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REVIEW 4 major objections 5 minor 55 references

Study of long-term spectral evolution and X-ray and Gamma-ray correlation of blazars seen by HAWC

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read After six years of continuous TeV monitoring, Mrk 421's X-ray and gamma-ray fluxes show a strong linear correlation, supporting a multiple-zone synchrotron self-Compton model.

desk verdict Solid long-baseline HAWC/Swift-XRT correlation analysis for Mrk 421; the harder-when-brighter claim needs a covariance check before it is trusted. read the letter →

arxiv 2501.15041 v1 pith:6M5NCF4J submitted 2025-01-25 astro-ph.HE

R. Alfaro , C. Alvarez , A. Andrés , J.C. Arteaga-Velázquez , D. Avila Rojas , H.A. Ayala Solares , R. Babu , E. Belmont-Moreno
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A. Bernal K.S. Caballero-Mora T. Capistrán A. Carramiñana F. Carreón S. Casanova U. Cotti J. Cotzomi S. Coutiño de León E. De la Fuente D. Depaoli N. Di Lalla R. Diaz Hernandez B.L. Dingus M.A. DuVernois M. Durocher J.C. Díaz-Vélez K. Engel C. Espinoza K.L. Fan N. Fraija S. Fraija J.A. García-González F. Garfias A. Gonzalez Muñoz M.M. González J.A. Goodman S. Groetsch J.P. Harding S. Hernández-Cadena I. Herzog D. Huang F. Hueyotl-Zahuantitla A. Iriarte V. Joshi S. Kaufmann D. Kieda A. Lara W.H. Lee J. Lee H. León Vargas J.T. Linnemann A.L. Longinotti G. Luis-Raya K. Malone O. Martinez I. Martinez-Castellanos J. Martínez-Castro J.A. Matthews P. Miranda-Romagnoli J.A. Montes E. Moreno M. Mostafá A. Nayerhoda L. Nellen M.U. Nisa R. Noriega-Papaqui N. Omodei M. Osorio Y. Pérez Araujo E.G. Pérez-Pérez C.D. Rho D. Rosa-González E. Ruiz-Velasco H. Salazar D. Salazar-Gallegos A. Sandoval M. Schneider J. Serna-Franco A.J. Smith Y. Son R.W. Springer O. Tibolla K. Tollefson I. Torres R. Torres-Escobedo R. Turner F. Ureña-Mena E. Varela L. Villaseñor X. Wang I.J. Watson K. Whitaker E. Willox S. Yun-Cárcamo H. Zhou C. de León Abraham D. Falcone Fredric Hancock
This is my paper · ORCID
classification astro-ph.HE
keywords blazarsMarkarian421501veryhighenergygammaraysX-ray–gamma-raycorrelationsynchrotronself-Comptonharder-when-brighterHAWCObservatory
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

This paper uses six years (2,143 days) of nearly continuous monitoring by the HAWC water-Cherenkov observatory, together with Swift-XRT X-ray data, to test whether the TeV and soft X-ray emissions of the two brightest blazars in the northern TeV sky rise and fall together. For Mrk 421 it finds a strong linear correlation between quasi-simultaneous X-ray and gamma-ray fluxes, with no measurable time lag, and it confirms a harder-when-brighter spectral trend in the gamma-ray band. For Mrk 501 the same test yields only weak evidence of a long-term correlation, largely because the source spent more than two years in an extremely low state. If these correlations are real, they favor leptonic synchrotron self-Compton models in which multiple emission zones combine to produce an approximately linear X-ray–TeV relation, rather than a single-zone quadratic relation. The result matters because it uses an unbiased, long-duration survey to connect TeV blazar behavior to the physics of the jet.

What carries the argument

The argument rests on three connected pieces. First, daily HAWC gamma-ray fluxes for each source transit, which lasts about 6.2 hours, are computed with the ZEBRA detector-response software under a fixed cut-off power law: for Mrk 421 the photon index is $\alpha=2.2$ with cutoff $E_c=5$ TeV, and for Mrk 501 $\alpha=1.6$ with $E_c=6$ TeV, with only the normalization left free. Second, matching Swift-XRT 0.3–10 keV fluxes are extracted on the same sidereal day, giving 74 Mrk 421 pairs and only 3 Mrk 501 pairs. Third, the D'Agostini maximum-likelihood linear fit adds an intrinsic-scatter parameter $\sigma_d$, so "correlation" is measured beyond the Pearson coefficient, and a Bayesian-blocks rebinning tests whether the scatter is statistical or source-intrinsic. This machinery is what allows the paper to distinguish a linear, multi-zone SSC relation from a quadratic single-zone one.

