Bethe–Heitler Cascades and Hard Gamma-Ray Spectra in Flaring TeV Blazars: 1ES 0414009 and 1ES 1959650

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The essay deals with the spectral energy distribution (SED) modeling of two TeV BL Lac Objects by using both leptonic and hadronic models. The work is well done and written and, in my opinion, suitable for the publication. However, there are some minor issues that must be addressed before the publication. Please find below the list of issues:

1. Abstract: lines 1-7 are not suitable for an abstract, which should explain immediately the content of the papers. Lines 1-7 are more appropriate for an Introduction. Please delete them or move to Sect. 1.
2. Line 1 (but see also the whole text). AGN is the acronym of Active Galactic Nuclei. The word nuclei is the plural of nucleus. Therefore, AGN is already plural. There is no need to add "s" (AGNs). 
3. Line 19-20: Jetted AGN is the most general classification term, which includes flat-spectrum radio quasars (FSRQs), BL Lac Objects (BLOs), jetted Narrow-Line Seyfert 1 galaxies, misaligned AGN,....and so on. The term blazar refers to two sub-classes of jetted AGN, namely FSRQs and BLOs (it is the result of the contraction of the words BL Lac and quasar: bl-asar → blazar, by assonance with blaze). Please rewrite that sentence.
4. Line 65: what do you mean with "softer sources"? Please explain.
5. Line 92: the cited paper refers to the X-ray observations done with the scanning modulation collimator onboard HEAO-1, which operates in the 0.9-13.3 keV energy band. The energy band 0.2 keV - 10 MeV indicated by the authors is the sum of the bands of all the instruments onboard HEAO-1.
6. Line 137-144: the whole part is rather questionable. For example, compare with Tavecchio's papers cited by the authors themselves. I understand that the authors are in favour of the hadronic model, but these sentences are too strong, given the overwhelming evidence in favour of the leptonic models. Please smooth these sentences.
7. Table 4: the values of the jet powers are too small and not consistent with the observed gamma-ray emission. For example, 1ES 1959 has a radiative power 8.33x10³⁷ erg/s. Looking at the SED in Fig. 2 of Tavecchio et al. (2010) -- cited by the authors -- one can see that the gamma-ray emission has a peak luminosity of ~10⁴⁴ erg/s (the peak flux is νF_ν~10^-11 erg/cm²/s similar to the peak flux in Fig. 2 of the authors' work). There must be some error somewhere. A couple of suggestions on where to search for: I noted a rather small magnetic field, while the emitting region is a bit far. If one assumes a conic jet, the distance of the blob from the black hole is approximately ten times the size of the blob. Given the gravitational radii (or 0414, the black hole mass is 2x10⁹ M_⊙, which implies r_g~3x10¹⁴ cm; for 1959, the mass is 3.16x10⁸ M_⊙, which implies r_g~4.7x10¹³ cm), the distance of the emitting regions are ~3000 and ~1500r_g, respectively. These are not dramatically far distances, but when coupled with small magnetic field given by the authors in Table 3 (5-6x10^-2 G), might generate some problems. The farther the blob is, the stronger the magnetic field must be, not the opposite. Another problem might be that the authors averaged the data from overlapping energy bands of different instruments, as written at the line 366. If these data were not simultaneous, this can result is quite wrong conclusions. 
8. Line 357: the correct citation for the first detection of an orphan flare is H. Krawczynski et al., 2004, ApJ 601, 151, published one year before the paper cited by the authors. 
9. Line 366-368: again, the averaging of not simultaneous data can be a significant source of error in a SED modeling.

 

Author Response

Reviewer 1:

 

Regarding the suggested changes in the writing of the text, we have accepted all of them and they are in bold and red color along the text.

 

The followings are our point-by-point responses:

 

1) Abstract: lines 1-7 are not suitable for an abstract, which should explain immediately the content of the papers. Lines 1-7 are more appropriate for an Introduction. Please delete them or move to Sect. 1.

 

We have removed these lines from the abstract.

