Self-organized criticality in multi-pulse gamma-ray bursts

Abstract

The variability in multi-pulse gamma-ray bursts (GRBs) may help to reveal the mechanism of underlying processes from the central engine. To investigate whether the self-organized criticality (SOC) phenomena exist in the prompt phase of GRBs, we statistically study the properties of GRBs with more than 3 pulses in each burst by fitting the distributions of several observed physical variables with a Markov Chain Monte Carlo approach, including the isotropic energy E_iso, the duration time T, and the peak count rate P of each pulse. Our sample consists of 454 pulses in 93 GRBs observed by the CGRO/BATSE satellite. The best-fitting values and uncertainties for these power-law indices of the differential frequency distributions are: {\alpha }_E^d=1.54\pm 0.09, {\alpha }_T^d={1.82}_{-0.15}^{+0.14} and {\alpha }_P^d={2.09}_{-0.19}^{+0.18}, while the power-law indices in the cumulative frequency distributions are: {\alpha }_E^c={1.44}_{-0.10}^{+0.08}, {\alpha }_T^c={1.75}_{-0.13}^{+0.11} and {\alpha }_P^c={1.99}_{-0.19}^{+0.16}. We find that these distributions are roughly consistent with the physical framework of a Fractal-Diffusive, Self-Organized Criticality (FD-SOC) system with the spatial dimension S = 3 and the classical diffusion β=1. Our results support that the jet responsible for the GRBs should be magnetically dominated and magnetic instabilities (e.g., kink model, or tearing-model instability) lead the GRB emission region into the SOC state.

Keywords

gamma-ray burst / general methods: statistical

References

[1] P. Meszaros and M. J. Rees, Tidal heating and mass loss in neutron star binaries- Implications for gamma-ray burst models, Astrophys. J. 397, 570 (1992)

[2] B. Paczynski, Gamma-ray bursters at cosmological distances, Astrophys. J. Lett. 308, L43 (1986)

[3] B. D. Metzger, D. Giannios, and S. Horiuchi, Heavy nuclei synthesized in gamma-ray burst outflows as the source of ultrahigh energy cosmic rays, Mon. Not. R. Astron. Soc. 415(3), 2495 (2011)

[4] A. Goldstein, P. Veres, E. Burns, M. S. Briggs, R. Hamburg, et al., An ordinary short gamma-ray burst with extraordinary implications: Fermi-GBM detection of GRB 170817A, Astrophys. J. Lett. 848(2), L14 (2017)

[5] Z. G. Dai, X. Y. Wang, and X. F. Wu, X-ray flares from postmerger millisecond pulsars, Science 311(5764), 1127 (2006)

[6] A. I. MacFadyen and S. E. Woosley, Collapsars: Gammaray bursts and explosions in “failed supernovae” Astrophys. J. 524(1), 262 (1999)

[7] D. N. Burrows, P. Romano, A. Falcone, et al., Bright X-ray flares in gamma-ray burst afterglows, Science 309(5742), 1833 (2005)

[8] E. W. Liang, B. Zhang, P. T. O’Brien, R. Willingale, L. Angelini, D. N. Burrows, S. Campana, G. Chincarini, A. Falcone, N. Gehrels, M. R. Goad, D. Grupe, S. Kobayashi, P. Meszaros, J. A. Nousek, J. P. Osborne, K. L. Page, and G. Tagliaferri, Testing the curvature effect and internal origin of gamma-ray burst prompt emissions and X-ray flares with swift data, Astrophys. J. 646(1), 351 (2006)

[9] B. Zhang, Y. Z. Fan, J. Dyks, S. Kobayashi, P. Meszaros, D. N. Burrows, J. A. Nousek, and N. Gehrels, Physical processes shaping gamma-ray burst X-ray afterglow light curves: Theoretical implications from the swift X-ray telescope observations, Astrophys. J. 642(1), 354 (2006)

[10] C. Liu and J. Mao, GRB X-ray flare properties among different GRB subclasses, Astrophys. J. 884(1), 59 (2019)

[11] M. L. Goodman, C. Kwan, B. Ayhan, and E. L. Shang, A new approach to solar flare prediction, Front. Phys. 15(3), 34601 (2020)

[12] F. Y. Wang and H. Yu, SGR-like behaviour of the repeating FRB 121102, J. Cosmol. Astropart. Phys. 2017, 023 (2017)

[13] B. Li, L. B. Li, Z. B. Zhang, et al., Statistical properties of the repeating fast radio burst source FRB 121102, arXiv: 1901.03484 (2019)

[14] G. Q. Zhang, F. Y. Wang, and Z. G. Dai, Similar behaviors between FRB 121102 and solar type III radio bursts, arXiv: 1903.11895 (2019)

