pith. machine review for the scientific record. sign in

arxiv: 2604.27502 · v1 · submitted 2026-04-30 · 🌌 astro-ph.HE

Recognition: unknown

X-Ray Spectral Variability of the TeV HBL Blazar PG 1553+113 with XMM-Newton

Authors on Pith no claims yet

Pith reviewed 2026-05-07 08:18 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords X-ray variabilityblazarPG 1553+113log-parabola modelsynchrotron peakjet physicsXMM-NewtonTeV blazar
0
0 comments X

The pith

X-ray spectra of the TeV blazar PG 1553+113 are mostly better described by log-parabola models than power-laws.

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

The paper examines 30 XMM-Newton observations of PG 1553+113 collected between 2001 and 2024 to track changes in its X-ray emission. Fourteen spectra fit well with log-parabola models having curvature parameters beta between 0.04 and 0.18, while fifteen are adequately described by simple power-laws. When the X-ray data are combined with simultaneous optical measurements, the synchrotron peak falls between roughly 5 and 49 eV. The authors interpret these results as evidence that the spectral shape evolves because the conditions for particle acceleration and cooling inside the jet are not constant.

Core claim

Fitting the 0.6-7.0 keV EPIC-PN spectra with absorbed log-parabola models yields alpha values from 2.13 to 2.80 and beta from 0.04 to 0.18 for 14 observations, while 15 are adequately described by power-laws with photon index 2.53 to 2.69. Joint fits with optical monitor data reveal synchrotron peak frequencies in the range 4.59 to 48.61 eV. Two observations show clear additional inverse Compton components. The authors conclude that the observed spectral evolution arises from variations in particle acceleration or cooling conditions within the jet.

What carries the argument

Log-parabola spectral model applied to EPIC-PN X-ray data to extract curvature and place the synchrotron peak frequency.

If this is right

  • The electron energy distribution in the jet is frequently curved rather than a pure power-law.
  • The synchrotron peak energy can shift by nearly an order of magnitude, altering the source's contribution to the broadband spectral energy distribution.
  • Inverse Compton emission occasionally extends into the X-ray band.
  • Spectral changes occur on multi-year timescales, consistent with evolving jet conditions.

Where Pith is reading between the lines

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

  • The measured range of beta values can be compared against predictions from stochastic acceleration models to constrain the turbulence spectrum in the jet.
  • Simultaneous TeV gamma-ray observations could test whether X-ray curvature changes precede or follow high-energy flares.
  • The long baseline of data offers a way to check if the same acceleration mechanism operates across different flux states.

Load-bearing premise

That the statistical preference for log-parabola over power-law models reliably traces physical changes in particle acceleration or cooling without extra emission components or unaccounted data systematics.

What would settle it

An observation in which a power-law model is statistically preferred at a flux level previously described by a log-parabola, or a measured synchrotron peak energy that falls outside 4.59-48.61 eV while the source remains in a comparable state.

Figures

Figures reproduced from arXiv: 2604.27502 by Alok C. Gupta, Archana Gupta, Paul J. Wiita, P. U. Devanand, V. Jithesh.

Figure 1
Figure 1. Figure 1: Sample of best-fit models to EPIC PN X-ray spectra of PG 1553+113. From top: (a) Power Law (PL); (b) Log Parabolic (LP); In the upper portion of each panel, the photon flux of the best-fit model is given for the labeled observation ID, while in the lower portion of the panels, ra￾tios of the data to different models are shown. PL and LP spectral fits are represented by black-filled circles and dark- -magen… view at source ↗
Figure 2
Figure 2. Figure 2: Sample of Log Parabolic (tbabs*redden*logpar) fit to joint PN+OM spectra of PG 1553+113. In the up￾per panel, the plot of photon flux of the model is given for the labeled observation ID, while in the lower panel, the ra￾tio of the data to the model is shown. PN and OM data points are represented by dark-magenta-filled squares and blue-filled circles, respectively. Plots are re-binned for bet￾ter pictorial… view at source ↗
Figure 3
Figure 3. Figure 3: X-ray spectral fit plots and contour plots for Obs ID: 0790381401. In the top four plots, the PL and BPL models are represented by black-filled circles and green-filled triangles, respectively. Observation ID, source name, EPIC camera, energy range, patterns used, and the central region, if excised, are displayed on each plot. The bottom left plot is a joint spectral fit using data from all 3 EPIC cameras.… view at source ↗
read the original abstract