 

2) Line 1 (but see also the whole text). AGN is the acronym of Active Galactic Nuclei. The word nuclei is the plural of nucleus. Therefore, AGN is already plural. There is no need to add "s" (AGNs).

 

We have removede the letter “s” from AGNs.

 

3) Line 19-20: Jetted AGN is the most general classification term, which includes flat-spectrum radio quasars (FSRQs), BL Lac Objects (BLOs), jetted Narrow-Line Seyfert 1 galaxies, misaligned AGN,....and so on. The term blazar refers to two sub-classes of jetted AGN, namely FSRQs and BLOs (it is the result of the contraction of the words BL Lac and quasar: bl-asar → blazar, by assonance with blaze). Please rewrite that sentence.

 

We have rewritten the sentence as “Blazars, a subclass of jetted AGN that includes flat-spectrum radio quasars (FSRQs) and BL Lac objects (BLOs), exhibit non-thermal continuum emission originating from relativistic jets aligned close to our line of sight”.

 

4) Line 65: what do you mean with "softer sources"? Please explain.

 

In this context, “softer sources” refers to astrophysical sources with photon spectra that decline more steeply with energy, that is, sources that emit more low-energy photons than high-energy ones. More technically, a “soft” spectrum has a steep spectral index, meaning the flux drops off rapidly as energy increases. This is in contrast to a “hard” spectrum, where the decline with energy is slower, and more high-energy photons are present.

 

5) Line 92: the cited paper refers to the X-ray observations done with the scanning modulation collimator onboard HEAO-1, which operates in the 0.9-13.3 keV energy band. The energy band 0.2 keV - 10 MeV indicated by the authors is the sum of the bands of all the instruments onboard HEAO-1.

 

We thank the reviewer for the information and we have corrected the energy band in the text.

 

6) Line 137-144: the whole part is rather questionable. For example, compare with Tavecchio's papers cited by the authors themselves. I understand that the authors are in favour of the hadronic model, but these sentences are too strong, given the overwhelming evidence in favour of the leptonic models. Please smooth these sentences.

 

We thank the reviewer and we have smoothed the sentences as “During intense X-ray flares in 2016–2017, the source exhibited very hard X-ray spectra, with the 0.3–300 GeV photon index also remaining hard during the same periods [63]. While reproducing such hard gamma-ray spectra can be challenging for standard leptonic models, certain hadronic scenarios may offer a more natural explanation under specific conditions [64]. For example, the proton blazar model introduced by Mannheim [20] predicts X-ray spectra with photon indices in the range 1.5–1.7 and can account for uncorrelated X-ray–TeV variability, a feature reported for this source [58]. Nonetheless, leptonic models remain widely favored in the literature (e.g., [12]), and further multiwavelength studies are needed to distinguish between competing scenarios.”

 

7) Table 4: the values of the jet powers are too small and not consistent with the observed gamma-ray emission. For example, 1ES 1959 has a radiative power 8.33x10³⁷ erg/s. Looking at the SED in Fig. 2 of Tavecchio et al. (2010) -- cited by the authors -- one can see that the gamma-ray emission has a peak luminosity of ~10⁴⁴ erg/s (the peak flux is νF_ν~10^-11 erg/cm²/s similar to the peak flux in Fig. 2 of the authors' work). There must be some error somewhere. A couple of suggestions on where to search for: I noted a rather small magnetic field, while the emitting region is a bit far. If one assumes a conic jet, the distance of the blob from the black hole is approximately ten times the size of the blob. Given the gravitational radii (or 0414, the black hole mass is 2x10⁹ M_⊙, which implies r_g~3x10¹⁴ cm; for 1959, the mass is 3.16x10⁸ M_⊙, which implies r_g~4.7x10¹³ cm), the distance of the emitting regions are ~3000 and ~1500r_g, respectively. These are not dramatically far distances, but when coupled with small magnetic field given by the authors in Table 3 (5-6x10^-2 G), might generate some problems. The farther the blob is, the stronger the magnetic field must be, not the opposite. Another problem might be that the authors averaged the data from overlapping energy bands of different instruments, as written at the line 366. If these data were not simultaneous, this can result is quite wrong conclusions.

