Red Supergiant problem viewed from the nebular phase spectroscopy of type II supernovae

Keiichi Maeda; Qiliang Fang; Takashi J. Moriya

REVIEW 3 major objections 4 minor 2 cited by

Red Supergiant problem viewed from the nebular phase spectroscopy of type II supernovae

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper claims that nebular [O I] spectroscopy of 50 Type II supernovae yields a luminosity distribution for their red supergiant progenitors with an upper cutoff at log L/Lsun = 5.21, making the red supergiant problem statistically…

desk verdict A genuinely new nebular-spectroscopy cross-check on the RSG problem, with an honest but conditional 2–3 sigma claim that rests on faint-end completeness and a 12-SN calibration. read the letter →

arxiv 2504.14502 v1 pith:IGBHLT7Q submitted 2025-04-20 astro-ph.HE

Qiliang Fang , Takashi J. Moriya , Keiichi Maeda This is my paper · ORCID

classification astro-ph.HE

keywords redsupergiantproblemTypeIIsupernovaenebularspectroscopy[OI]emissionprogenitormassdistributionmass-luminosityrelationcore-collapsesupernovaprogenitors

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 red supergiant problem is real: across 50 Type II supernovae whose late-time spectra are used to infer progenitor zero-age main-sequence masses, the derived luminosity distribution cuts off at log L/Lsun = 5.21 (+0.09, -0.07), with no progenitor above 5.5. The absence of bright red supergiant progenitors is statistically significant at the 2–3 sigma level, and converting the cutoff through stellar mass–luminosity relations gives an upper ZAMS mass of about 20.6 solar masses. If correct, this independent nebular-spectroscopy route agrees with pre-SN imaging and plateau light-curve modeling, pointing to a physical cause such as failed explosions or envelope stripping rather than a purely observational artifact.

What carries the argument

The load-bearing object is the fractional [O I] flux f[O I] (and its H-alpha-regulated form f[O I]/(1 - f_Halpha)), measured from standardized nebular spectra and compared with single-red-supergiant spectral model tracks for 12, 15, and 19 solar-mass progenitors. Because f[O I] is a relative flux, it is insensitive to distance, flux calibration, and moderate extinction. The authors convert f[O I] into a nebular ZAMS mass, then use the overlap between nebular spectroscopy and pre-SN imaging to build an empirical mass–luminosity relation, deliberately avoiding code-dependent oxygen-mass-to-luminosity conversions that scatter by roughly 0.2 dex. They show the inferred luminosity distribution is invariant under affine reparameterizations of the nebular mass scale, provided the transformed masses stay within 9–25 solar masses, which is what makes the upper luminosity cutoff robust to spectral-model and initial-condition uncertainties.

What would settle it

A single Type II supernova with a securely measured progenitor luminosity above log L/Lsun = 5.5 (equivalent to a ZAMS mass above about 25 solar masses) whose nebular [O I] flux also places it above the 19-solar-mass track would contradict the claimed upper cutoff. A less demanding check is to recompute the 12-object calibration using multi-band pre-SN luminosities that correct the single-band underestimates discussed for some red supergiants; if the corrected relation pushes the fitted upper cutoff above 5.5, or moves the 99.8th percentile above 5.44, the reported deficit disappears.

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Extended reading notes

Core claim

Using the fractional flux of the nebular [O I] doublet relative to the 5000–8500 Angstrom spectrum, the authors assign each of 50 Type II supernovae a zero-age main-sequence mass distribution, combining two limiting measurements: the raw fractional flux and the same quantity with the H-$\alpha$ line removed. They calibrate the transformation from this spectroscopically inferred mass to red supergiant luminosity on 12 supernovae with pre-SN images, obtaining a strong rank correlation after excluding one outlier, then apply it to the full sample. The resulting luminosity distribution, fit with a bounded power law dN/dlogL proportional to L^(1+Gamma_L), has an upper cutoff log Lup = 5.21 (+0.09, -0.07), implying that the lack of progenitors above log L = 5.5 is significant at 2–3 $\sigma$. No individual object has median log L above 5.5, and the brightest inferred progenitor is at 5.33 (+0.21, -0.18). Under the single-red-supergiant assumption and the KEPLER mass–luminosity relation, this cutoff corresponds to an upper ZAMS mass of 20.63 (+2.42, -1.64) solar masses, consistent with independent upper limits near 18–23 solar masses from pre-SN imaging and plateau light-curve modeling.

