REVIEW 3 major objections 5 minor 15 references
Spectral analysis of the blazars Markarian 421 and Markarian 501 with the HAWC Gamma-Ray Observatory
T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash
Pith's one-line read The intrinsic TeV spectra of Mrk 421 and Mrk 501 differ: Mrk 421 cuts off near 5.2 TeV, while Mrk 501 does not.
desk verdict Solid HAWC spectra of two blazars, but the claimed Mrk 421 cutoff is not statistically established because no ΔTS between nested models is reported. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The machinery that carries the argument is forward-folding spectral fitting: a candidate intrinsic model is multiplied by the EBL attenuation $\exp(-\tau(E,z))$, convolved with the HAWC detector response, and compared with binned photon counts through a Poisson maximum-likelihood statistic $TS = 2\ln(L_1/L_0)$. Event energies come from a ground-parameter estimator that uses the charge measured 40 m from the shower axis and divides the data into quarter-decade energy bins from 0.316 to 100 TeV; fits are restricted to above 1 TeV because the energy resolution is poor below that. The two candidate shapes are a single power law and a power law with an exponential cutoff, and the preferred shape is selected by comparing the resulting global-fit test statistics.
What would settle it
Re-fit the same HAWC data with an alternative EBL model whose optical depth at 5 TeV differs substantially from the adopted one: if Mrk 421's fitted cutoff moves outside roughly 3-8 TeV or disappears, the claim of an intrinsic ~5.2 TeV cutoff is weakened. A longer exposure that reveals a break in Mrk 501's spectrum above 10 TeV would falsify the pure-power-law description.
Extended reading notes
Core claim
After forward-folding candidate models through the detector response, the paper's central finding is that the intrinsic spectrum of Mrk 421 is best described by $dN/dE = N_0 (E/E_0)^{-2.22 \pm 0.10} \exp(-E/(5.24 \pm 1.02~\mathrm{TeV}))$, while Mrk 501 is well described by a single power law with index $2.40 \pm 0.06$ and no cutoff. The EBL attenuation factor $\exp(-\tau)$ from the adopted model is applied before fitting, so the quoted parameters and the difference between the sources are presented as intrinsic. The detection significance for each source is expressed through $TS = 2\ln(L_1/L_0)$, with $\sqrt{TS}=48$ for Mrk 421 and $\sqrt{TS}=22$ for Mrk 501. The paper reports these as preliminary results.
Load-bearing premise
The load-bearing premise is that the adopted extragalactic background light model gives the correct absorption: the observed spectrum is divided by that model's predicted attenuation before fitting, so a different EBL opacity would change the fitted intrinsic indices and especially the Mrk 421 cutoff.
Editorial extensions
If this is right
- Mrk 421's emission model must reproduce an exponential cutoff at a few TeV, not just a continuation of the power law.
- Mrk 501's intrinsic spectrum can be treated as a pure power law across the HAWC energy range, so the two blazars cannot share a single simple spectral template.
- Since both sources have nearly equal redshifts, the reported difference is not mainly a distance or EBL effect under the adopted EBL model.
- The fitted index and cutoff values provide concrete quantitative anchors for leptonic and hadronic jet models and for comparisons with the synchrotron component.
Reading between the lines
- The paper leaves open whether the Mrk 421 cutoff is set inside the jet or by photon-photon absorption near the source; one testable extension is to watch whether the cutoff energy shifts during flaring activity, which would track the compactness of the emission region.
- Applying the same EBL-corrected analysis to other high-synchrotron-peaked blazars could reveal whether a cutoff near a few TeV is a common feature; if it is, it would point to a shared limit on particle acceleration in these jets.