We thank the reviewer for their careful and insightful analysis. We agree that the jet power values reported in the previous version appeared underestimated and were not consistent with the high observed gamma-ray luminosity. In the revised version of the paper, we have redone the SED fitting using the full, unaveraged dataset, avoiding any averaging across non-simultaneous data from overlapping energy bands. This was an important correction, as we now recognize that the previous averaging likely diluted the peak fluxes and resulted in an underestimation of the modelled radiative output. As a result of using the unbinned and unaveraged data, the derived jet powers, including the radiative luminosity, are now significantly higher and much more consistent with the literature, including with the gamma-ray peak luminosities reported by Tavecchio et al. (2010). The new model fits reproduce the observed SED peaks more accurately and yield radiative jet powers in better agreement with the expected physical energetics. The L_rad parameter in our work has now a value of 5.78 x 10⁴¹ erg/s, while the one from Tavecchio’s work is about 7.04 x 10⁴² erg/s (This value was estimated using the parameters from Table 5).

We also thank the reviewer for pointing out the potential tension between the emission region distance and the magnetic field strength. In the revised fits, we find that the magnetic field values have increased (now typically in the range of ~0.1 G), helping to restore a more physically consistent configuration when considering the emitting region's distance in terms of gravitational radii. This change aligns better with expectations from a conical jet structure and supports the overall plausibility of the model.

These updates are reflected in the revised Tables 3 and 4 of the paper.

 

8) Line 357: the correct citation for the first detection of an orphan flare is H. Krawczynski et al., 2004, ApJ 601, 151, published one year before the paper cited by the authors.

 

We thank the reviewer and we have corrected the reference in the text.

 

9) Line 366-368: again, the averaging of not simultaneous data can be a significant source of error in a SED modeling.

 

Thank you for your comment. You are absolutely right that using non-simultaneous data can introduce significant uncertainties in SED modeling. In the revised version of the manuscript, we have re-performed the fitting using the unbinned and non-averaged dataset, improving the spectral resolution and preserving finer details in the data.

The lines 366-368 were removed from the text.

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript effectively presents two sinplified model treatments to account for radio to hard gamma ray emissions from the 1ES04014+009 and 1ES1959+650 flaring Blazars. The first approach applies the classic leptonic, synchrotron-inverse Compton model, while the second adds hadronic contributions, especially focusing on the Bethe-Heitler cascade pairs and resulting emissions.  A key model simplification is the one-zone assumption for the Blazar jets. While this hides important Blazar dynamical physics, it does enable manageable numerical treatments of the radiative processes, so is acceptable for a start. The modeling reveals that the leptonic model can account reasonably well for much of the observed spectral components, the hadronic contributions substantially improve the gamma ray emission models.

 

The manuscript is well organized and clearly written. I encourage Universe to publish it as is.

Author Response

Reviewer 2:

 

This manuscript effectively presents two sinplified model treatments to account for radio to hard gamma ray emissions from the 1ES04014+009 and 1ES1959+650 flaring Blazars. The first approach applies the classic leptonic, synchrotron-inverse Compton model, while the second adds hadronic contributions, especially focusing on the Bethe-Heitler cascade pairs and resulting emissions. A key model simplification is the one-zone assumption for the Blazar jets. While this hides important Blazar dynamical physics, it does enable manageable numerical treatments of the radiative processes, so is acceptable for a start. The modeling reveals that the leptonic model can account reasonably well for much of the observed spectral components, the hadronic contributions substantially improve the gamma ray emission models.

The manuscript is well organized and clearly written. I encourage Universe to publish it as is.

 

We sincerely thank the reviewer for their positive and constructive feedback. We are pleased to know that the manuscript was found to be well-organized and clearly written.

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript "Bethe-Heitler cascades and hard Gamma-Ray spectra in flaring TeV Blazars: 1ES 0414+009 and 1ES 1959+650" by S. V. B. da Silva et al. (universe-3645505) presents the modeling analysis of the broad-band spectral energy distribution (SED) of two prominent TeV gamma-ray-emitting blazars, 1ES 0414+009 and 1ES 1959+650. The authors argue that leptonic modeling assuming the standard one-zone synchrotron + synchrotron self-Compton (SSC) scenario is insufficient for properly describing the SED. Instead, the hard gamma-ray spectra observed during flaring could be modeled by also including inverse-Compton (IC) scattering of electrons and positrons produced via the Bethe-Heitler process.