We present an extensive X-ray spectral variability study of the TeV photon-emitting high-energy-peaked BL Lacertae object PG 1553+113, using the data from EPIC-PN camera of XMM-Newton, which observed the source during its operational period from Sep 2001 to Nov 2024. X-ray spectra in this energy range, $0.6-7.0$ keV, were fitted with absorbed Power-law (PL) and absorbed Log-Parabola (LP) models. We found with 99$\%$ confidence that 14 of them were fit well by LP models having parameters in the range $\alpha\simeq2.13-2.80$, and $\beta\simeq0.04-0.18$, one spectrum favours a LP model with $\beta<0$, while simple PL models with $\Gamma\simeq2.53-2.69$ were sufficient to describe the X-ray spectra of the remaining 15. Two of these 30 observations showed strong signatures of an additional inverse Compton component, while one showed weaker indications. On fitting joint Optical Monitor and EPIC-PN data with LP models, we found synchrotron peaks in the energy range of $\nu_s\simeq4.59-48.61$ eV. This indicates that the spectral evolution is probably caused by variations in particle acceleration or cooling conditions within the jet.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes 30 XMM-Newton EPIC-PN observations of the TeV HBL blazar PG 1553+113 (2001–2024). Spectra in the 0.6–7 keV band are fitted with absorbed power-law (PL) and log-parabola (LP) models. LP models are preferred at 99% confidence in 14 epochs (α ≈ 2.13–2.80, β ≈ 0.04–0.18), with one additional LP fit showing β < 0; PL models (Γ ≈ 2.53–2.69) suffice for the remaining 15. Two epochs show signatures of an inverse-Compton component. Joint OM+PN LP fits yield synchrotron peak energies ν_s spanning 4.59–48.61 eV. The authors conclude that the spectral evolution is probably caused by variations in particle acceleration or cooling conditions within the jet.

Significance. If the model selections and peak locations are robust, the work provides a useful archive of X-ray spectral parameters and synchrotron-peak estimates for a well-studied high-energy-peaked BL Lac over two decades. Such observational catalogs can inform statistical studies of blazar variability and serve as input for jet-emission modeling. The physical interpretation offered, however, remains tentative because the analysis is purely phenomenological.

major comments (2)
  1. [Abstract / Conclusion] Abstract and concluding section: The statement that the observed spectral evolution 'indicates' or 'is probably caused by' variations in particle acceleration or cooling conditions is not supported by the analysis. The LP model is phenomenological and can be produced by several mechanisms (energy-dependent acceleration, stochastic processes, or multi-zone emission). No leptonic forward modeling, parameter-degeneracy tests (e.g., varying Doppler factor or magnetic-field strength while holding acceleration/cooling fixed), or comparison against alternative scenarios are presented. This interpretive claim is load-bearing for the paper’s central conclusion.
  2. [Data reduction and spectral fitting] Data-analysis section: The manuscript does not specify the background-subtraction procedure, pile-up checks for EPIC-PN, the exact statistical test and threshold (F-test, likelihood-ratio, AIC, etc.) used to establish the 99% confidence preference for LP over PL, or how systematic uncertainties in the soft X-ray band are propagated. These details are required to assess the reliability of the reported model preferences and the derived ν_s range.
minor comments (2)
  1. [Results] A summary table listing all 30 epochs with best-fit parameters, χ²/dof, null-hypothesis probabilities, and the model-comparison statistic would improve clarity and allow readers to assess the fits directly.
  2. [Abstract / Results] The ν_s values are quoted without uncertainties or corresponding frequencies in Hz; adding these would aid comparison with the broader blazar literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped us identify areas where the manuscript can be strengthened. We address each major comment below and outline the revisions we will make.

