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Observing Supernova Neutrino Light Curves with Super-Kamiokande.VI. A Practical Data Analysis Technique Considering Realistic Experimental Backgrounds

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Pith's one-line read Simulations of core-collapse supernova neutrinos in Super-Kamiokande, with realistic experimental backgrounds included, show that the time of the last detected event can differentiate between competing nuclear equations of state and…

desk verdict Useful incremental step adding realistic SK backgrounds to the Tlast method, but the 5σ background-rejection claim does not survive a trials-corrected Poisson check. read the letter →

arxiv 2505.19721 v3 pith:NUK5T5H4 submitted 2025-05-26 astro-ph.HE hep-ex

Fumi Nakanishi , Ken'ichiro Nakazato , Masayuki Harada , Yusuke Koshio , Ryuichiro Akaho , Yosuke Ashida , Akira Harada , Masamitsu Mori
show 4 more authors
Kohsuke Sumiyoshi Yudai Suwa Roger A. Wendell Masamichi Zaizen
This is my paper · ORCID
classification astro-ph.HEhep-ex
keywords Core-collapsesupernovaeSupernovaneutrinosNeutrinoastronomyNeutronstarsSuper-KamiokandeProto-neutronstarcoolingNuclearequationofstateBackward-timeanalysis
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 claims that the time of the last neutrino event seen by Super-Kamiokande from a nearby supernova can distinguish between competing nuclear equations of state and proto-neutron-star masses, even when realistic detector backgrounds are included. The authors build mock observations that combine simulated supernova-neutrino signals with measured background rates, apply the detector's fiducial-volume and spallation cuts, and define a last-event time $T_{\rm last}$ via a sliding time window with an energy threshold. If the claim holds, a single galactic supernova at about 10 kpc would yield a direct probe of the equation of state of dense nuclear matter, going beyond what total event counts alone can tell.

What carries the argument

The central mechanism is the $T_{\rm last}$ determination procedure: count events above an energy threshold $E_{\rm th}$ within a sliding time window of width $T_{\rm wid}$, advance the window forward in time, and define $T_{\rm last}$ as the time of the latest event in the last non-empty window. The pair $(T_{\rm wid},E_{\rm th})=(5\,\mathrm{s},8\,\mathrm{MeV})$ is chosen so that the selected last event is inconsistent with the measured background at more than $5\sigma$ significance, assuming a background rate of $8.2\times10^{-3}\,\mathrm{s}^{-1}$ in the fiducial volume after the spallation cut. The backward-time analysis then uses $T_{\rm last}$ as the time origin for cumulative event counts, and the time difference between the 500th-to-last and 1000th-to-last events serves as a statistically sharper observable.

What would settle it

Use SK's archived quiescent data to measure the background rate above 8 MeV in the fiducial volume after the spallation cut; if it differs from the rate derived from Mori et al. (2022), the $5\sigma$ selection thresholds and all $T_{\rm last}$ distributions shift. A quicker check is to rerun the mock pipeline with the background rate doubled and see whether the Shen-versus-Togashi separation in the $T_{\rm last}$ distributions survives.

Watch

Extended reading notes

Core claim

The paper's central discovery is that $T_{\rm last}$, the time of the last observed neutrino event selected with a 5-second sliding window and an 8 MeV energy threshold, carries enough information to differentiate between core-collapse supernova models with different proto-neutron-star masses and different nuclear equations of state. In particular, the Shen equation of state gives the shortest $T_{\rm last}$ and the Togashi equation of state the longest, with the LS220 and Furusawa-Togashi cases in between; the backward-time cumulative distribution from $T_{\rm last}$ and the time difference between the 500th-to-last and 1000th-to-last events sharpen the separation. A Bayesian calculation using these timing observables can constrain the equation of state, with shorter $T_{\rm last}$ indicating a lower central density and larger neutron-star radius, and longer $T_{\rm last}$ indicating abundant heavy nuclei near the surface.