[15] M. J. Aschwanden, A macroscopic description of a generalized self-organized criticality system: Astrophysical applications, Astrophys. J. 782(1), 54 (2014)

[16] M. J. Aschwanden, N. B. Crosby, M. Dimitropoulou, M. K. Georgoulis, S. Hergarten, J. McAteer, A. V. Milovanov, S. Mineshige, L. Morales, N. Nishizuka, G. Pruessner, R. Sanchez, A. S. Sharma, A. Strugarek, and V. Uritsky, 25 years of self-organized criticality: Solar and astrophysics, Space Sci. Rev. 198(1–4), 47 (2016)

[17] J. I. Katz, A model of propagating brittle failure in heterogeneous media, J. Geophys. Res.: Solid Earth 91(B10), 10412 (1986)

[18] P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality: An explanation of the 1/f noise, Phys. Rev. Lett. 59, 381 (1987)

[19] P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality, Phys. Rev. A 38, 364 (1988)

[20] M. J. Aschwanden and J. M. McTiernan, Reconciliation of waiting time statistics of solar flares observed in hard X-rays, Astrophys. J. 717(2), 683 (2010)

[21] M. J. Aschwanden, A statistical fractal-diffusive avalanche model of a slowly-driven self-organized criticality system, Astron. Astrophys. 539, A2 (2012)

[22] F. Y. Wang and Z. G. Dai, Self-organized criticality in Xray flares of gamma-ray-burst afterglows, Nat. Phys. 9(8), 465 (2013)

[23] B. E. Stern and R. Svensson, Evidence for “chain reaction” in the time profiles of gamma-ray bursts, Astrophys. J. Lett. 469, L109 (1996)

[24] F. Y. Wang, Z. G. Dai, S. X. Yi, and S. Q. Xi, Universal behavior of X-ray flares from black hole systems, Astrophys. J. Suppl. 216(1), 8 (2015)

[25] Y. P. Li, F. Yuan, Q. Yuan, Q. D. Wang, P. F. Chen, J. Neilsen, T. Fang, S. Zhang, and J. Dexter, Statistics of X-ray flares of sagittarius A*: Evidence for solar-like selforganized criticality phenomena, Astrophys. J. 810(1), 19 (2015)

[26] C. Guidorzi, S. Dichiara, F. Frontera, R. Margutti, A. Baldeschi, and L. Amati, A common stochastic process rules gamma-ray burst prompt emission and X-ray flares, Astrophys. J. 801(1), 57 (2015)

[27] S. X. Yi, S. Q. Xi, H. Yu, F. Y. Wang, H. J. Mu, L. Z. Lü, and E. W. Liang, Comprehensive study of the X-ray flares from gamma-ray bursts observed by swift, Astrophys. J. Suppl. 224(2), 20 (2016)

[28] S. X. Yi, H. Yu, F. Y. Wang, and Z. G. Dai, Statistical distributions of optical flares from gamma-ray bursts, Astrophys. J. 844(1), 79 (2017)

[29] A. M. Beloborodov, B. E. Stern, and R. Svensson, Power density spectra of gamma-ray bursts, Astrophys. J. 535(1), 158 (2000)

[30] Z. L. Uhm and B. Zhang, On the curvature effect of a relativistic spherical shell, Astrophys. J. 808(1), 33 (2015)

[31] J. J. Geng, Y. F. Huang, X. F. Wu, L. M. Song, and H. S. Zong, Probing magnetic fields of GRB X-ray flares with polarization observations, Astrophys. J. 862(2), 115 (2018)

[32] M. J. Aschwanden, Thresholded power law size distributions of instabilities in astrophysics, Astrophys. J. 814(1), 19 (2015)

[33] G. J. Fishman, C. A. Meegan, R. B. Wilson, et al., The BATSE experiment for the GRO- Solar flare hard Xray and γ-ray capabilities, Bull. Am. Astron. Soc. 21, 860 (1989)

[34] C. A. Meegan, G. J. Fishman, R. B. Wilson, W. S. Paciesas, G. N. Pendleton, J. M. Horack, M. N. Brock, and C. Kouveliotou, Spatial distribution of γ-ray bursts observed by BATSE, Nature 355(6356), 143 (1992)

[35] N. Gehrels, E. Chipman, and D. Kniffen, The Compton gamma ray observatory, Astrophys. J. Suppl. 92, 351 (1994)

[36] J. Hakkila and R. D. Preece, Unification of pulses in long and short gamma-ray bursts: Evidence from pulse properties and their correlations, Astrophys. J. 740(2), 104 (2011)

[37] D. Yonetoku, T. Murakami, T. Nakamura, R. Yamazaki, A. K. Inoue, and K. Ioka, Gamma-ray burst formation rate inferred from the spectral peak energy-peak luminosity relation, Astrophys. J. 609(2), 935 (2004)