The topic of the paper may be sufficiently interesting for the community so that the manuscript deserves eventual publication. However, I have a couple of comments and suggestions for the authors that could lead to the improvement of the manuscript. In particular, I think the main claim of this study needs a more solid foundation. My comments are grouped into two categories below, major issues and minor suggestions.

Major issues:

1) One would expect the two different SED fits (SSC only, Sect. 4.1, and lepto-hadronic, Sect. 4.2) are based on the same measurement data. But by comparing Fig. 1 to Fig. 3, and Fig. 2 to Fig. 4, it seems that the latter figures display much more data points. What is the reason of this difference? Why isn't it discussed in the text? The comparison of the figures is also complicated by the fact that the horizontal axes are scaled in frequency (Hz) and energy (eV) in Figs. 1-2 and Figs. 3-4, respectively.

2) The legends in Figs. 3 & 4 display lots of data sources with abbreviations never explained, and references never cited. It is not acceptable this way. Even if individual literature references are not given (even though that would be correct, by giving proper credit to others' work), at least the abbreviations should be resolved and a common reference should be given which the reader can use for tracing the original data points back.

3) The paper claims (in Sect. 5, line 368) that "a purely leptonic model is insufficient to explain the high-energy gamma-ray emissions observed in both sources". But I did not find a quantitative evaluation of the differences between the two fits. In which (statistical) sense one is less sufficient than the other? This should be discussed in details before station that "the inclusion of hadronic interactions (...) significantly improves the fit" (line 372). What does significance mean here?       

Minor suggestions and questions:

1) page 1, line 18
The first sentence of the text is inaccurate: "Active galactic nuclei (AGNs) are among the most numerous extragalactic objects in astronomy" - this is simply not true! Ordinary (inactive) galaxies by far outnumber AGNs at any redshift.

2) page 2, line 31; page 6, line 179:
Some abbreviations like IC and MCMC are not explained when used for the first time in the text. In general, given the large number of abbreviations, I recommend adding an extra section at the end of the paper with the comprehensive list of all abbreviations (the MDPI LaTeX template allows for this).

3) page 4, lines 77, 88 + Section 2 title
The term "distant blazars" is not quite justified and can be misleading here, as the redshifts (0.287 and especially 0.047) are not particularly high. Even among Tev-detected blazars, there are objects at around z=1 listed in the TeVCat (https://www.tevcat.org/). Please either avoid calling them "distant" or at least explain more accurately in which sense you consider them distant.     

4) page 4, line 82:
we introduce our sample (single, not plural - there is only one sample containing 2 objects)

5) page 7, line 221:
You mention that the distance of the radiation region from the black hole is fixed to 10^17 cm (default value). I wounder how justified it is, and how the modeling results are affected if alternative values are used here. In particular, how sensitive is the size of the emission region on this initial parameter (page 8, line 252).

6) page 8, Table 3:
Many of the numbers are given up to so many decimal digits that are likely insignificant. For example, if the results obtained for the bulk Lorentz factor are not accurate to 0.001 level (which I doubt), then it is incorrect to list them with so many digits. Please revise the numbers and round them to meaningful digits. 

7) page 8, Table 3:
Comparing the parameters obtained for the two different sources, the particle number density stands out as having wildly different values (~0.2 vs. 38.8 particles per cubic cm). Does it make sense physically? If yes, what can be the reason for such a large difference? How is it compared to values obtained in other similar sources in the literature?

8) page 8, around line 240 + page 9, around line 270:
You repeat numbers which are already listed in Tables 3 and 4. This is not necessary, occupies extra space, and it makes the text harder to digest for the reader.

9) page 12, Fig. 3:
There is a dashed-lined circle at ~10^12 eV but without any explanation. 
  