- Repeating the fits with alternative EBL models is a direct robustness check: the same data could either confirm the 5.2 TeV cutoff as intrinsic or expose it as partly an artifact of the adopted absorption.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper reports a time-averaged spectral analysis of the blazars Mrk 421 and Mrk 501 using 837 days of HAWC data (June 2015 to December 2017). The authors fit power-law (PL) and power-law-with-exponential-cutoff (PL+CO) models to counts in energy bins above 1 TeV, applying a forward-folding maximum-likelihood procedure and correcting the intrinsic spectrum for extragalactic background light (EBL) absorption using the Gilmore et al. (2012) model. They conclude that the intrinsic spectrum of Mrk 421 is better described by a PL+CO with photon index 2.22 ± 0.10 and cutoff energy 5.24 ± 1.02 TeV, while Mrk 501 is consistent with a single power law of index 2.40 ± 0.06 without a cutoff.
Significance. If the results hold, this would be one of the first HAWC measurements of the intrinsic VHE spectra of these two archetypal high-synchrotron-peaked BL Lacs above 1 TeV, and it would suggest a spectral difference between them that could bear on blazar emission models. The analysis uses standard procedures: the HAWC maximum-likelihood framework, a published energy estimator, and a widely used EBL model. The paper is transparent about using statistical uncertainties only and about its preliminary character. However, the central claim of curvature in Mrk 421 and its absence in Mrk 501 is not statistically quantified, and systematic uncertainties—especially energy-scale and EBL-model dependence—are not addressed. Because the model comparison statistic is missing, the significance of the paper's main conclusion cannot currently be assessed.
major comments (3)
- [§4, Table 1] The central claim that Mrk 421 is better described by PL+CO rests on a model comparison that is never reported. Since the power law is nested in PL+CO (Ec → ∞), the likelihood-ratio test statistic ΔTS = TS(PL+CO) − TS(PL) is the appropriate measure, and the paper should quote it for both sources. Without ΔTS, the reported Ec = 5.24 ± 1.02 TeV for Mrk 421 cannot be distinguished from a marginal preference for an extra parameter, and the statement that Mrk 501's fits have 'very similar' TS values is unverifiable. I request the ΔTS values, and ideally a profile likelihood in Ec, for both sources.
- [§4, Table 1] The uncertainties quoted in Table 1 are statistical only, but the key parameter, Ec = 5.24 ± 1.02 TeV, lies in the energy range where HAWC's energy-scale systematics are most relevant, given the energy estimator described in Section 2 and reference [10]. The authors should either estimate and propagate systematics from the detector response and energy scale or at least bound their effect on Ec. In addition, the EBL model of Gilmore et al. (2012) is used without testing alternatives; because the intrinsic cutoff is obtained by dividing the observed spectrum by exp(−τ), repeating the fits with another EBL model (e.g., Domínguez et al. 2011 or Franceschini et al. 2008) would demonstrate whether the Mrk 421 cutoff is robust or an artifact of the chosen τ(E).
- [§4, Table 1] The treatment of Mrk 501's cutoff is not quantitatively supported. The text states that the PL and PL+CO fits have 'very similar' TS values and that the fitted cutoff is larger than 700 TeV, but no numbers are reported, and the value '∞' in Table 1 is not a fit result. The authors should give the fitted Ec for Mrk 501 with its uncertainty, or a lower limit, and the ΔTS between PL and PL+CO; this is necessary to justify the claim that Mrk 501 is 'well described' by a power law without requiring a cutoff. As written, the comparison between the two sources is not established.
minor comments (5)
- [§3, Eqs. (3.2) and (3.3)] Equations (3.2) and (3.3) are labeled 'PL' and 'PL+CO', but they include the EBL attenuation factor exp(−τ). Since the text says the input model is the intrinsic one and is then attenuated, these equations should be clarified as the observed (attenuated) models actually compared with the data, with the intrinsic models written without exp(−τ).
- [Table 1] The column header '√TS' is ambiguous; the table should state that this is the detection significance in units of σ, not a spectral-fit test statistic.
- [Figure 1] The figure caption should explain how upper limits are plotted, since Section 3 states that bins with TS < 25 are replaced by 95% confidence upper limits; the caption currently does not mention this.
- [Abstract, §4, §5] The results are repeatedly called 'preliminary' (Abstract, Section 4, Section 5). If this is intended as a journal publication, the authors should either present the analysis as final or explicitly state which aspects remain preliminary (e.g., systematic uncertainties).
