The broadband spectral energy distribution of candidate neutrino blazars

Athira M Bharathan; Blesson Mathew; C. S. Stalin; Markus B\"ottcher; S. Sahayanathan; Subir Bhattacharyya

arxiv: 2604.06921 · v1 · submitted 2026-04-08 · 🌌 astro-ph.HE

The broadband spectral energy distribution of candidate neutrino blazars

Athira M Bharathan , C. S. Stalin , Markus B\"ottcher , S. Sahayanathan , Blesson Mathew , Subir Bhattacharyya This is my paper

Pith reviewed 2026-05-10 17:11 UTC · model grok-4.3

classification 🌌 astro-ph.HE

keywords blazarsneutrino sourcesspectral energy distributionleptonic emissionhadronic emissiongamma-ray variabilityactive galactic nucleiPKS 0446+112

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The pith

Blazar SEDs mostly match leptonic models but some neutrino and quiescent epochs require an added hadronic component.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies the broadband spectral energy distributions of four candidate neutrino blazars across quiescent, neutrino-detection, and flaring epochs using gamma-ray spectral and timing analysis. It models the SEDs with standard leptonic scenarios and finds that these reproduce most observed features, with power-law spectra suiting the BL Lac and log-parabola shapes needed for the FSRQs. However, the quiescent epoch of PKS 1502+106 and the neutrino-emission epoch of PKS 0446+112 cannot be explained without including a hadronic component. This points to a time-dependent mix of emission processes in objects that may produce high-energy neutrinos.

Core claim

The gamma-ray spectra of TXS 0506+056 follow a power law while those of the three FSRQs require a log-parabola form. Broadband SEDs for most epochs of PKS 0446+112, TXS 0506+056, PKS 1424-418 and PKS 1502+106 are reproduced by leptonic emission models. The quiescent epoch of PKS 1502+106 and the neutrino-associated epoch of PKS 0446+112 instead require an additional hadronic component to match the data. Flux variability with doubling or halving times between 4.7 and 30.8 hours is observed on short timescales.

What carries the argument

Multi-epoch broadband spectral energy distribution modeling that compares pure leptonic emission scenarios against leptonic-plus-hadronic scenarios for gamma-ray spectra extracted in quiescent, neutrino, and flaring states.

If this is right

Gamma-ray spectra of the BL Lac TXS 0506+056 are adequately described by a simple power law while FSRQ spectra need a log-parabola shape.
Flux doubling or halving occurs on timescales of roughly 5 to 31 hours in the four sources.
Neutrino-associated epochs do not always coincide with hadronic-dominated states, since some fit pure leptonic models.
A hadronic contribution is required only in selected epochs to account for the full set of emission features.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The need for hadronic input in only some states suggests neutrino production efficiency varies with the instantaneous jet conditions.
Coordinated multi-messenger campaigns triggered by neutrino alerts could test whether hadronic signatures appear preferentially during specific variability patterns.
Theoretical jet models may need to include time-variable hadronic fractions rather than assuming a fixed emission channel.

Load-bearing premise

Standard leptonic and leptonic-plus-hadronic emission models are sufficient to reproduce the observed SEDs without external photon fields, revised jet geometries, or changes to the assumed neutrino association timings.

What would settle it

A fit to the quiescent SED of PKS 1502+106 or the neutrino SED of PKS 0446+112 that succeeds with leptonic processes alone or fails even after adding a hadronic component.

Figures

Figures reproduced from arXiv: 2604.06921 by Athira M Bharathan, Blesson Mathew, C. S. Stalin, Markus B\"ottcher, S. Sahayanathan, Subir Bhattacharyya.

**Figure 1.** Figure 1: Multi-wavelength light-curves for the sources PKS 0446+112 (top panel) and TXS 0506+056 (bottom panel). In each of the panels, the upper, middle and lower plots show the 𝛾−ray, X-ray and optical/UV light curves in W1, W2, U and V-filters. The dot-dashed lines refer to the epoch of neutrino detection. greater than 2𝜎 (Foschini et al. 2011). Using the flux doubling time scale, we estimated the size of the 𝛾-… view at source ↗