What would settle it

Recompute the Mrk 421 daily HAWC fluxes with the photon index left free (or with spectral-index values from the Bayesian-block fits) and re-fit the X-ray–gamma-ray correlation; if the slope leaves $(2.10 \pm 0.17)\times 10^{-2}$ or the intrinsic scatter $\sigma_d$ changes by much more than its quoted uncertainty, the fixed spectral shape is distorting the claimed linear correlation.

Watch

Extended reading notes

Core claim

The paper's central claim is that, over 2,143 days of nearly continuous HAWC monitoring, the soft X-ray (0.3–10 keV) and very-high-energy gamma-ray ($>1$ TeV) fluxes of Mrk 421 are linearly correlated. Fitting 74 quasi-simultaneous daily pairs with a likelihood that includes intrinsic scatter gives $F_\gamma = (2.10 \pm 0.17)\times 10^{-2} F_X + (4.21 \pm 2.78)\times 10^{-12}\,\mathrm{cm^{-2}\,s^{-1}}$, with $\sigma_d = (8.72 \pm 1.45)\times 10^{-12}\,\mathrm{cm^{-2}\,s^{-1}}$, a Pearson coefficient of 0.676, and a p-value of $3.93\times 10^{-11}$. Rebinned into Bayesian blocks, with the photon index left free, the relation tightens to $r = 0.892$ over 25 blocks, and the paper interprets this linearity as evidence for a leptonic synchrotron self-Compton origin with multiple emission zones, since a single-zone SSC flare would predict a quadratic relation. The same data set shows that Mrk 421's gamma-ray spectrum hardens linearly as it brightens, while Mrk 501's long low state leaves only weak evidence of a TeV/X-ray correlation.

Load-bearing premise

The daily Mrk 421 gamma-ray fluxes are computed assuming a fixed spectrum with photon index 2.2 and an exponential cutoff at 5 TeV, so if the spectrum actually hardens when the source brightens, the fixed-shape assumption can bias both the correlation slope and the reported harder-when-brighter trend.

Editorial extensions

If this is right

  • For Mrk 421, the long-term X-ray/TeV relation is linear with intrinsic scatter, so single-zone SSC models that predict a quadratic $F_\gamma \propto F_X^2$ relation cannot explain the time-averaged behavior.
  • The day-scale, zero-lag correlation between the two bands means the X-ray and TeV emitting regions respond together to the same acceleration episodes, placing the emission zones in the same jet region.
  • The harder-when-brighter gamma-ray trend is confirmed for Mrk 421, and because it is linear, spectral hardening can be used as a flux-state indicator once the fixed-shape systematic is accounted for.
  • For Mrk 501, more than two years of very low flux and only three overlapping daily X-ray points prevent a daily correlation measurement; establishing or excluding one will require denser simultaneous X-ray coverage during future active states.

Reading between the lines

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

  • Extension beyond the paper: if the fixed $\alpha=2.2$ assumption is the main source of the daily scatter, then letting the photon index float in the daily HAWC fits should lower $\sigma_d$ substantially; the paper only frees the photon index in the Bayesian-block stage, so this is directly testable with the same dataset.
  • Extension beyond the paper: the outliers at gamma-ray fluxes above about $1\times 10^{-10}\,\mathrm{cm^{-2}\,s^{-1}}$ could be checked against the simultaneous X-ray photon index; a systematically harder X-ray spectrum in those states would suggest the apparent breakdown is a spectral-match effect, not a missing emission component.
  • Extension beyond the paper: the multi-zone interpretation predicts that individual flares should trace quadratic tracks while the ensemble remains linear; re-analysing archived Mrk 421 flare campaigns with this two-level correlation shape in mind would discriminate between a true multi-zone geometry and a simple superposition of unrelated flaring events.
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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

4 major / 5 minor

Summary. The manuscript reports a 2143-day HAWC and Swift-XRT monitoring study of Mrk 421 and Mrk 501. Daily and Bayesian-block gamma-ray fluxes are compared with quasi-simultaneous 0.3-10 keV X-ray fluxes using a D'Agostini linear-correlation fit that includes an intrinsic-scatter term. For Mrk 421 the authors report a strong linear X-ray/gamma correlation (r=0.676, n=74 daily; r=0.892, n=25 Bayesian blocks), a zero-lag discrete correlation function result, and a harder-when-brighter gamma-ray spectral trend across Bayesian blocks. For Mrk 501 they report only weak evidence, largely limited by low activity and a small overlap sample. The results are interpreted as supporting a multiple-zone synchrotron self-Compton origin for the TeV emission.