10) page 15 and later, References:
Some titles are printed in all capital letters. This is not necessary.

Author Response

Reviewer 3:

 

Regarding the suggested changes in the writing of the text, we have accepted all of them and they are in bold and red color along the text.

 

The followings are our point-by-point responses:

 

Major issues:

 

1) One would expect the two different SED fits (SSC only, Sect. 4.1, and lepto-hadronic, Sect. 4.2) are based on the same measurement data. But by comparing Fig. 1 to Fig. 3, and Fig. 2 to Fig. 4, it seems that the latter figures display much more data points. What is the reason of this difference? Why isn't it discussed in the text? The comparison of the figures is also complicated by the fact that the horizontal axes are scaled in frequency (Hz) and energy (eV) in Figs. 1-2 and Figs. 3-4, respectively.

 

Thank you for pointing this out. The apparent discrepancy in the number of data points between Figs. 1–2 and Figs. 3–4 arises from a difference in the treatment of the observational data. Specifically, the SSC-only fits shown in Figs. 1 and 2 were originally performed using rebinned multiwavelength, while the lepto-hadronic models in Figs. 3 and 4 were based on the full, unbinned dataset, which resulted in the visible discrepancy in the number of data points.

In the revised version of the manuscript, we have addressed this inconsistency by re-performing the SSC fits using the unbinned dataset as well. All SED modeling presented in the current version is now based on the same full-resolution data, ensuring a consistent and fair comparison between models.

Regarding the horizontal axes: Figs. 1–2 present frequency (Hz) along the bottom axis and energy (eV) along the top axis to aid interpretation. So they can be compared to Figs. 3–4, which display only energy on the horizontal axis.

 

2) The legends in Figs. 3 & 4 display lots of data sources with abbreviations never explained, and references never cited. It is not acceptable this way. Even if individual literature references are not given (even though that would be correct, by giving proper credit to others' work), at least the abbreviations should be resolved and a common reference should be given which the reader can use for tracing the original data points back.

 

We thank the reviewer for pointing this out. We agree that figure legends should be fully self-contained and properly credited. In the revised manuscript we now explicitly refer to Tables 1 and 2 in the figure captions, which describe the observational data used in the modeling.

 

3) The paper claims (in Sect. 5, line 368) that "a purely leptonic model is insufficient to explain the high-energy gamma-ray emissions observed in both sources". But I did not find a quantitative evaluation of the differences between the two fits. In which (statistical) sense one is less sufficient than the other? This should be discussed in details before stating that "the inclusion of hadronic interactions (...) significantly improves the fit" (line 372). What does significance mean here?

 

We thank the reviewer for pointing out the need for a more rigorous justification of our claim that the leptonic model is insufficient and that the lepto-hadronic model significantly improves the fit. We have rewritten this sentence in text as follows:

 

“Initial modeling using a purely leptonic scenario yielded fits that could not adequately reproduce the observed hard gamma-ray spectra during flaring states, particularly above 10$^{11}$ eV. We therefore extended our analysis to a lepto-hadronic model, incorporating proton-proton (pp) and proton-photon (p$\gamma$) interactions within the jet environment. The inclusion of the p$\gamma$ component indicates that hadronic processes may play a substantial role in the high-energy emission of these two HBLs during flaring episodes.”

 

Minor suggestions and questions:

 

1) page 1, line 18:

The first sentence of the text is inaccurate: "Active galactic nuclei (AGNs) are among the most numerous extragalactic objects in astronomy" - this is simply not true! Ordinary (inactive) galaxies by far outnumber AGNs at any redshift.

 

We agree with the reviewer and we have corrected it by saying “Active galactic nuclei (AGN) constitute a prominent population of energetic extragalactic sources, with blazars representing an extreme subclass of radio-loud AGN”. This sentence is in the text in bold and reds color.

 

2) page 2, line 31; page 6, line 179:

Some abbreviations like IC and MCMC are not explained when used for the first time in the text. In general, given the large number of abbreviations, I recommend adding an extra section at the end of the paper with the comprehensive list of all abbreviations (the MDPI LaTeX template allows for this).