Load-bearing premise

The whole argument rests on the assumption that the fractional [O I] flux from the adopted single-red-supergiant nebular models tracks oxygen mass, and therefore ZAMS mass, monotonically, and that the mass–luminosity relation fitted with only twelve overlapping objects—whose pre-SN luminosities are taken at face value—represents the entire Type II supernova population.

Editorial extensions

If this is right

A hard upper luminosity cutoff near log L = 5.2 implies that stars above roughly 20–25 solar masses rarely die as Type II supernovae with intact hydrogen envelopes.
The consistency among nebular spectroscopy, pre-SN imaging, and plateau light-curve modeling narrows the allowed explanation to physics that removes or quenches the most massive red supergiants: failed explosions, eruptive mass loss, or binary stripping.
The H-alpha-regulated form of the [O I] fractional flux provides a route to use nebular spectroscopy even for progenitors with partially stripped envelopes or circumstellar interaction, since it removes the most contaminated spectral line.
Because the [O I] fractional flux is distance- and extinction-independent, the method can be extended to larger samples from current and future transient surveys without requiring deep pre-SN archival images for every event.
If the cutoff is physical, searches for failed supernovae or disappearing massive stars should find them preferentially in the 20–30 solar-mass range, and the rate of such events should roughly match the missing fraction implied by the luminosity function.

Reading between the lines

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

If the cutoff reflects explodability rather than mass loss, surveys for disappearing stars should recover a missing fraction of Type II progenitors concentrated just above about 20 solar masses; the paper does not predict this rate, but its luminosity function quantifies the gap.
The invariance of log L under affine transformations of the nebular mass scale suggests that future improvements to nebular modeling will shift the inferred masses without moving the luminosity cutoff; reanalysis with new model grids would test this directly.
Because the calibration rests on pre-SN luminosities for only 12 objects, a multi-band bolometric campaign for a handful of future nearby Type II supernovae would either harden or dissolve the reported 2–3 sigma significance.
The same fractional-flux technique could be applied to stripped-envelope or superluminous supernovae that show oxygen nebular lines, but it would need an independent mass–luminosity calibration for those classes.

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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

Good paper to know about. It does something not done before: it takes a 50-SN nebular [O I] sample, converts to MZAMS via the Jerkstrand models, calibrates an empirical MZAMS-logL relation using 12 SNe with pre-SN imaging, and fits a bounded power-law to the resulting luminosity distribution. The headline result—logLup = 5.21 with the RSG problem at 2–3 sigma—is a new statistical statement, and the methods are transparent enough to follow. The robustness tests are a real strength: affine transformations of the mass scale, a Dessart+21 model comparison, a fixed Salpeter slope, and pseudo-SNe all get explicit treatment. The paper also flags its own weak spots, including the completeness discussion and the statement that the truth likely lies between the two f[O I] extremes. Credit where due: this will be the reference for the nebular-spectroscopy route to the RSG problem, and the citation pattern is appropriate.

The soft spots are not fatal, but they matter. The 2–3 sigma significance is substantially carried by the faint end. When they restrict to logL > 4.6 (N=33), the significance drops below 1 sigma, as the paper itself shows. The completeness treatment is acknowledged as arbitrary—pseudo-SNe with a uniform 10–12 Msun plus Gaussian tail—and there is no quantitative selection function for the nebular sample in terms of [O I] sensitivity versus distance and extinction. The empirical calibration rests on 12 overlapping SNe, and SN 2013ej is excluded on an energy argument that is plausible but not quantitatively modeled. These are load-bearing assumptions for the headline claim, and they are not fully secured. Still, the central methodology holds up: the inferred LDF is consistent with Davies & Beasor (2020), and the internal checks are honest.