[38] A. Goldstein, R. D. Preece, R. S. Mallozzi, M. S. Briggs, G. J. Fishman, C. Kouveliotou, W. S. Paciesas, and J. M. Burgess, The BATSE 5B gamma-ray burst spectral catalog, Astrophys. J. Suppl. 208(2), 21 (2013)

[39] D. Band, J. Matteson, L. Ford, B. Schaefer, D. Palmer, B. Teegarden, T. Cline, M. Briggs, W. Paciesas, G. Pendleton, G. Fishman, C. Kouveliotou, C. Meegan, R. Wilson, and P. Lestrade, BATSE observations of gamma-ray burst spectra (I): Spectral diversity, Astrophys. J. 413, 281 (1993)

[40] L. Amati, F. Frontera, M. Tavani, J. J. M. in’t Zand, A. Antonelli, E. Costa, M. Feroci, C. Guidorzi, J. Heise, N. Masetti, E. Montanari, L. Nicastro, E. Palazzi, E. Pian, L. Piro, and P. Soffitta, Intrinsic spectra and energetics of BeppoSAX gamma-ray bursts with known redshifts, Astron. Astrophys. 390(1), 81 (2002)

[41] J. P. Norris, J. T. Bonnell, D. Kazanas, J. D. Scargle, J. Hakkila, and T. W. Giblin, Long-lag, wide-pulse gammaray bursts, Astrophys. J. 627(1), 324 (2005)

[42] D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, EMCEE: The MCMC hammer, Publications of the Astronomical Society of the Pacific 125, 306 (2013)

[43] F. Lyu, Y. Wang, Y. Liang, T. T. Lin, Y. D. Hu, and E. W. Liang, Comparison between the time-integrated spectrum and the peak time spectrum of gamma-ray bursts and possible implications, Sci. China Phys. Mech. Astron. 58(3), 5575 (2015)

[44] P. Meszaros and M. J. Rees, Relativistic fireballs and their impact on external matter: Models for cosmological gamma-ray bursts, Astrophys. J. 405, 278 (1993)

[45] T. Piran, A. Shemi, and R. Narayan, Hydrodynamics of relativistic fireballs, Mon. Not. R. Astron. Soc. 263(4), 861 (1993)

[46] S. J. Hou, B. B. Zhang, Y. Z. Meng, X. F. Wu, E. W. Liang, H. J. Lü, T. Liu, Y. F. Liang, L. Lin, R. Lu, J. S. Huang, and B. Zhang, Multicolor blackbody emission in GRB 081221, Astrophys. J. 866(1), 13 (2018)

[47] Y. Z. Meng, J. J. Geng, B. B. Zhang, J. J. Wei, D. Xiao, L. D. Liu, H. Gao, X. F. Wu, E. W. Liang, Y. F. Huang, Z. G. Dai, and B. Zhang, The origin of the prompt emission for short GRB 170817A: Photosphere emission or synchrotron emission? Astrophys. J. 860(1), 72 (2018)

[48] Y. Z. Meng, L. D. Liu, J. J. Wei, X. F. Wu, and B. B. Zhang, The time-resolved spectra of photospheric emission from a structured jet for gamma-ray bursts, Astrophys. J. 882(1), 26 (2019)

[49] B. Zhang and H. Yan, The internal-collision-induced magnetic reconnection and turbulence (ICMART) model of gamma-ray bursts, Astrophys. J. 726(2), 90 (2011)

[50] F. Lyu, E. W. Liang, Y. F. Liang, et al., Distributions of gamma-ray bursts and blazars in the L_p–E_p-plane and possible implications for their radiation physics, Astrophys. J. 793, 36 (2014)

[51] Z. L. Uhm and B. Zhang, Fast-cooling synchrotron radiation in a decaying magnetic field and γ-ray burst emission mechanism, Nat. Phys. 10(5), 351 (2014)

[52] R. D. Blandford and R. L. Znajek, Electromagnetic extraction of energy from Kerr black holes, Mon. Not. R. Astron Soc. 179(3), 433 (1977)

[53] Y. D. Hu, E. W. Liang, S. Q. Xi, F. K. Peng, R. J. Lu, L. Z. Lü, and B. Zhang, Internal energy dissipation of gamma-ray bursts observed with swift: Precursors, prompt gamma-rays, extended emission, and late X-ray flares, Astrophys. J. 789(2), 145 (2014)

[54] B. Zhang and B. Zhang, Gamma-ray burst prompt emission light curves and power density spectra in the ICMART model, Astrophys. J. 782(2), 92 (2014)

[55] A. Lazarian, G. L. Eyink, A. Jafari, et al., 3D turbulent reconnection: Theory, tests, and astrophysical implications, Phys. Plasmas 27, 012305 (2020)

RIGHTS & PERMISSIONS

Higher Education Press