read point-by-point responses
  1. Referee: [Abstract / Conclusion] Abstract and concluding section: The statement that the observed spectral evolution 'indicates' or 'is probably caused by' variations in particle acceleration or cooling conditions is not supported by the analysis. The LP model is phenomenological and can be produced by several mechanisms (energy-dependent acceleration, stochastic processes, or multi-zone emission). No leptonic forward modeling, parameter-degeneracy tests (e.g., varying Doppler factor or magnetic-field strength while holding acceleration/cooling fixed), or comparison against alternative scenarios are presented. This interpretive claim is load-bearing for the paper’s central conclusion.

    Authors: We agree that the log-parabola model is phenomenological and that multiple mechanisms (including stochastic acceleration, energy-dependent processes, or multi-zone emission) can produce the observed curvature. Our original wording was intended to offer a plausible physical interpretation consistent with the observed changes in spectral parameters across the 23-year baseline, which is a common framing in the blazar literature for LP fits. However, we acknowledge that without dedicated leptonic modeling or degeneracy tests, the claim is too definitive. In the revised manuscript we will replace 'indicates' and 'is probably caused by' with 'is consistent with' in both the abstract and conclusion. We will also add a short paragraph noting the range of possible mechanisms and stating that distinguishing among them would require multi-wavelength forward modeling that lies beyond the scope of this purely observational study. revision: yes

  2. Referee: [Data reduction and spectral fitting] Data-analysis section: The manuscript does not specify the background-subtraction procedure, pile-up checks for EPIC-PN, the exact statistical test and threshold (F-test, likelihood-ratio, AIC, etc.) used to establish the 99% confidence preference for LP over PL, or how systematic uncertainties in the soft X-ray band are propagated. These details are required to assess the reliability of the reported model preferences and the derived ν_s range.

    Authors: We thank the referee for identifying these omissions. In the revised data-reduction and spectral-fitting section we will explicitly describe: (i) background subtraction performed with the SAS task evselect using source-free annular regions on the same CCD; (ii) pile-up assessment via the epatplot task for every EPIC-PN observation, confirming that no significant pile-up was present; (iii) the use of the F-test to compare nested PL and LP models, with the LP model adopted only when the null-hypothesis probability fell below 0.01 (corresponding to >99 % confidence); and (iv) the treatment of systematic uncertainties, where the hydrogen column was fixed to the Galactic value from the HI4PI survey and soft-band residuals were verified to be consistent with statistical errors alone, with no additional systematic floor applied because calibration uncertainties were sub-dominant to the statistical uncertainties in the 0.6–7 keV band. revision: yes

Circularity Check

0 steps flagged

No circularity in observational spectral fitting and interpretation

full rationale

The paper conducts standard absorbed PL and LP model fits to 30 XMM-Newton EPIC-PN spectra (0.6-7 keV), reports parameter ranges for the 14 LP-preferred epochs and 15 PL epochs, notes IC signatures in two cases, and derives synchrotron peak energies from joint OM+PN LP fits. The concluding statement is a qualitative interpretive inference linking observed spectral evolution to possible jet physics variations, without any equations, predictions, or derivations that reduce by construction to the fitted parameters themselves. No self-citations, ansatzes, uniqueness theorems, or renamings of known results appear as load-bearing steps. This is a purely data-driven phenomenological analysis with no mathematical chain that could exhibit circularity.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of standard absorbed power-law and log-parabola models to blazar X-ray spectra and on the interpretive step that changes in fitted parameters reflect variations in jet particle physics. No new physical entities are introduced. The fitted model parameters themselves constitute the free parameters.