I would send this to review. It deserves a serious referee, mainly to push on completeness modeling and the 2013ej exclusion, and to ask the abstract to match the robustness section. I would also bring it to the reading group—it is a clean example of how far a 50-object sample plus a 12-object calibration can take a marginal claim.

Referee Report

3 major / 4 minor

Summary. This paper re-assesses the red supergiant (RSG) problem using nebular-phase spectroscopy of 50 Type II supernovae. The authors measure the fractional flux of [O I] lambda lambda 6300,6363 relative to the integrated 5000-8500 A spectrum, compare it with the Jerkstrand et al. (2012, 2014) models to infer MZAMS,neb for each object, and then convert to progenitor luminosity using an empirically calibrated MZAMS,neb-logL relation based on 12 SNe with pre-SN imaging (after excluding SN 2013ej). The resulting luminosity distribution is fitted with a bounded power law via an emcee Monte Carlo procedure, yielding logLup = 5.21^{+0.09}_{-0.07} and a claimed 2-3 sigma significance for the RSG problem. The paper also compares this result with upper mass cutoffs from plateau light-curve modeling and pre-SN imaging, concluding that the consistency across methods suggests a real physical problem.

Significance. If the central claim is robust, this paper provides a valuable independent probe of the RSG problem with a sample roughly twice as large as previous direct-imaging studies, using a qualitatively different diagnostic (nebular [O I] emission) and a carefully propagated Monte Carlo uncertainty treatment. The affine-invariance robustness test in Section 4.3 is a genuine strength: it demonstrates that the inferred luminosities are insensitive to a large family of transformations of MZAMS,neb. The paper is also commendably transparent about its limitations, including the non-monotonic behavior of M9 models, the arbitrariness of the pseudo-SN completeness correction, and the fact that its own bright-only completeness test reduces the claimed significance below 1 sigma. Because the paper ships enough detail to reproduce the statistical machinery and explicitly compares with multiple independent methods, it is a useful contribution to the RSG problem literature, provided the significance claim is brought in line with the robustness tests.

major comments (3)

[Section 5, 'Excluding Low-Luminosity Progenitors'] The paper's own robustness test excluding progenitors with logL < 4.6 (N = 33) yields logLup = 5.25^{+0.26}_{-0.12} and the text explicitly states that the significance of the RSG problem is reduced to below 1 sigma. This directly contradicts the abstract and Section 5 headline that the RSG problem is significant at the 2-3 sigma level, and it shows that the headline significance is carried by the assumed treatment of the faint end. Because the nebular spectroscopy sample has no quantified selection function (e.g., [O I] flux sensitivity versus distance and host extinction), the 2-3 sigma claim is not secured. Please either add a quantitative selection model or rephrase the central claim to reflect the sensitivity of the significance to the faint-end completeness assumption.
[Section 4.2, Table 1; Section 4.3] The empirical MZAMS,neb-logL relation that sets the entire luminosity scale is calibrated on only 12 objects after excluding SN 2013ej. The exclusion is justified by an energy argument and by reference to a forthcoming work, rather than by a quantitative model of the systematic uncertainty; and the pre-SN luminosities are mostly from Davies & Beasor (2018), which is disputed by Healy et al. (2024) and Beasor et al. (2025) as potentially underestimating luminosities through single-band photometry. The affine-transform robustness test in Section 4.3 does not address this concern because it keeps the pre-SN luminosity measurements fixed while transforming MZAMS. Please show that logLup is stable under a plausible systematic shift of the calibration luminosities, or quantify and propagate the bolometric-correction systematics into the LDF fit.
[Section 3, mass assignment below M12; Section 5, pseudo SNe] Objects with f[O I] below the M12 track are assigned a uniform 10-12 M_sun distribution with a 1 M_sun Gaussian tail, and the pseudo-SN completeness correction in Section 5 is, in the authors' own words, 'somewhat arbitrary.' The M9-model comparison in Figure 4 shows that the f[O I]-MZAMS relation is non-monotonic in this regime, so the assigned distribution is not calibrated to the data. Since the fiducial 2-3 sigma significance is recovered only when pseudo SNe are added (Npseudo up to 30), the significance statement rests on an unmodelled completeness correction. Please replace the pseudo-SN prescription with a selection function derived from the [O I] flux sensitivity of the surveys used, or provide a sensitivity analysis over a plausible range of missing-object luminosity distributions.