Load-bearing premise

The load-bearing premise is that the background rate above 5 MeV in the fiducial volume after the spallation cut, $8.2\times10^{-3}\,\mathrm{s}^{-1}$ taken from Mori et al. (2022), is a known constant when choosing the 5 s / 8 MeV selection; if the real background rate or spectrum differs during a supernova burst, the $5\sigma$ thresholds and all $T_{\rm last}$ distributions shift.

Editorial extensions

If this is right

  • A galactic supernova at 10 kpc could yield a measured $T_{\rm last}$ that separates the Shen and Togashi equations of state, with shorter $T_{\rm last}$ implying a less compact neutron star and longer $T_{\rm last}$ implying heavy nuclei near the surface.
  • The backward-time cumulative distribution anchored at $T_{\rm last}$, and especially the time gap between the 500th-to-last and 1000th-to-last events, reduces statistical scatter and helps separate models with similar light curves such as LS220 and Furusawa-Togashi.
  • Late-phase neutrino emission depends mainly on proto-neutron-star mass and radius, not on the progenitor's zero-age main-sequence mass; changing $M_{\rm ZAMS}$ from 15 to 40 solar masses leaves the late-phase timing information essentially unchanged.
  • The same $T_{\rm last}$-based analysis can be applied to any neutrino detector with event-by-event timing, not only Super-Kamiokande.

Reading between the lines

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

  • The authors do not draw this conclusion, but the $T_{\rm last}$ sliding window is a one-number summary of the event-time series; using the full spectrum of inter-event intervals on the same mock data could sharpen EOS discrimination further than the $T_{500}$--$T_{1000}$ gap alone.
  • A testable extension is to apply the same background-aware framework to pre-supernova neutrinos from the silicon-burning phase, where the shorter emission window makes background treatment even more critical for an early-warning trigger.
  • Scaling the same simulation to a larger water Cherenkov detector with a bigger fiducial volume should push the distance at which EOS separation works beyond 10 kpc, because the signal scales with detector mass while the background rate per kiloton stays roughly constant.
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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. This paper develops a practical analysis framework for identifying the last supernova-neutrino event, Tlast, in Super-Kamiokande, with realistic backgrounds. Signal events are generated with SKSNSim for proto-neutron-star cooling models using four nuclear equations of state (Shen, LS220, Togashi, and Furusawa-Togashi) and several baryon masses, while background events are sampled from the in-situ SK measurement of Mori et al. (2022). After applying fiducial-volume and spallation cuts, the authors choose a time window Twid = 5 s and energy threshold Eth = 8 MeV, claim that these provide 5-sigma background rejection, and define Tlast as the last event found by a forward-sliding window. Tlast distributions from 1000 realizations are compared across models, and a backward-time analysis using the cumulative event count from Tlast and the time difference T500 - T1000 is used in a Bayesian model-selection calculation. The paper concludes that Tlast can differentiate core-collapse supernova models with different PNS masses and equations of state, and in particular that the Shen and Togashi EOSs can be effectively distinguished.

Significance. If the background-rejection step is quantitatively sound, this paper delivers a practical, ready-to-use recipe for the next galactic supernova and demonstrates that timing information alone carries EOS-discriminating power beyond the total event count. The strengths are the clearly specified Monte Carlo pipeline, the use of actual SK background rates from Mori et al. (2022), the large number of realizations, and the public release of the simulation code and neutrino light-curve data. The central new claim, however, rests on the unsupported assertion that background contamination is negligible, so the practical applicability claimed in the title and conclusion is not yet established.