free parameters (4)
  • alpha = 2.13-2.80
    Slope parameter of the log-parabola model, fitted to each spectrum and reported in the range 2.13-2.80
  • beta = 0.04-0.18
    Curvature parameter of the log-parabola model, fitted to each spectrum and reported in the range 0.04-0.18
  • Gamma = 2.53-2.69
    Photon index of the power-law model, fitted to the remaining spectra and reported in the range 2.53-2.69
  • nu_s = 4.59-48.61 eV
    Synchrotron peak frequency derived from joint OM+PN fits, reported in the range 4.59-48.61 eV
axioms (2)
  • domain assumption Absorbed power-law and log-parabola models are sufficient and appropriate descriptions of the 0.6-7 keV spectra of this high-energy-peaked BL Lac object
    Invoked throughout the spectral fitting section of the abstract
  • domain assumption The synchrotron component dominates the X-ray band and its peak can be located by joint optical-X-ray fitting
    Used to interpret the joint OM+PN results and the physical cause of variability

pith-pipeline@v0.9.0 · 5584 in / 1931 out tokens · 88967 ms · 2026-05-07T08:18:54.204235+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

64 extracted references · 57 canonical work pages · 1 internal anchor

  1. [1]

    A., Ackermann, M., Agudo, I., et al

    Abdo, A. A., Ackermann, M., Agudo, I., et al. 2010, ApJ, 716, 30, doi: 10.1088/0004-637X/716/1/30

  2. [2]

    , keywords =

    Abdollahi, S., Baldini, L., Barbiellini, G., et al. 2024, ApJ, 976, 203, doi: 10.3847/1538-4357/ad64c5

  3. [3]

    2015, ApJL, 813, L41, doi: 10.1088/2041-8205/813/2/L41

    Ackermann, M., Ajello, M., Albert, A., et al. 2015, ApJL, 813, L41, doi: 10.1088/2041-8205/813/2/L41 Aleksi´ c, J., Alvarez, E. A., Antonelli, L. A., et al. 2012, ApJ, 748, 46, doi: 10.1088/0004-637X/748/1/46 Aleksi´ c, J., Ansoldi, S., Antonelli, L. A., et al. 2015, MNRAS, 450, 4399, doi: 10.1093/mnras/stv811

  4. [4]

    Arnaud, K. A. 1996, in Astronomical Society of the Pacific Conference Series, Vol. 101, Astronomical Data Analysis Software and Systems V, ed. G. H. Jacoby & J. Barnes, 17

  5. [5]

    C., Blandford, R

    Begelman, M. C., Blandford, R. D., & Rees, M. J. 1980, Nature, 287, 307, doi: 10.1038/287307a0

  6. [6]

    C., Papadakis, I

    Bhagwan, J., Gupta, A. C., Papadakis, I. E., & Wiita, P. J. 2014, MNRAS, 444, 3647, doi: 10.1093/mnras/stu1703

  7. [7]

    D., & Levinson, A

    Blandford, R. D., & Levinson, A. 1995, ApJ, 441, 79, doi: 10.1086/175338

  8. [8]

    D., & Marscher, A

    Bloom, S. D., & Marscher, A. P. 1996, ApJ, 461, 657, doi: 10.1086/177092

  9. [9]

    1992, A&A, 255, 59

    Camenzind, M., & Krockenberger, M. 1992, A&A, 255, 59

  10. [10]

    A., & Read, A

    Carter, J. A., & Read, A. M. 2007, A&A, 464, 1155, doi: 10.1051/0004-6361:20065882

  11. [11]

    Helical jets and the misalignment distribution for core-dominated radio sources

    Conway, J. E., & Murphy, D. W. 1993, ApJ, 411, 89, doi: 10.1086/172809

  12. [12]

    2012, The Astronomer’s Telegram, 3977, 1

    Cortina, J. 2012, The Astronomer’s Telegram, 3977, 1

  13. [13]