minor comments (4)

[Section 2] The text says 'Figure 1 illustrates this fitting procedure using SNe 2014G and 2023ixf as examples,' but the multi-Gaussian line fitting is shown in Figure 3, not Figure 1.
[Figure 3 caption] The word 'psuedo-continuum' in the caption should be 'pseudo-continuum.'
[Equation (6)] The notation dN/dlogL proportional to L^{1+Gamma_L} should clarify that L denotes the linear luminosity in solar units, since the fit parameters and the text are quoted in logL; as written, the functional form is ambiguous.
[Section 3] The subscript in f[O I],reg is typeset inconsistently, with 'f[O,I],reg' appearing in at least one place; please standardize the notation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the luminosity cutoff is derived from nebular [O I] masses and an observation-calibrated mass-luminosity relation, not fitted to the pre-SN luminosities that define the RSG problem.

full rationale

The derivation chain is self-contained and independent of the quantity it claims to predict. The paper measures fractional [O I] fluxes from nebular spectra, converts them to MZAMS,neb using external spectral models (Jerkstrand et al. 2012, 2014), and then calibrates an empirical MZAMS,neb-logL relation using a small overlapping sample with pre-SN imaging luminosities. This calibrated relation is applied to the full 50-SN sample to produce the luminosity distribution, whose upper cutoff is then fitted with a power law. The central claim, logLup = 5.21, is not an input to the calibration: the full-sample MZAMS,neb distribution is derived purely from [O I] spectroscopy, and the paper explicitly shows that no object sits above the M19 track, so the absence of luminous progenitors is not constructed by the luminosity calibration. The robustness tests with affine transformations of MZAMS,neb further show that the inferred logL values and the cutoff are stable, indicating that the result does not reduce to the choice of calibration. The self-citations (e.g., Fang et al. 2025a) are not load-bearing for the upper cutoff; the exclusion of SN 2013ej is justified by external energy arguments and by the correlation analysis, and removing it does not by construction force the final cutoff. The acknowledged completeness concerns and the reduced significance when low-luminosity progenitors are excluded are statistical robustness issues, not circularity. No step was found where a parameter fitted to the outcome is renamed as a prediction, or where a model assumption is imported solely from the authors' prior work. The analysis therefore contains no significant circular component.

Assumptions & free parameters 5 free parameters · 5 assumptions · 1 invented entities

The paper's central result depends on a handful of fitted parameters (the LDF cutoffs and slope), several domain assumptions about the relation between [O I] flux and mass, and the representativeness of the calibration sample. There are no new physical entities proposed; the 'pseudo SNe' are an explicit modeling device. The arithmetic is transparent, but the assumptions are strong enough that the 2-3 sigma significance is conditional on them.

free parameters (5)

power-law slope Gamma_L = -0.89 (+0.36, -0.38)
Fitted by emcee to the observed LDF. Degenerate with the cutoffs, and the paper shows the result depends on this fit.
lower luminosity cutoff log Llow = 4.28 (+0.09, -0.11)
Fitted as part of the bounded power-law model. Shifts to 4.42 if Gamma_L is fixed to -1.675.
upper luminosity cutoff log Lup = 5.21 (+0.09, -0.07)
The central fitted parameter of the LDF. Converts to Mup = 20.63 (+2.42, -1.64) Msun via KEPLER MLR.
MZAMS distribution for objects below M12 track = uniform 10-12 Msun plus Gaussian tail with sigma=1 Msun
Ad hoc choice for low-mass progenitors, affecting the faint end of the LDF and thus Gamma_L and log Llow.
pseudo-continuum scatter allowance in Monte Carlo = 20% (0.08 dex)
Chosen by hand to set the uncertainty in f[O I] measurement; affects all individual MZAMS,neb uncertainties.