major comments (3)
  1. [Section 3.3, Table 1] The 5-sigma background-rejection claim is not demonstrated by a transparent calculation. Section 3.2 gives the post-cut background rate as 8.2e-3 s^-1 above 5 MeV, and Section 3.3 states that Eth = 8 MeV rejects about 98% of background, yielding roughly 1.6e-4 s^-1 above 8 MeV. For the chosen Twid = 5 s, the expected number of background events per window is then about 8e-4, so the probability of observing at least one background event is about 8e-4, which is a roughly 3-sigma one-sided fluctuation rather than 5 sigma. The caption of Table 1 says all listed (Twid, Eth) pairs exclude background at greater than 5 sigma, but the Poisson calculation is not shown. Please provide the exact test, including whether it is one- or two-sided, which background rate is used, and how the Eth-dependent spectrum is integrated, and correct the criterion if the calculation does not reach 5 sigma.
  2. [Section 4.2, Figures 13 and 14] The assertion that the background impact in Figures 13 and 14 is negligible is unsupported because the promised comparison with background-free mock samples is not shown. The sliding-window algorithm searches the entire post-burst interval, so a lone background event after the true signal tail can define Tlast. With a background rate of approximately 1.6e-4 s^-1 above 8 MeV over a 200 s search, the expected number of such events is about 0.03, meaning a few percent of realizations will have a background event selected as Tlast. This biases Tlast late and preferentially affects the long-Tlast Togashi models that are central to the paper's discrimination claim. Please quantify the false-positive rate directly, report the with- and without-background Tlast distributions (for example by overlaying them), and revise the claim accordingly.
  3. [Section 3.2 and Section 3.3, Figure 3] The background rate and spectral shape are treated as fixed inputs with no uncertainty, yet they determine both the 5-sigma thresholds of Table 1 and all Tlast distributions. Since the background rate of 8.2e-3 s^-1 above 5 MeV is an empirical estimate, the robustness of the chosen Twid and Eth and of the final model-separation probabilities to plausible variations in this rate (for example a factor of two, or a different spectral index above 8 MeV) should be shown. Without such a sensitivity study, the claim that the analysis is realistic is not fully supported.
minor comments (5)
  1. [Section 5] In the conclusion, the symbol TSlast appears to be a typo for Tlast; please correct it.
  2. [Figures 13 and 14] The model labels in these figures are rendered as unreadable glyph sequences; please replace them with legible labels or a separate legend.
  3. [Section 3.3] The statement that Tlast is inconsistent with the measured background at more than 5 sigma significance should specify whether the significance is one-sided or two-sided and how the sliding-window search over time is treated.
  4. [Section 4.2, Equation (4)] The Bayesian probabilities are computed with PDFs obtained from the same simulation pipeline that generated the mock data; a sentence stating that the quoted percentages are an in-sample, idealized upper bound on discrimination would prevent over-interpretation.
  5. [Section 1] The first paragraph contains a stray phrase, 'and makes their observation', after a citation; please fix the grammar.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the Tlast analysis is a forward-model sensitivity study; the claimed model discrimination follows from simulated signal properties, not from fitting or self-citation.

full rationale

The paper’s derivation chain is a forward simulation: PNS cooling models from the publicly released Paper I/II simulations are input to SKSNSim to generate signal events; backgrounds are drawn from the measured SK rate of Mori et al. (2022); Tlast is defined by a sliding-window algorithm whose (Twid, Eth) are chosen solely from the background rate under Poisson statistics; and the Tlast PDFs and Bayesian posteriors are computed from the same simulated samples. No parameter is fitted to the claimed outcome, and no uniqueness theorem or prior result by the authors is invoked to forbid alternatives. The fact that the Bayesian PDFs are generated from the same models used to produce mock observations makes this an in-sample sensitivity study, not a circular derivation: the EOS separation visible in Tlast is a property of the forward-modeled signal, not an input assumption. Self-citations to Papers I/II supply input physics and methods, but the central claim is derived by simulation rather than assumed from those citations. The skeptic’s concern about the unquantified 5-sigma background/trials correction is a statistical robustness issue, not a circularity, and does not affect this verdict.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

No new particles, fields, or forces are postulated. Tlast is an analysis observable, not an invented physical entity. The central claim rests mainly on prior PNS cooling simulations, the adopted SK background rate, and several explicitly chosen analysis thresholds.

