angle scales as $(dE_{\\rm IC}/d\\Omega_*)^2/\\Gamma^5$, which enhances emission from jet angles around 10 to 20 degrees relative to the gamma-ray brightness. For the structured jet model inferred from the afterglow of GRB 170817A ($s_1=5.5$, $s_2=3.5$, $\\Delta\\theta\\simeq 3.4^\\circ$, $\\hat{\\Gamma}\\simeq 250$, $\\theta_v\\simeq 15^\\circ$), the paper predicts that the off-axis muon-neutrino fluence is comparable to the on-axis prediction in the TeV energy range and orders of magnitude above the off-axis uniform-jet expectation.","pith_inferences":["Because the angular profile of neutrino energy follows $\\tau_{p\\gamma}\\propto \\Gamma^{-5}$ in the low-opacity regime, the same broadening should apply to other products of proton-photon interactions, such as ultra-high-energy cosmic rays that escape before energy losses.","The paper's comparison assumes the afterglow-derived jet also describes the prompt outflow; if future prompt-emission fits for GRB 170817A favor a narrower core, the enhancement at 15 degrees would shrink, and comparing prompt and afterglow structures becomes a direct test of jet dissipation physics.","Using the same formalism with alternative short-GRB jet profiles, for example a sharper core or different power-law indices, would bracket how generic the off-axis enhancement is across structured-jet models."],"forward_implications":["The reference signal for neutrino searches from compact-binary mergers must be the structured-jet fluence, not the on-axis uniform-jet prediction rescaled by a single Doppler factor; using the latter can underestimate the expected off-axis signal by orders of magnitude.","Equation (23) gives a practical route to convert existing on-axis neutrino calculations into off-axis predictions for any jet structure and viewing angle whenever the internal spectrum varies only mildly across the shell.","For GRB 170817A-like events, the TeV off-axis neutrino fluence can be comparable to the on-axis fluence, so a large viewing angle does not by itself suppress the neutrino signal as much as it suppresses the gamma-ray signal.","The predicted fluence remains below the current 90% confidence upper limits, so the immediate consequence is not a detection but a corrected expected signal for stacking and future searches."],"supporting_citations":[{"why":"Supplies the afterglow-fitted structured jet model (s1=5.5, s2=3.5, Δθ≈3.4°, Γ≈250, E≈2.5e52 erg, θv≈15°) on which the GRB 170817A neutrino predictions are built.","marker":"Ghirlanda et al. 2019"},{"why":"Defines the on-axis internal-shock proton-photon neutrino production formalism that this paper generalizes to arbitrary viewing angles and jet structures.","marker":"Waxman & Bahcall 1997"},{"why":"Provides the Doppler-cubed fluence relation for a uniformly moving source that Eq. (10) and the structured-jet integral extend.","marker":"Granot et al. 2002"},{"why":"Introduces the dE_*/dΩ parametrization of jet energy and the angular fluence derivation used in Eq. (12).","marker":"Salafia et al. 2015"},{"why":"Provides the Fermi-GBM prompt spectrum (α≈0.14, ε_peak≈215 keV) and fluence that normalize the gamma-ray and neutrino emission.","marker":"Goldstein et al. 2017"},{"why":"Provides the naive off-axis η-scaling applied to GRB 170817A neutrino predictions and the combined 90% confidence upper limits used for comparison.","marker":"Albert et al. 2017"},{"why":"Supplies the internal-shock energy-dissipation efficiency used in Appendix A to distribute kinetic energy into internal energy.","marker":"Kobayashi et al. 1997"},{"why":"Supplies the SOPHIA Monte-Carlo generator used to compute the proton-photon neutrino spectra in Eq. (B7).","marker":"Mücke et al. 2000"},{"why":"Supplies the treatment of synchrotron losses of secondary charged particles before decay in the neutrino cascade calculation.","marker":"Lipari et al. 2007"}],"fun_headline_variants":["Off-axis GRB neutrinos match on-axis for structured jets","Structured jets make off-axis GRB neutrinos rival on-axis","Neutrino fluence from off-axis GRB jets: structured jets rival on-axis","GRB 170817A: off-axis neutrino fluence rivals on-axis","Structured jets: off-axis GRB neutrinos shine as bright"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the afterglow-derived jet structure and Lorentz-factor profile also describe the prompt-emission outflow at the internal-shock radius, and that the internal photon target spectrum is captured by one of the two adopted peak models; if the prompt jet is narrower, slower, or has a different photon spectrum, the claimed off-axis neutrino enhancement can weaken or disappear.","fun_headline_variants_meta":{"raw":{"variants":["Off-axis GRB neutrinos match on-axis for structured jets","Structured jets make off-axis GRB neutrinos rival on-axis","Neutrino fluence from off-axis GRB jets: structured jets rival on-axis","GRB 170817A: off-axis neutrino fluence rivals on-axis","Structured jets: off-axis GRB neutrinos shine as bright"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001144,"raw_usage":{"total_tokens":4709,"prompt_tokens":871,"completion_tokens":3838,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":487,"completion_tokens_details":{"reasoning_tokens":3742}},"tokens_in":487,"tokens_out":3838,"duration_ms":25285,"temperature":1.0,"reasoning_tokens":3742,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:30:23.473758+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the off-axis neutrino fluence using Eq. (20) with a prompt-emission-constrained jet profile for GRB 170817A, of the kind fixed by the gamma-ray time structure and Doppler factor rather than by the afterglow fit; if the TeV fluence at $\\theta_v\\simeq 15^\\circ$ falls to within a factor of a few of the naive uniform-jet $D_{\\rm off}^3/D_{\\rm on}^3$ rescaling, the claimed enhancement rests on the afterglow-profile assumption and would not survive alternative prompt-jet structures.","supporting_citations":[{"cited_title":"Rev.] 10.1103/PhysRevD.75.123005 , D75, 123005","cited_arxiv_id":null,"evidence_quote":"Supplies the treatment of synchrotron losses of secondary charged particles before decay in the neutrino cascade calculation."}],"review_version":1}