assumptions (5)

domain assumption The [O I] lambda 6300,6363 flux is a monotone tracer of oxygen mass and hence MZAMS for SNe II.
Used throughout Section 3; the models show non-monotonicity for M9 models, which the paper explicitly excludes, revealing the assumption is fragile at low masses.
domain assumption The Jerkstrand et al. (2012, 2014) nebular models represent the observed SNe II sample.
The models assume single RSG progenitors with fixed explosion energy 1.2e51 erg and massive H envelope; the paper partially addresses this via f[O I],reg and the robustness test, but the central calibration depends on the models.
domain assumption The MHe core - logL relation is universal across stellar evolution codes (Eq. 2).
Used to convert Mup to MZAMS and to compare with light curve modeling. The paper shows it is consistent across KEPLER, MESA, HOSHI with 0.025 dex scatter, so this is a reasonably supported assumption.
domain assumption The empirical MLR derived from 12 overlapping SNe is representative of all 50 SNe.
Section 4.2; the paper excludes SN 2013ej as an outlier and shows the correlation improves, but this is a small sample and the selection of the overlap sample is not random.
domain assumption The nebular spectroscopy sample is representative of the SNe II population, with completeness that can be approximated by adding pseudo SNe.
Section 5; the paper explicitly states the sample is probably incomplete at low luminosities and uses pseudo SNe to test the effect, which changes Gamma_L and log Llow significantly.

invented entities (1)

Pseudo SNe
purpose: Artificial low-luminosity data points added to test the effect of incompleteness on the LDF parameters.
The paper states 'the exact luminosity distribution of these missing progenitors is unknown, and our assignment is somewhat arbitrary.' This is a hypothetical construct for a sensitivity test, but it is not a falsifiable entity with independent evidence.

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Cite this review

Pith. "Pith review of Red Supergiant problem viewed from the nebular phase spectroscopy of type II supernovae." pith.science (2026). https://pith.science/paper/IGBHLT7Q

@misc{pith2026250414502,
  author       = {Pith},
  title        = {Pith review of: Red Supergiant problem viewed from the nebular phase spectroscopy of type II supernovae},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IGBHLT7Q}},
  note         = {Machine review of arXiv:2504.14502}
}

abstract

The red supergiant (RSG) problem refers to the observed dearth of luminous RSGs identified as progenitors of Type II supernovae (SNe II) in pre-SN imaging. Understanding this phenomenon is essential for studying pre-SN mass loss and the explodability of core-collapse SNe. In this work, we re-assess the RSG problem using late-phase spectroscopy of a sample of 50 SNe II. The [O I] $\lambda\lambda$6300,6363 emission in the spectra is employed to infer the zero-age main sequence (ZAMS) mass distribution of the progenitors, which is then transformed into a luminosity distribution via an observation-calibrated mass-luminosity relation. The resulting luminosity distribution reveals an upper cutoff at log $L/L_{\odot} = 5.21^{+0.09}_{-0.07}$ dex, and the RSG problem is statistically significant at the 2$\sigma$ to 3$\sigma$ level. Assuming single RSG progenitors that follow the mass-luminosity relation of KEPLER models, this luminosity cutoff corresponds to an upper ZAMS mass limit of $20.63^{+2.42}_{-1.64}$ $M_{\odot}$. Comparisons with independent measurements, including pre-SN imaging and plateau-phase light curve modeling, consistently yield an upper ZAMS mass limit below about 25 $M_{\odot}$, with a significance level of 1-3$\sigma$. While each individual method provides only marginal significance, the consistency across multiple methodologies suggests that the lack of luminous RSG progenitors may reflect a genuine physical problem. Finally, we discuss several scenarios to account for this issue should it be confirmed as a true manifestation of stellar physics.

Figures

Figures reproduced from arXiv: 2504.14502 by the authors.