free parameters (6)
  • Analysis time window Twid = 5 s
    Chosen from Table 1 among pairs satisfying the 5-sigma background-rejection criterion; changing it shifts Tlast distributions as shown in Figure 7.
  • Energy threshold Eth = 8.0 MeV
    Chosen together with Twid to achieve 5-sigma background rejection while keeping signal efficiency near 47%; it affects Tlast and the backward-time curves.
  • 5-sigma detection significance requirement = 5 sigma (Poisson)
    Adopted to define acceptable Twid/Eth pairs; it is a stated analysis choice, not derived from the data.
  • Supernova distance D = 10 kpc
    Fixed scenario; event counts scale as D^-2, so Tlast values would shift for other distances.
  • Spallation cut signal loss = 20%
    Applied as a random reduction of signal events following SK studies (Abe et al. 2024); it reduces late-time statistics and affects Tlast.
  • Uniform model prior = 1/32 per model
    Assumed for the Bayesian selection; not physically motivated but explicitly stated in Section 4.2.
assumptions (5)
  • domain assumption PNS cooling light curves from Papers I/II (flux-limited diffusion, spherical symmetry) faithfully represent late-phase neutrino emission.
    Invoked in Section 2.1; the models ignore multi-D convection and full Boltzmann transport, so EOS differences in Tlast may differ in reality.
  • domain assumption The SK background rate above 5 MeV after FV and spallation cuts (8.2e-3 s^-1) from Mori et al. (2022) is constant during a supernova burst.
    Used to set Table 1 thresholds; burst-time variations in spallation or radioactivity could invalidate the 5-sigma selection.
  • domain assumption Initial conditions for Furusawa-Togashi models are identical to Togashi models because early PNS matter is uniform.
    Section 2.2, justified by Sumiyoshi et al. (2023); if non-uniform matter appears early, the comparison shifts.
  • standard math Strumia-Vissani IBD cross section and SKSNSim detector response are accurate for sub-100 MeV neutrinos.
    Equation (2) and Section 3.1; accepted toolkit in the field.
  • standard math Event counts follow Poisson statistics for background rejection.
    Section 3.3; reasonable for rare events but ignores systematics.

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Cite this review

Pith. "Pith review of Observing Supernova Neutrino Light Curves with Super-Kamiokande.VI. A Practical Data Analysis Technique Considering Realistic Experimental Backgrounds." pith.science (2026). https://pith.science/paper/NUK5T5H4

@misc{pith2026250519721,
  author       = {Pith},
  title        = {Pith review of: Observing Supernova Neutrino Light Curves with Super-Kamiokande.VI. A Practical Data Analysis Technique Considering Realistic Experimental Backgrounds},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NUK5T5H4}},
  note         = {Machine review of arXiv:2505.19721}
}
read the original abstract

Neutrinos from supernovae, especially those emitted during the late phase of core collapse, are essential for understanding the final stages of massive star evolution. We have been dedicated to developing methods for the analysis of neutrinos emitted during the late phase and observed at Super-Kamiokande (SK). Our previous studies have successfully demonstrated the potential of various analysis methods in extracting essential physical properties; however, the lack of background consideration has limited their practical application. In this study, we address this issue by incorporating a realistic treatment of the experimental signal and background events with the on-going SK experiment. We therefore optimize our analysis framework to reflect realistic observational conditions, including both signal and background events. Using this framework we study several long-time supernova models, simulating the late phase neutrino observation in SK and focusing in particular on the identification of the last observed event. We discuss the possibility of model discrimination methods using timing information from this last observed event.

Figures

Figures reproduced from arXiv: 2505.19721 by the authors.