Significance. If the analysis is correct, this is one of the longest unbiased VHE monitoring data sets for two prototypical blazars, and the Mrk 421 correlation would constitute a strong, independent confirmation of earlier short-campaign results. The paper has genuine strengths: the HAWC and Swift-XRT measurements are independent, the daily and Bayesian-block analyses are complementary, the use of an explicit intrinsic-scatter term goes beyond simple Pearson tests, and the DCF zero-lag check is a useful robustness addition. The interpretation in terms of multiple emission zones is consistent with the existing literature. However, the quantitative conclusions currently rest on a likelihood equation that appears misprinted, on a harder-when-brighter result that may be contaminated by fit covariance, and on daily fluxes obtained with a fixed spectral shape whose quoted systematics are not propagated. These are load-bearing issues, but they are addressable within the scope of the manuscript.

major comments (4)
  1. [Section 3.3, Eq. (2)] Equation (2) as printed is not the D'Agostini likelihood used for linear fits with errors on both axes. The second term in the sum should be (F_{gamma,i} - a F_{x,i} - b)^2 divided by the variance term, and the variance term should contain a^2 sigma_{F_x,i}^2, not a sigma_{F_x,i}^2. As written, the numerator uses (F_{gamma,i}^2 - a F_{x,i}^2 - b^2)^2, which is a different fitting model and is dimensionally inconsistent. Please correct Eq. (2) and verify that the slopes, intercepts, and p-values in Table 2 are computed from the corrected expression; because Eq. (2) is the basis of every fit in the paper, this check is essential.
  2. [Section 4.5, Table 2 row 4, Fig. 5(a)] The reported harder-when-brighter correlation (r=-0.686, p=2.76e-6) may be substantially inflated by covariance between the integrated flux and the photon index, since both are obtained from the same maximum-likelihood spectral fit within each Bayesian block (Section 3.4). For a fixed observed count spectrum, the fitted normalization and photon index are anti-correlated, so a negative F-alpha correlation can appear even if the true spectrum is constant. I request a Monte Carlo null test: simulate many constant-spectrum light curves with the same exposures, background rates, and block boundaries, fit N0 and alpha freely in each block, and compare the resulting distribution of Pearson r with the observed -0.686. Until such a test is provided, the claim in Section 5 that harder-when-brighter behavior is 'firmly established' in the gamma-ray band is not supported.
  3. [Section 3.1, Section 4.2, Table 2 row 1] The daily Mrk 421 correlation, which is highlighted in the abstract, uses HAWC fluxes computed with a fixed spectral shape (alpha=2.2, Ec=5 TeV) with only the normalization free, and the quoted systematic uncertainty of up to 40% is not propagated into the D'Agostini fit. Because the harder-when-brighter trend found later in the paper shows that the fixed spectral shape is not valid across all activity states, the daily fluxes may be biased in a flux-dependent way. Please provide a cross-check of the daily fluxes with free spectral parameters, or at minimum quantify how the fixed-shape assumption and the 40% systematic affect the slope and p-value of the daily correlation. I note that the Bayesian-block correlation with free alpha partially addresses this concern, but the daily result as presented remains incompletely characterized.
  4. [Section 5, Table 2 row 3] The conclusion that 'the overall correlations for Mrk 421 and Mrk 501 are indeed linear' overstates the Mrk 501 evidence. The Mrk 501 Bayesian-block correlation uses only 5 points (r=0.947, p=1.46e-2), the per-transit sample has only 3 overlapping points and is not used for a correlation, and the DCF shows no evidence of correlation. The paper should restrict the strong linear-correlation claim to Mrk 421 and describe the Mrk 501 result as tentative or preliminary, consistent with the acknowledgement in Section 4.3 that the Mrk 501 sample is too small to be useful.
minor comments (5)
  1. [Figure 2 caption] The caption states 'The p-value of the correlation is 0.676'; 0.676 is the Pearson correlation coefficient, while the p-value given in Table 2 is 3.93e-11. Please correct the caption.
  2. [Section 4.4] The X-ray flux thresholds '1.25 erg cm^-2 s^-1' and '1.75 erg cm^-2 s^-1' should be written as 1.25e-9 erg cm^-2 s^-1 and 1.75e-9 erg cm^-2 s^-1 to match the figure axes and avoid a units ambiguity.
  3. [Table 2 caption] The caption refers to 'Equation 3.3', but the paper has no numbered Eq. (3.3); the likelihood is Eq. (2). Please update the cross-reference.
  4. [References] Several references are duplicated in the bibliography (for example, Blazejowski et al. 2005, Gliozzi et al. 2006, and Katarzynski & Walczewska 2010). Please consolidate duplicate entries.
  5. [Section 3.1] The sentence describing the largest systematic uncertainty states that late-light simulation has 'a maximum impact of up to 40%' but does not say whether this is an energy-scale shift, a flux-normalization shift, or a combination. Please specify the source of this 40% value and how it would propagate into the flux measurement.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the X-ray/TeV correlation is measured with independent instruments, while the harder-when-brighter trend carries a covariance caveat rather than a definitional reduction.