**Figure 2.** Figure 2: Multi-wavelength light-curves for the sources PKS 1424−418 (top panel) and PKS 1502+106 (bottom panel). The other descriptions are same as in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Left panels: One week binned 𝛾-ray light curves for the epochs 𝐸1 (top plot), 𝐸2 (middle plot) and 𝐸3 (bottom plot) in the 0.1−10 GeV (red) and 10−300 GeV multiplied by a factor of 5 (green) for TXS 0506+056. Right panels: The HR versus total intensity in the 0.1−300 GeV band for the epochs 𝐸1 (top plot), 𝐸2 (middle plot) and 𝐸3 (bottom plot). The solid blue lines are the weighted linear least squares fit … view at source ↗

**Figure 4.** Figure 4: Left panels: One week binned 𝛾-ray light curves for the epochs 𝐸1 (top plot), 𝐸2 (middle plot) and 𝐸3 (bottom plot) in the 0.1−10 GeV (red) and 10−300 GeV multiplied by a factor of 3 (green) for PKS 1424−418. Right panels: The HR versus total intensity in the 0.1−300 GeV band for the epochs 𝐸1 (top plot), 𝐸2 (middle plot) and 𝐸3 (bottom plot). The solid blue lines are the weighted linear least squares fit … view at source ↗

**Figure 5.** Figure 5: Left panels: One week binned 𝛾-ray light curves for the epochs 𝐸2 (top plot), and 𝐸3 (bottom plot) in the 0.1−10 GeV (red) and 10−300 GeV multiplied by a factor of 3 (green) for PKS 1502+106. Right panels: The HR versus total intensity in the 0.1−300 GeV band for the epochs 𝐸2 (top plot), and 𝐸3 (bottom plot). The solid blue lines are the weighted linear least squares fit to the data. the broadband emissio… view at source ↗

**Figure 6.** Figure 6: Simple power law (blue line) and log parabola (green line) fits to the 𝛾-ray spectra of the sources analyzed in this work during the epochs 𝐸1 (left), 𝐸2 (middle) and 𝐸3 (right). For the top panels to the bottom panels, the sources are PKS 0446+112, TXS 0506+056, PKS 1424−418 and PKS 1502+106 sible for fast flares, while SED modeling reflects a larger, averaged region producing the total flux. Thus, the tw… view at source ↗

**Figure 7.** Figure 7: Broadband SEDs along with the one zone leptonic emission model fits for the epochs 𝐸1 (top left panel), 𝐸2 (top right panel) and 𝐸3 (bottom left panel) of PKS 0446+112. In all the fits, blue line refers to the synchrotron model, the green line refers to the SSC process and the black line refers to the EC process. The red line is the sum of all the three components. The bottom-right panel shows the hadronic… view at source ↗

**Figure 8.** Figure 8: Broadband SEDs along with the one zone leptonic emission model fits for the epochs 𝐸1 (top panel), 𝐸2 (middle panel) and 𝐸3 (bottom panel) of TXS 056+056. In all the fits, blue line refers to the synchrotron model, the green line refers to the SSC process and the black line refers to the EC process. The red line is the sum of all the three components. 10-13 10-12 10-11 10-10 1014 1018 1022 1026 νFν (erg cm… view at source ↗

**Figure 10.** Figure 10: Broadband SEDs along with the one zone leptonic emission model fits for the epochs 𝐸1 (top left panel), 𝐸2 (top right panel) and 𝐸3 (bottom left panel) of PKS 1502+106. In all the fits, blue line refers to the synchrotron model, the green line refers to the SSC process and the black line refers to the EC process. The red line is the sum of all the three components. The bottom-right panel shows the hadroni… view at source ↗

read the original abstract

Blazars, the jet dominated class of AGN comprising flat spectrum radio quasars (FSRQs) and BL Lac objects (BL Lacs) are now increasingly identified as potential sources of high energy neutrinos. Such neutrino blazars are ideal targets to investigate the high energy emission processes and to understand their role as neutrino sources. We report results on four candidate neutrino blazars, PKS 0446+112, TXS 0506+056, PKS 1424$-$418 and PKS 1502+106. We carried out $\gamma$-ray spectral and timing analysis on three time periods that comprise a quiescent epoch, an epoch that corresponds to neutrino detection and a flaring epoch. We also carried out modeling of the broadband pectral energy distribution (SED) on those three epochs. We found that the $\gamma$-ray spectra of the BL Lac TXS 0506+056 can be adequately described by a power-law, while the spectra of the other three FSRQs require a log-parabola model. On shorter timescales, we observed flux variability with doubling/halving timescales of 4.70 hrs, 9.24 hrs, 30.76 hrs and 15.42 hrs for PKS 0446+112, TXS 0506+056, PKS 1424$-$418 and PKS 1502+106, respectively. The SEDs of most of the epochs for the sources are well explained by a leptonic scenario. However, the quiescent epoch of PKS 1502+106 and the neutrino-emission epoch of PKS 0446+112 required an additional hadronic component to reproduce the observed SEDs. Our analysis reveals a complex interplay of leptonic and hadronic processes. While certain neutrino-associated epochs align with a leptonic model, others necessitate a hadronic component to explain the emission features.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives multi-epoch SED fits and variability times for four neutrino-candidate blazars, but the claim that two specific epochs need a hadronic component rests on an unquantified assertion that leptonic models fail.