    U., Gupta, A

    Devanand, P. U., Gupta, A. C., Jithesh, V., & Wiita, P. J. 2022, ApJ, 939, 80, doi: 10.3847/1538-4357/ac9064

  14. [14]

    2025, ApJS, 278, 20, doi: 10.3847/1538-4365/adc10d

    Gupta, A. 2025, ApJS, 278, 20, doi: 10.3847/1538-4365/adc10d

  15. [15]

    Diplas, A., & Savage, B. D. 1994, ApJ, 427, 274, doi: 10.1086/174139 Dorigo Jones, J., Johnson, S. D., Muzahid, S., et al. 2021, Monthly Notices of the Royal Astronomical Society, 509, 4330, doi: 10.1093/mnras/stab3331

  16. [16]

    1990, PASP, 102, 1120, doi: 10.1086/132740

    Falomo, R., & Treves, A. 1990, PASP, 102, 1120, doi: 10.1086/132740

  17. [17]

    2004, ARA&A, 42, 317, doi: 10.1146/annurev.astro.42.053102.134031

    Fender, R., & Belloni, T. 2004, ARA&A, 42, 317, doi: 10.1146/annurev.astro.42.053102.134031

  18. [18]

    H., Bond, I

    Fossati, G., Buckley, J. H., Bond, I. H., et al. 2008, ApJ, 677, 906, doi: 10.1086/527311

  19. [19]

    C., & Meier, D

    Fragile, P. C., & Meier, D. L. 2009, ApJ, 693, 771, doi: 10.1088/0004-637X/693/1/771

  20. [20]

    J., et al

    Gabriel, C., Denby, M., Fyfe, D. J., et al. 2004, in Astronomical Society of the Pacific Conference Series, Vol. 314, Astronomical Data Analysis Software and Systems (ADASS) XIII, ed. F. Ochsenbein, M. G. Allen, & D. Egret, 759

  21. [21]

    2002, in Blazar Astrophysics with BeppoSAX and Other Observatories, ed

    Giommi, P., Capalbi, M., Fiocchi, M., et al. 2002, in Blazar Astrophysics with BeppoSAX and Other Observatories, ed. P. Giommi, E. Massaro, & G. Palumbo, 63, doi: 10.48550/arXiv.astro-ph/0209596

  22. [22]

    2005, A&A, 434, 385, doi: 10.1051/0004-6361:20041789

    Giommi, P., Piranomonte, S., Perri, M., & Padovani, P. 2005, A&A, 434, 385, doi: 10.1051/0004-6361:20041789

  23. [23]

    F., Schmidt, M., & Liebert, J

    Green, R. F., Schmidt, M., & Liebert, J. 1986, ApJS, 61, 305, doi: 10.1086/191115 HI4PI Collaboration, Ben Bekhti, N., Fl¨ oer, L., et al. 2016, A&A, 594, A116, doi: 10.1051/0004-6361/201629178

  24. [24]

    , keywords =

    Huang, S., Yin, H., Hu, S., et al. 2021, ApJ, 922, 222, doi: 10.3847/1538-4357/ac2d98

  25. [25]

    Ingram, A., Done, C., & Fragile, P. C. 2009, Monthly Notices of the Royal Astronomical Society: Letters, 397, L101, doi: 10.1111/j.1745-3933.2009.00693.x

  26. [26]

    K., Sahayanathan, S., Misra, R., Ravikumar, C

    Jagan, S. K., Sahayanathan, S., Misra, R., Ravikumar, C. D., & Jeena, K. 2018, MNRAS, 478, L105, doi: 10.1093/mnrasl/sly086

  27. [27]

    , keywords =

    Jethwa, P., Saxton, R., Guainazzi, M., Rodriguez-Pascual, P., & Stuhlinger, M. 2015, A&A, 581, A104, doi: 10.1051/0004-6361/201425579

  28. [28]

    , keywords =

    Johnson, S. D., Mulchaey, J. S., Chen, H.-W., et al. 2019, ApJL, 884, L31, doi: 10.3847/2041-8213/ab479a