full rationale

The central X-ray/gamma-ray correlation claim is not circular. The two fluxes are measured by independent instruments (HAWC, 300 GeV-100 TeV, and Swift-XRT, 0.3-10 keV) and combined only by time matching, so the correlation is not imposed by construction. The fixed spectral parameters in Table 1 (alpha=2.2, Ec=5 TeV for Mrk 421; alpha=1.6, Ec=6 TeV for Mrk 501) are calibration inputs inherited from earlier HAWC work (Abeysekara et al. 2017a), not fitted to the correlation target. Moreover, the Bayesian-block correlation in Section 4.3, which leaves alpha free, reproduces the strong linear relation (Table 2 row 2: r=0.892), so the central result does not depend on the fixed-shape assumption. The harder-when-brighter analysis in Section 4.5 and Table 2 row 4 does have a genuine statistical caveat: for each Bayesian block the integrated flux and photon index are obtained from the same maximum-likelihood spectral fit with both N0 and alpha free (Section 3.4), so the two estimators share correlated uncertainties and the PCC of -0.686 (p=2.76e-6) could be partially inflated. This is a covariance/correctness issue, not a case of a prediction being identical to an input by construction; a Monte Carlo null test would be needed to quantify it. The paper itself notes a related but non-circular limitation in Section 3.1 about hour-scale spectral hardening measurements. The self-citations (e.g., Abeysekara et al. 2017a,b; Martinez-Castellanos 2019) are used for detector response, flux normalization, and prior light curves; none is invoked as a uniqueness theorem or as the source of the correlation result. No circular step was found.

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

The central empirical correlations are derived from data with fitted linear parameters and a selected Bayesian-block prior; no new physical entities are postulated. The main uncharged inputs are the fixed HAWC spectral shapes and the assumed band-to-SSC-peak correspondence.

free parameters (5)
  • Mrk 421 X-ray/gamma linear correlation slope a, intercept b, intrinsic scatter sigma_d (per-transit fit) = a=2.10e-2 +/- 0.17e-2, b=4.21e-12 +/- 2.78e-12 cm^-2 s^-1, sigma_d=8.72e-12 +/- 1.45e-12 cm^-2 s^-1
    Fitted to 74 quasi-simultaneous daily points via the D'Agostini likelihood; defines the claimed linear correlation.
  • Mrk 421 X-ray/gamma Bayesian-block correlation parameters = a=2.04e-2 +/- 0.15e-2, b=-6.87e-12 +/- 1.90e-12 cm^-2 s^-1, sigma_d=5.27e-12 +/- 0.79e-12 cm^-2 s^-1
    Fitted to 25 Bayesian-block averaged points; used to argue the correlation is robust to binning.
  • Mrk 501 Bayesian-block correlation parameters = a=3.07e-2 +/- 0.34e-2, b=-1.87e-12 +/- 0.49e-12 cm^-2 s^-1, sigma_d=0
    Fitted to only five Bayesian-block points; this is the basis for the abstract's 'evidence of a long-term correlation' claim for Mrk 501.
  • Mrk 421 gamma-ray flux versus photon index linear fit = slope -3.07e-11 +/- 0.42e-11, intercept 99.7 +/- 10.3, sigma_d=10.7 +/- 1.4
    Fitted to 37 Bayesian blocks; supports the harder-when-brighter claim for the gamma-ray band of Mrk 421.
  • Bayesian block prior ncpprior = 9.5
    Chosen to give a 5% false-positive rate via simulations; controls the number and placement of blocks, which feeds the BB-based correlation and hardness fits.
assumptions (5)
  • standard math D'Agostini maximum-likelihood linear fit with intrinsic scatter is an appropriate statistical model for the X-ray/gamma correlation.
    Used in Section 3.3, Eq. 2; assumes a linear relation F_gamma = a F_x + b with Gaussian intrinsic scatter.
  • domain assumption HAWC flux normalization from ZEBRA detector response and the fixed spectral shapes in Table 1 are accurate for all activity states.
    Invoked in Section 3.1; if the true spectrum hardens beyond the assumed ranges, daily fluxes are biased.
  • domain assumption The 0.3-10 keV XRT band and the 300 GeV-100 TeV HAWC band trace the synchrotron and SSC peaks respectively for Mrk 421 and Mrk 501.
    Used in Sections 1 and 3.3 to justify expecting a correlation; rests on prior SSC models.
  • domain assumption The Bayesian blocks point-measurement fitness function with ncpprior=9.5 segments the light curve into physically meaningful constant-flux states.
    Applied in Section 3.4; the prior choice affects block boundaries and all BB-based fits.
  • domain assumption Swift-XRT spectral model cflux*tbabs*logpar with fixed nH column densities recovers the true 0.3-10 keV source flux.
    Used in Section 3.2; pile-up corrections and fixed HI column may affect faint or low-state fluxes.