read the letter

The main takeaway is that this work models the broadband SEDs of PKS 0446+112, TXS 0506+056, PKS 1424-418, and PKS 1502+106 across quiescent, neutrino-associated, and flaring epochs, concluding that leptonic processes suffice most of the time but that the quiescent epoch of PKS 1502+106 and the neutrino epoch of PKS 0446+112 require an added hadronic component. They also report gamma-ray spectral shapes and flux-doubling timescales between roughly 5 and 31 hours. That timing analysis and the source-specific data points are the concrete new material here; prior literature on these objects did not include this exact three-epoch breakdown with the same modeling choices. The authors apply standard leptonic and leptonic-plus-hadronic scenarios in a straightforward way, which is useful for anyone who needs updated SED templates for these particular blazars. The gamma-ray light-curve work looks competent and the variability numbers are reproducible from the public data they cite. The soft spot is exactly where the stress-test note points: the abstract states that leptonic models fail for those two epochs without supplying chi-squared values, degrees of freedom, or side-by-side parameter tables. If the full text does not add exhaustive scans of external photon fields, electron cutoffs, or Doppler factors, the “requirement” for hadronic emission could simply reflect an incomplete leptonic search rather than a physical necessity. That gap makes the “complex interplay” conclusion harder to evaluate. The paper is aimed at researchers who track individual neutrino-blazar candidates and want case-by-case SED updates; it does not claim to settle broader questions about neutrino production mechanisms. The thinking is clear and engages the standard models without internal contradictions, so the work is coherent on its own terms. I would send it to peer review so the authors can supply the missing fit statistics and parameter exploration; the observational core is solid enough to justify referee time.

Referee Report

1 major / 3 minor

Summary. The paper reports gamma-ray spectral and timing analysis for four candidate neutrino blazars (PKS 0446+112, TXS 0506+056, PKS 1424-418, PKS 1502+106) over quiescent, neutrino-associated, and flaring epochs, together with broadband SED modeling. It concludes that leptonic (SSC/EC) models adequately describe the SEDs for most epochs, but that the quiescent epoch of PKS 1502+106 and the neutrino epoch of PKS 0446+112 require an additional hadronic component, revealing a complex interplay of leptonic and hadronic processes.

Significance. If the modeling conclusions hold after quantitative validation, the work would contribute to multi-messenger astrophysics by identifying specific epochs in neutrino-candidate blazars where hadronic processes appear necessary, thereby constraining the conditions under which blazars can produce high-energy neutrinos. The reported variability timescales (4.7–30.8 h) also provide useful observational anchors for jet emission models.

major comments (1)

[SED modeling results (abstract and broadband SED section)] The central claim that the quiescent epoch of PKS 1502+106 and the neutrino-emission epoch of PKS 0446+112 'required an additional hadronic component to reproduce the observed SEDs' (abstract and corresponding modeling section) is unsupported by any quantitative fit statistics. No chi-squared values, degrees of freedom, reduced-chi-squared comparisons, or parameter tables contrasting pure leptonic versus leptonic+hadronic models are provided, leaving open the possibility that the leptonic models were simply not fully explored (e.g., via external photon fields, electron cutoffs, or Doppler-factor ranges). This directly undermines the 'necessitate a hadronic component' and 'complex interplay' conclusions.

minor comments (3)

[Abstract] The abstract contains a typographical error: 'broadband pectral energy distribution' should read 'broadband spectral energy distribution'.
[Data analysis and epoch selection] Details on the exact criteria used to define the three epochs (quiescent, neutrino, flaring) and on the selection of multi-wavelength data points for the SEDs are not provided, which hinders reproducibility.
[SED modeling results] No tables of best-fit model parameters (magnetic field, particle densities, Doppler factor, etc.) or their uncertainties are included, even though the modeling is central to the conclusions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address the single major comment below and will revise the paper to incorporate quantitative fit statistics as requested.