Figure 1
Figure 1. Luminosity (upper) and average energy (lower) of ¯νe emitted during PNS cooling as a function of time after the bounce. The left panel is for PNS models with a baryon mass of Mb = 1.62M⊙, where thin and thick lines correspond to models with MZAMS = 15M⊙ and 40M⊙, respectively, and solid (black), dashed (green), dotted-dashed (red), and dotted (blue) lines correspond to models with the Shen EOS, the Togashi EOS, the … view at source ↗
Figure 2
Figure 2. Schematic diagram of the Tlast determination method. Dwall and Eth represent the distance from the wall of the inner tank, and the energy threshold, respectively. A 20% random reduction is applied to simulate the expected signal loss due to spallation background rejection. The blue blocks indicate the flow of the Tlast determination method, while the green blocks represent the generated events [PITH_FULL_IMAGE:figu… view at source ↗
Figure 3
Figure 3. Background rate for the FV (orange), FV with spallation cut (violet), and outside FV (black) samples in SK. Background rates are generated according to Mori et al. (2022). In the present analysis, we use the background rate above 5 MeV following that study. cut are applied to ensure a low-background environment. Averaged over all models, approximately 69% of the signal events remain after applying the FV cut, and ab… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: An example scatter plot showing the visible energy of the observed events in SK as a function of time from the supernova explosion based on a single simulation. Signal events, represented by the orange points, and background events, represented by the gray points, are …
Figure 5
Figure 5. Figure 5: T true last distribution for PNS models with a baryon mass of Mb = 1.40M⊙, represented as follows: black for the Shen EOS, red for the LS220 EOS, blue for the Furusawa￾Togashi EOS, and green for the Togashi EOS case. This plot is made from 1000 MC realizations; the ver…
Figure 6
Figure 6. Figure 6: Schematic diagram of Tlast determination method. It represents supernova neutrino and background events plotted over time, with their corresponding energy values represented on the vertical axis. Green box shows supernova neutrino events whose energy is more than Eth a…
Figure 7
Figure 7. Figure 7: The Tlast distribution for each combination of Twid and Eth. Panel (a), (b), (c), and (d) correspond to Shen EOS, LS220 EOS, Furusawa-Togashi EOS, and Togashi EOS, respectively. Here, the PNS models with mass of Mb = 1.40M⊙ and MZAMS = 15M⊙ are shown [PITH_FULL_IMAGE:…
Figure 8
Figure 8. Figure 8: Tlast distribution. The black, red, blue, and green lines represent Shen EOS, LS220 EOS, Furusawa-Togashi EOS, and Togashi EOS, respectively. The horizontal axis shows Tlast for each MC realization and the vertical axis shows the number of MC realizations in 1 sec bins…
Figure 9
Figure 9. Figure 9: Average interval between signal events as a func￾tion of time after the bounce. The black, red, blue, and green represent Shen EOS, LS220 EOS, Furusawa-Togashi EOS, and Togashi EOS, respectively. profile depending on the EOS model and PNS mass. In particular, the Shen …
Figure 10
Figure 10. Figure 10: Backward time analysis comparing different EOSs. The horizontal axis represents backward time, which sets the last observed event as the time origin, and the vertical axis represents the cumulative event number from that event. The black, red, blue, and green represen…
Figure 11
Figure 11. Figure 11: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 12
Figure 12. Figure 12: The time difference distribution between the 500-th-to-last event and 1000-th-to-last event. The black, red, blue, and green lines represent Shen, LS220, Furusawa-Togashi, and Togashi EOS, respectively. The horizontal axis shows the difference between time of the 500-…
Figure 13
Figure 13. Figure 13: The probability of model selection for each model (vertical axis) given a certain Tlast (horizontal axis), with a bin width of 4 sec. The color gradients represent different models: Shen (gray to black), LS220 (light red to red), Furusawa-Togashi (light blue to blue),…
Figure 14
Figure 14. Figure 14: The probability of model selection (vertical axis) given a certain time difference (horizontal axis), with a bin width of 0.5 sec. The color gradients are the same as [PITH_FULL_IMAGE:figures/full_fig_p013_14.png]

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