- [§5] The phrase 'photon-photon attenuation inside the source' is speculative; since EBL attenuation has already been removed, the residual curvature could also be described as intrinsic spectral curvature. Suggest rephrasing to avoid confusion.
Circularity Check
No significant circularity: the spectral parameters are direct fits to HAWC data with an external EBL model; the missing model-comparison statistic is a statistical-support issue, not circularity.
full rationale
The paper's derivation chain is a standard data-to-fit analysis. HAWC events are reconstructed and binned using an energy estimator; the LiFF maximum-likelihood framework convolves trial spectral models with the detector response and compares them with observed counts; the best-fit parameters are obtained by maximizing the likelihood. The intrinsic spectra are obtained by attenuating the trial intrinsic models with the EBL opacity from Gilmore et al. (2012), an external model, before convolution. The reported photon indices and cutoff energies are therefore fitted parameters directly tied to the HAWC data, not quantities recycled from other fitted values, and no prediction is derived from the fit itself. The flux points shown in Figure 1 are standard unfolding products with alpha and Ec fixed from the global fit, not independent predictions, so they introduce no circularity. The citations to HAWC instrument papers for detector performance, the energy estimator, and the likelihood framework are self-citations in the narrow sense, but these are calibration and infrastructure papers with independent validation outside the present result, so they do not count as load-bearing circularity. The EBL model is external and independent of the Mrk 421 and Mrk 501 spectra. The skeptic's concern that no Delta-TS between the power-law and power-law-with-cutoff models is reported is a legitimate limitation for model selection, but it concerns statistical evidence and does not mean the conclusion is equivalent to its inputs by construction. No circular step is present, so the score is 0.
Assumptions & free parameters
free parameters (6)
- N0 (Mrk 421 normalization) =
(4.77 ± 0.25) × 10^-11 TeV^-1 cm^-2 s^-1
- alpha_421 =
2.22 ± 0.10
- Ec_421 =
5.24 ± 1.02 TeV
- N0 (Mrk 501 normalization) =
(1.40 ± 0.12) × 10^-11 TeV^-1 cm^-2 s^-1
- alpha_501 =
2.40 ± 0.06
- Ec_501 =
Infinity (fit > 700 TeV)
assumptions (4)
- domain assumption HAWC detector response and empirical energy estimator are correctly calibrated as described in refs [8, 9, 10].
- domain assumption The EBL optical depth tau(E,z) from Gilmore et al. (2012) [13] is the correct attenuation.
- domain assumption The source gamma-ray emission is modeled as a point source with a single time-averaged spectral shape.
- domain assumption The true spectrum belongs to one of the two tested shapes (PL or PL+CO).
Cite this review
Pith. "Pith review of Spectral analysis of the blazars Markarian 421 and Markarian 501 with the HAWC Gamma-Ray Observatory." pith.science (2026). https://pith.science/paper/UEQGXMO3
@misc{pith2026190901179,
author = {Pith},
title = {Pith review of: Spectral analysis of the blazars Markarian 421 and Markarian 501 with the HAWC Gamma-Ray Observatory},
year = {2026},
howpublished = {\url{https://pith.science/paper/UEQGXMO3}},
note = {Machine review of arXiv:1909.01179}
}
abstract
The High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory surveys the very high energy sky in the $\sim300$ to 100 TeV energy range and has detected two high-synchrotron-peaked BL Lacertae objects, Markarian 421 and Markarian 501 in a period of time of 837 days between June 2015 and December 2017. In this work, we present the detailed time-average spectral analysis. Using an extragalactic background light model, we address the difference in the intrinsic spectral properties between the two blazars above 1 TeV, preliminary results show that the intrinsic spectrum of Mrk 421 is better described by a power-law with an exponential energy cut-off function with photon index $\alpha_{421}=2.22\pm0.10$ and energy cut-off $Ec_{421}=5.24\pm1.02$ TeV, and for Mrk 501 the intrinsic spectrum is well described by a power-law with spectral index $\alpha_{501}=2.40\pm0.06$, without requiring an energy cut-off.
Figures
Reference graph
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Reviewed August 14, 2026 · model on record in the stance chip above.
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