 

We have explained those abbreviations in the text and we have added a list of all abbreviations in the text.

 

3) page 4, lines 77, 88 + Section 2 title:

The term "distant blazars" is not quite justified and can be misleading here, as the redshifts (0.287 and especially 0.047) are not particularly high. Even among Tev-detected blazars, there are objects at around z=1 listed in the TeVCat (https://www.tevcat.org/). Please either avoid calling them "distant" or at least explain more accurately in which sense you consider them distant.

 

We agree with the reviewer and we removed the word distant.

 

4) page 4, line 82:

We introduce our sample (single, not plural - there is only one sample containing 2 objects)

 

We agree with the reviewer and we have corrected it in the text.

 

5) page 7, line 221:

You mention that the distance of the radiation region from the black hole is fixed to 10^17 cm (default value). I wounder how justified it is, and how the modeling results are affected if alternative values are used here. In particular, how sensitive is the size of the emission region on this initial parameter (page 8, line 252).

 

We thank the reviewer for raising this important point. In our modeling with JetSet, we initially adopted the default value of R_H=10¹⁷ cm for the distance of the emission region (blob) from the black hole, as is commonly assumed in one-zone leptonic models for blazars. This value is motivated by typical dissipation distances inferred from SED modeling of blazars, particularly for BL Lacs, where the emission region is often located beyond the broad-line region (BLR).

To assess the robustness of our results, we conducted additional tests by varying R_H over an order of magnitude (e.g., 1016–1018cm). We found that for BL Lac-type objects, which typically lack a strong external radiation field, the model is less sensitive to the exact value of R_H, as synchrotron self-Compton (SSC) dominates. In such cases, the main constraint on R_b (emission region size) comes from variability and Doppler boosting, rather than from the assumed distance from the black hole.

 

6) page 8, Table 3:

Many of the numbers are given up to so many decimal digits that are likely insignificant. For example, if the results obtained for the bulk Lorentz factor are not accurate to 0.001 level (which I doubt), then it is incorrect to list them with so many digits. Please revise the numbers and round them to meaningful digits.

 

We agree with the reviewer and we let only two decimal digits for all quantities in Table 3.

 

7) page 8, Table 3:

Comparing the parameters obtained for the two different sources, the particle number density stands out as having wildly different values (~0.2 vs. 38.8 particles per cubic cm). Does it make sense physically? If yes, what can be the reason for such a large difference? How is it compared to values obtained in other similar sources in the literature?

 

We thank the reviewer for this insightful question. In the revised version of the paper, we have redone the SED fitting using the full, unaveraged dataset, avoiding any averaging across non-simultaneous data from overlapping energy bands. This was an important correction, as we now recognize that the previous averaging likely diluted the peak fluxes and resulted in an underestimation of some parameters. The particle number densities derived for the two sources are now 45.11 cm⁻³ (1ES 0414+009) and 12.47 cm⁻³ (1ES 1959+650). While these values differ by approximately a factor of 3.6, they are physically reasonable within the context of purely leptonic one-zone synchrotron self-Compton (SSC) models. The particle number density is influenced by multiple factors such as the size of the emitting region, magnetic field strength, and Doppler factor. These parameters are fitted individually for each source and can vary significantly, leading to differences in the resulting electron densities.

Moreover, in one-zone SSC models, different parameter sets can reproduce the observed SED equally well. This degeneracy means that the particle number density can vary depending on the balance between magnetic and particle energy densities, as well as assumptions about variability timescales and minimum/maximum Lorentz factors. The derived number densities (12–45 cm⁻³) fall within the range commonly found in leptonic modeling of BL Lac objects and HBLs (e.g., Tavecchio et al. 1998; Finke et al. 2008), and are not atypical for compact, high-energy emitting regions in blazar jets.

 

References:

Fabrizio Tavecchio et al 1998 ApJ 509 608.

Justin D. Finke et al 2008 ApJ 686 181.

 

8) page 8, around line 240 + page 9, around line 270:

You repeat numbers which are already listed in Tables 3 and 4. This is not necessary, occupies extra space, and it makes the text harder to digest for the reader.