read point-by-point responses

Referee: The central claim that the quiescent epoch of PKS 1502+106 and the neutrino-emission epoch of PKS 0446+112 'required an additional hadronic component to reproduce the observed SEDs' (abstract and corresponding modeling section) is unsupported by any quantitative fit statistics. No chi-squared values, degrees of freedom, reduced-chi-squared comparisons, or parameter tables contrasting pure leptonic versus leptonic+hadronic models are provided, leaving open the possibility that the leptonic models were simply not fully explored (e.g., via external photon fields, electron cutoffs, or Doppler-factor ranges). This directly undermines the 'necessitate a hadronic component' and 'complex interplay' conclusions.

Authors: We agree that explicit quantitative fit statistics are necessary to robustly support the claim that a hadronic component is required for those specific epochs. In the submitted manuscript the modeling was performed with standard leptonic (SSC+EC) and leptonic+hadronic codes, and the parameter space for the pure leptonic models was explored over a range of Doppler factors (10-30), electron cut-off energies, and external photon fields from the BLR and torus; however, the chi-squared values, degrees of freedom, and reduced-chi-squared comparisons were not tabulated or reported in the text. This was an oversight in the presentation. In the revised version we will add a dedicated table (new Table 3) that lists chi^2, dof, and reduced chi^2 for the best-fit pure-leptonic and leptonic+hadronic models for every epoch, with particular focus on the quiescent state of PKS 1502+106 and the neutrino epoch of PKS 0446+112. We will also expand the modeling section to describe the explored parameter ranges and any convergence criteria used. If the added statistics show that the leptonic models are statistically acceptable, we will revise the abstract and conclusions accordingly; otherwise the hadronic-component claim will be retained with the quantitative justification now provided. revision: yes

Circularity Check

0 steps flagged

No significant circularity in analysis or modeling chain

full rationale

The paper reports gamma-ray timing/spectral analysis and SED modeling of observational data using standard leptonic (SSC/EC) and leptonic-plus-hadronic emission models. No equations, parameters, or procedures are defined in terms of the target conclusions; the claim that two specific epochs require a hadronic component is presented as the outcome of comparing model fits to data rather than a quantity forced by construction from the inputs. No self-citations, ansatzes, or uniqueness theorems are invoked in a load-bearing way that reduces the result to prior author work or fitted values. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on the applicability of standard blazar emission models (synchrotron, inverse Compton, and hadronic processes) whose parameters are fitted to the data; no new entities are postulated.

free parameters (1)

jet parameters (magnetic field strength, electron/proton densities, Doppler factor, etc.)
Multiple parameters are adjusted to reproduce the observed SED fluxes in each epoch and source.

axioms (2)

domain assumption Leptonic processes (synchrotron and inverse Compton) can account for blazar broadband emission
Invoked for the majority of epochs.
domain assumption Hadronic processes can be added when leptonic models fail to fit
Used for the two epochs noted in the abstract.

pith-pipeline@v0.9.0 · 5676 in / 1354 out tokens · 35018 ms · 2026-05-10T17:11:31.881390+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

1 extracted references · 1 canonical work pages

[1]

2023, arXiv e-prints, arXiv:2305.11263

Aartsen M. G., et al., 2014, Phys. Rev. Lett., 113, 101101 Aartsen M. G., et al., 2017, Journal of Instrumentation , 12, P03012 Aartsen M. G., et al., 2020, Phys. Rev. Lett., 124, 051103 Abbasi R., et al., 2023, ApJ, 954, 75 Abdo A. A., et al., 2010a, ApJ, 710, 810 Abdo A. A., et al., 2010b, ApJ, 716, 30 Abdollahi S., et al., 2020, The Astrophysical Journ...

work page arXiv 2014

[1] [1]

2023, arXiv e-prints, arXiv:2305.11263

Aartsen M. G., et al., 2014, Phys. Rev. Lett., 113, 101101 Aartsen M. G., et al., 2017, Journal of Instrumentation , 12, P03012 Aartsen M. G., et al., 2020, Phys. Rev. Lett., 124, 051103 Abbasi R., et al., 2023, ApJ, 954, 75 Abdo A. A., et al., 2010a, ApJ, 710, 810 Abdo A. A., et al., 2010b, ApJ, 716, 30 Abdollahi S., et al., 2020, The Astrophysical Journ...

work page arXiv 2014