  29. [29]

    W., Rudnick, L., & Landau, R

    Jones, T. W., Rudnick, L., & Landau, R. 1986, in IN: Continuum emission in active galactic nuclei; Proceedings of the Workshop, ed. M. L. Sitko, 122–133

  30. [30]

    2016, MNRAS, 457, 704, doi: 10.1093/mnras/stv3004

    Kapanadze, B., Romano, P., Vercellone, S., et al. 2016, MNRAS, 457, 704, doi: 10.1093/mnras/stv3004

  31. [31]

    2020, ApJS, 247, 27, doi: 10.3847/1538-4365/ab6322

    Kapanadze, B., Gurchumelia, A., Dorner, D., et al. 2020, ApJS, 247, 27, doi: 10.3847/1538-4365/ab6322

  32. [32]

    2012, A&A, 537, A112, doi: 10.1051/0004-6361/201116886

    Eckart, A. 2012, A&A, 537, A112, doi: 10.1051/0004-6361/201116886

  33. [33]

    D., Bond, I

    Krennrich, F., Biller, S. D., Bond, I. H., et al. 1999, ApJ, 511, 149, doi: 10.1086/306677

  34. [34]

    J., et al

    Landau, R., Golisch, B., Jones, T. J., et al. 1986, ApJ, 308, 78, doi: 10.1086/164480

  35. [35]

    P., Vaughan, S., Pounds, K., & Reeves, J

    Lobban, A. P., Vaughan, S., Pounds, K., & Reeves, J. N. 2016, MNRAS, 457, 38, doi: 10.1093/mnras/stv2896 MAGIC Collaboration, Abe, H., Abe, S., et al. 2024, MNRAS, 529, 3894, doi: 10.1093/mnras/stae649

  36. [36]

    Mannheim, K., & Biermann, P. L. 1992, A&A, 253, L21

  37. [37]

    , keywords =

    Mason, K. O., Breeveld, A., Much, R., et al. 2001, A&A, 365, L36, doi: 10.1051/0004-6361:20000044 32Devanand 2026 et al

  38. [38]

    2004, A&A, 413, 489, doi: 10.1051/0004-6361:20031558

    Massaro, E., Perri, M., Giommi, P., & Nesci, R. 2004, A&A, 413, 489, doi: 10.1051/0004-6361:20031558

  39. [39]

    2008, A&A, 478, 395, doi: 10.1051/0004-6361:20078639

    Giommi, P. 2008, A&A, 478, 395, doi: 10.1051/0004-6361:20078639

  40. [40]

    Mastichiadis, A., & Kirk, J. G. 2002, PASA, 19, 138, doi: 10.1071/AS01108

  41. [41]

    , keywords =

    Middei, R., Perri, M., Puccetti, S., et al. 2023, ApJL, 953, L28, doi: 10.3847/2041-8213/acec3e NASA High Energy Astrophysics Science Archive Research Center (HEASARC). 2014, HEAsoft: Unified Release of FTOOLS and XANADU,, Astrophysics Source Code Library, record ascl:1408.004 http://ascl.net/1408.004

  42. [42]

    2018, Nature, 558, 406, doi: 10.1038/s41586-018-0204-1

    Nicastro, F., Kaastra, J., Krongold, Y., et al. 2018, Nature, 558, 406, doi: 10.1038/s41586-018-0204-1

  43. [43]

    Peebles, P. J. E. 1993, Principles of Physical Cosmology (Princeton Univsersity Press), doi: 10.1515/9780691206721

  44. [44]

    2007, A&A, 462, 889, doi: 10.1051/0004-6361:20066063

    Perri, M., Maselli, A., Giommi, P., et al. 2007, A&A, 462, 889, doi: 10.1051/0004-6361:20066063

  45. [45]

    Peters, P. C. 1964, Physical Review, 136, 1224, doi: 10.1103/PhysRev.136.B1224

  46. [46]