 

We agree with the reviewer and we have removed the duplicated information from the text.

 

9) page 12, Fig. 3:

There is a dashed-lined circle at ~10^12 eV but without any explanation.

 

The dashed line circle is used to highlight the fluxes measured by Fermi-LAT and ARGO-YBJ observatory. We have explained the circle in the text.

 

10) page 15 and later, References:

Some titles are printed in all capital letters. This is not necessary.

 

We thank the reviewer and we have corrected the references.

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

I do appreciate the efforts of the authors for making the suggested corrections, especially for repeating the pure leptonic SED analysis with the same data as used for the lepto-hardronic fit. However, the comparison of Figs. 1 & 3, as well as Fig. 2 & 4, suggests that the date sets are still not identical. For example, radio data points (i.e., energy range ~10^{-6} - 10^{-8} eV) are obviously missing from Figs. 1 and 2. (Whether they were in fact included in the analysis I don't know, but even if they weren't, a note or an explanation about the difference would be required.)

A somewhat related problem is that while the captions of Fig. 3 and 4 refer to Tables 1 and 2, respectively, for the details of observing data, the figure legends actually list much more data sources than given in those tables. For example, GB6, RASS, WISE, NVSS, PMN, TGSS150, NED (presumably contains data collected from other literature references in itself), and many others are not yet referenced and explained at all. This needs to be fixed before the manuscript can be accepted for publication.

Author Response

Reviewer – Second Round:

 

1) I do appreciate the efforts of the authors for making the suggested corrections, especially for repeating the pure leptonic SED analysis with the same data as used for the lepto-hardronic fit. However, the comparison of Figs. 1 & 3, as well as Fig. 2 & 4, suggests that the date sets are still not identical. For example, radio data points (i.e., energy range ~10^{-6} - 10^{-8} eV) are obviously missing from Figs. 1 and 2. (Whether they were in fact included in the analysis I don't know, but even if they weren't, a note or an explanation about the difference would be required.)

 

We thank the reviewer for the careful examination of our revised figures and the valuable observation regarding the apparent absence of radio data points in Figs. 1 and 2.

We would like to clarify that the radio data were indeed included in the analysis for both the pure leptonic and lepto-hadronic fits. However, in Figs. 1 and 2, the radio fluxes appear to be missing due to a plotting artifact: the model-predicted fluxes in the high-energy regime are significantly higher than the radio flux values. As a result, the radio points lie well below the visible y-axis range of the plot and were not visually apparent.

This omission is purely visual and does not reflect a difference in the datasets used for the analysis. However, we emphasize that the inclusion of these radio data points does not alter the results or conclusions of our leptonic analysis. This is because the radio emission in such compact regions is typically subject to strong synchrotron self-absorption, meaning that the SSC model used, characterized by a single homogeneous zone, is not expected to reproduce the radio flux. As a result, the radio data do not provide meaningful constraints on the model parameters within the framework adopted in our analysis.

To avoid confusion, we revised the figures to better illustrate the full energy range and added to Figs. 1 and 2 captions the following information “Radio data points (low-energy range) are included for completeness but are not fitted, as synchrotron self-absorption in the compact emission region renders them unconstraining within this modeling framework”.

2) A somewhat related problem is that while the captions of Fig. 3 and 4 refer to Tables 1 and 2, respectively, for the details of observing data, the figure legends actually list much more data sources than given in those tables. For example, GB6, RASS, WISE, NVSS, PMN, TGSS150, NED (presumably contains data collected from other literature references in itself), and many others are not yet referenced and explained at all. This needs to be fixed before the manuscript can be accepted for publication.

 

We thank the reviewer for pointing out this important inconsistency. In the revised version of the manuscript, we have carefully updated Tables 1 and 2 to include all the data sources mentioned in the captions of Figures 3 and 4, respectively. For clarity, we have added appropriate references for each data source within the tables.

These changes ensure consistency between the figure captions and the tables, and we believe they improve the transparency and reproducibility of our analysis. We are grateful to the reviewer for bringing this to our attention.