**Figure 1.** Left panel: The nebular spectra from Jerkstrand et al. (2012), normalized to the integrated fluxes. The shaded regions mark the wavelength ranges that employed to calibrate the background fluxes. Right panel: The average fluxes in the colored regions as functions of time. The solid lines are the quadratic fits to the data points. ments, a quadratic form of fcon is applied: fcon = b2 λ 2 + b1 λ + b0, where λ is the w… view at source ↗

**Figure 2.** Examples of the removal the possible contamination from the host galaxy. Upper panels: SN 2014cx; lower panels: SN 2004dj. In the left panels, the uncalibrated spectra are normalized to the integrated flux within 5000 to 8500 ˚A. The colored strips highlight the wavelength regions used to determine and subtract the contamination flux fcon from the host galaxy, which is represented by the black dashed lines. A quadra… view at source ↗

**Figure 3.** The fitting to the line profiles of SNe 2014G (left) and 2023ixf (right). The black solid line is the normalized observed spectrum and the black dashed line is the psuedocontinuum. The light blue, pink and orange dashed lines represent the fits to the [O I] λλ6300,6363, Hα and the substructure respectively. The red solid line is the sum of the fitted profiles. 3. ESTIMATION OF ZAMS MASS In the upper panel of [PIT… view at source ↗

Figures from the paper (10 more)

**Figure 4.** Figure 4: Upper panel: The fractional fluxes of [O I] of individual SNe (labeled by different colors and markers) compared with the model tracks. The black dashed line is the average of the M15 and M19 tracks that represent the case when MZAMS = 17 M⊙. Lower panel: same as upp…

**Figure 6.** Figure 6: Comparison between the MZAMS measured with (f[O I]) and without (f[O I],reg) the contributions from the Hα flux. The dashed line represents y = x. The shaded region represent the case when the difference between the two measurements are within 0.5 M⊙. The dotted line …

**Figure 7.** Figure 7: The cumulative distribution of MZAMS measured from nebular spectra (denoted as MZAMS,neb). The black solid line represent the median values for each rank from the sorted method described in the main text. For illustration purposes, the 68% CI is not colored, while the …

**Figure 8.** Figure 8: The MHe core-MO-logL relations from different stellar evolution codes: MESA (green; Fang & Maeda 2023; Temaj et al. 2024), KEPLER (blue; Sukhbold et al. 2016, 2018; Ertl et al. 2020) and HOSHI (red; Takahashi et al. 2023) models. Upper panel: The MHe core-MO relation;…

**Figure 9.** Figure 9: Comparison between the MZAMS,neb with the luminosities of the progenitor RSGs. The shaded region is the 68% CI of the Monte-Carlo based linear regression described in the main text, when SN 2013ej is excluded. The dashed line is the prediction if the observations foll…

**Figure 11.** Figure 11: Upper panel: Comparison between the MD ZAMS of the nebular spectral models from Dessart et al. (2021) and their measured MJ ZAMS,neb using the method in the work; Lower panel: Comparison between log L estimated from MJ ZAMS,neb with logL estimated from other forms of …

**Figure 12.** Figure 12: Upper panel: The comparison of the observed LDF (black) and the model LDF with ΓL = -0.89, logLlow = 4.28 and log Lup = 5.21 (red). The uncolored regions surrounding the solid lines and the transparent regions are 68, 95 and 99.7% CIs. The thick dashed line represen…

**Figure 13.** Figure 13: Same as [PITH_FULL_IMAGE:figures/full_fig_p015_13.png]

**Figure 14.** Figure 14: The distributions of ΓL (left), log Llow (middle) and log Lup (right) from emcee routine as functions of the number of pseudo SNe, artificial data points that represents the faint RSG progenitors (Npseudo; see main text for definition). The solid lines represent the m…

**Figure 15.** Figure 15: The comparison of upper and lower cutoffs of MZAMS inferred using different methods. The pink and light blue circles are MZAMS converted from the luminosities cutoffs in this work and Davies & Beasor (2020), using the MLR of KEPLER models, while the triangles are co…

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Forward citations

Cited by 2 Pith papers

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The progenitor mass of SN 2022acko inferred from pre-explosion images (7.5 Msun) disagrees with masses from light-curve and spectral modeling (9-15 Msun), with the tension likely caused by model and calibration systematics.
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