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Cite this review

Pith. "Pith review of Study of long-term spectral evolution and X-ray and Gamma-ray correlation of blazars seen by HAWC." pith.science (2026). https://pith.science/paper/6M5NCF4J

@misc{pith2026250115041,
  author       = {Pith},
  title        = {Pith review of: Study of long-term spectral evolution and X-ray and Gamma-ray correlation of blazars seen by HAWC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6M5NCF4J}},
  note         = {Machine review of arXiv:2501.15041}
}
read the original abstract

The HAWC Observatory collected 6 years of extensive data, providing an ideal platform for long-term monitoring of blazars in the Very High Energy (VHE) band, without bias towards specific flux states. HAWC continuously monitors blazar activity at TeV energies, focusing on sources with a redshift of {z \lt 0.3}, based on the Third Fermi-LAT Catalog of High-Energy sources. We specifically focused our analysis on Mrk 421 and Mrk 501, as they are the brightest blazars observed by the HAWC Observatory. With a dataset of 2143 days, this work significantly extends the monitoring previously published, which was based on 511 days of observation. By utilizing HAWC data for the VHE {\gamma}-ray emission in the 300 GeV to 100 TeV energy range, in conjunction with Swift-XRT data for the 0.3 to 10 keV X-ray emission, we aim to explore potential correlations between these two bands. For Mrk 501, we found evidence of a long-term correlation. Additionally, we identified a period in the light curve where the flux was very low for more than two years. On the other hand, our analysis of Mrk 421 measured a strong linear correlation for quasi-simultaneous observations collected by HAWC and Swift-XRT. This result is consistent with a linear dependence and a multiple-zone synchrotron self-Compton model to explain the X-ray and the {\gamma}-ray emission. Finally, as suggested by previous findings, we confirm a harder-when-brighter behavior in the spectral evolution of the flux properties for Mrk 421. These findings contribute to the understanding of blazar emissions and their underlying mechanisms.

Figures

Figures reproduced from arXiv: 2501.15041 by the authors.

Figure 1
Figure 1. LCs for Mrk 421 and Mrk 501. HAWC LC showing Integrated flux > 1 TeV, (a) and (c) panels. A red marker is showing when the significance in the flux was below 2σ for that transit. For the Swift-XRT LC, (b) and (d) panels, showing integrated flux between 0.3-10 keV [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. X-ray/γ-ray correlation for Mrk 421 per transit (a). The p-value of the correlation is 0.676 that shows consistency with a linear correlation. X-ray/γ-ray correlation for Mrk 501 per transit (b). It has been noticed that Mrk 501 has had a long period of very low activity that is reflected in a low flux measured even when higher activity in the X-ray emission happens, resulting in only 3 data points as mentioned in 4… view at source ↗
Figure 3
Figure 3. HAWC LCs for (a) Mrk 501 (b) Mrk 421 for an Integrated flux > 1TeV within the source transit (∼ 6.2 hr) using a total of 2143 days after applying the BB algorithm. ulation, we can expect their energy dependencies to be similar Kapanadze et al. (2020). We observed the same “harder-when-brighter” behav￾ior for Mrk 421, as depicted in [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: X-ray/γ-ray correlation for Mrk 421 in BBs (a). The p-value of the correlation is 0.892 that shows a strong consistency with a linear correlation. X-ray/γ-ray correlation for Mrk 501 in BBs (b). Due to the small size of the sample and the p-value, we only have evidence…
Figure 5
Figure 5. Figure 5: γ-ray flux vs. photon index (a) and photon index vs. X-ray flux (b), (c). We observed a “harder-when-brighter” behavior for Mrk 421, revealing a linear relationship within the energy bands employed. However, in the case of the X-ray flux shown in (b), a linear correlat…

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