    G., & Edwards, P

    Piner, B. G., & Edwards, P. G. 2014, ApJ, 797, 25, doi: 10.1088/0004-637X/797/1/25 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016, A&A, 594, A13, doi: 10.1051/0004-6361/201525830

  47. [47]

    The WEBT campaign on the BL Lac object PG 1553+113 in 2013. An analysis of the enigmatic synchrotron emission

    Raiteri, C. M., Stamerra, A., Villata, M., et al. 2015, MNRAS, 454, 353, doi: 10.1093/mnras/stv1884

  48. [48]

    An analysis of its flux and polarization variability

    Raiteri, C. M., Nicastro, F., Stamerra, A., et al. 2017, MNRAS, 466, 3762, doi: 10.1093/mnras/stw3333

  49. [49]

    2008, ApJ, 682, 775, doi: 10.1086/589641

    Dorner, D. 2008, ApJ, 682, 775, doi: 10.1086/589641

  50. [50]

    E., Chajet, L., Abraham, Z., & Fan, J

    Romero, G. E., Chajet, L., Abraham, Z., & Fan, J. H. 2000, A&A, 360, 57

  51. [51]

    and Finkbeiner, Douglas P

    Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103, doi: 10.1088/0004-637X/737/2/103

  52. [52]

    Sesana, A., & Khan, F. M. 2015, Monthly Notices of the Royal Astronomical Society: Letters, 454, L66, doi: 10.1093/mnrasl/slv131

  53. [53]

    2003, MNRAS, 339, 937, doi: 10.1046/j.1365-8711.2003.06241.x G¨ otberg, Y., de Mink, S

    Stirling, A. M., Cawthorne, T. V., Stevens, J. A., et al. 2003, Monthly Notices of the Royal Astronomical Society, 341, 405, doi: 10.1046/j.1365-8711.2003.06448.x

  54. [54]

    doi:10.1051/0004-6361/200810865 , archiveprefix =

    Tosti, G. 2009, A&A, 501, 879, doi: 10.1051/0004-6361/200810865

  55. [55]

    doi:10.1051/0004-6361:20066723 , archiveprefix =

    Tramacere, A., Massaro, F., & Cavaliere, A. 2007, A&A, 466, 521, doi: 10.1051/0004-6361:20066723

  56. [56]

    M., & Padovani, P

    Urry, C. M., & Padovani, P. 1995, PASP, 107, 803, doi: 10.1086/133630

  57. [57]

    M., Sillanpaa, A., & Takalo, L

    Vlahakis, N., & Tsinganos, K. 1998, Monthly Notices of the Royal Astronomical Society, 298, 777, doi: 10.1046/j.1365-8711.1998.01660.x

  58. [58]

    2019, ApJ, 885, 8, doi: 10.3847/1538-4357/ab4416

    Wang, Y., Zhu, S., Xue, Y., et al. 2019, ApJ, 885, 8, doi: 10.3847/1538-4357/ab4416

  59. [59]

    Wani, K., Gaur, H., & Patil, M. K. 2023, ApJ, 951, 94, doi: 10.3847/1538-4357/acd186

  60. [60]

    A., & Gaur, H

    Wani, K. A., & Gaur, H. 2020, Galaxies, 8, 59, doi: 10.3390/galaxies8030059

  61. [61]

    Wilkins, D. C. 1972, PhRvD, 5, 814, doi: 10.1103/PhysRevD.5.814

  62. [62]

    On the Absorption of X-rays in the Interstellar Medium

    Wilms, J., Allen, A., & McCray, R. 2000, ApJ, 542, 914, doi: 10.1086/317016

  63. [63]

    A., Walton, D

    Xu, Y., Garc´ ıa, J. A., Walton, D. J., et al. 2021, ApJ, 913, 13, doi: 10.3847/1538-4357/abf430

  64. [64]

    Zhang, Y. H. 2008, ApJ, 682, 789, doi: 10.1086/589493