آنالیز و شبیه‌سازی انتشار پرتوهای کیهانی در محیط کهکشانی فراکتالی و همگن

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه گروه نجوم، دانشکده فیزیک، دانشگاه شهید باهنر کرمان، کرمان، ایران.

چکیده

طیف انرژی پرتوهای کیهانی طبق توزیع قانون توانی و شامل دو خصوصیت به نام زانو و قوزک است. چندین مدل برای توصیف زانو و قوزک وجود دارد، مانند مدل شوک شتاب‌دهنده، مدل منابع فراکهکشانی و مدل‌های انتشار که در اینجا به روی آنها تمرکز می‌کنیم. در این مقاله، ابتدا مسیر حرکت پرتوهای کیهانی با انرژی eV 1017 را از مرکز کهکشان برای هر دو مدل پخش عادی و غیرعادی شبیه‌سازی کردیم، تا تفاوت انتشار در محیط همگن و محیط فراکتالی را نشان دهیم. شبیه‌سازی‌ها نشان می‌دهد، انتشار عادی پرتوهای کیهانی در محیط کهکشانی زمان اقامت طولانی‌تر و چگالی انرژی بیشتری نسبت به انتشار غیرعادی ارائه می‌دهد. در این مقاله از برنامه‌ای استفاده کردیم که انتشار پرتوهای کیهانی را در یک مدل ساده میدان مغناطیسی کهکشانی، مطابق با همان محیط، شبیه‌سازی می‌کند و از تکنیک‌های تعریف‌شده در کلی و همکاران (2000) و کلی (2002) استفاده شده است. سپس زمان اقامت کهکشانی ذرات با انرژی‌های مختلف را در انتشار غیرعادی به‌دست آوردیم. نتایج تطابق خوبی با نظر لاگوتین دارد. لاگوتین و همکاران (2001ب) عنوان می‌کند زانو ناشی از انتشار غیرعادی ذرات در محیط کهکشانی فراکتالی است. به عبارت دیگر، زانو می‌تواند به‌علت مسافت‌های آزاد طولانی پرتوهای کیهانی بین ناهمگنی‌های میدان‌های مغناطیسی در محیط کهکشانی باشد و همچنین از این حقیقت باشد که ذرات می‌توانند در این میدان‌های مغناطیسی به مدت طولانی به دام بیفتند. این مقاله برای فهم این‌که خصوصیات طیفی در طیف انرژی پرتوهای کیهانی می‌تواند ناشی از طبیعت فراکتالی محیط کهکشانی باشد، مفید خواهد بود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Analysis and Simulation of the Propagation of Cosmic Rays in the Fractal and Homogeneous Galactic Medium

نویسندگان [English]

  • Hamid Arjomand Kermani
  • Aniseh Fasihi Harandi
Department of Astronomy, Faculty of Physics, Shahid Bahonar University of Kerman, Kerman, Iran.
چکیده [English]

The energy spectrum of cosmic rays exhibits a power-law distribution, meaning there are more particles at lower energies and fewer particles at higher energies. There is a feature known as the knee at about 3×1015eV in the energy spectrum of cosmic rays, and there is another feature called the ankle at about 1018eV. There are several models to explain the knee and ankle features in the energy spectrum of cosmic rays, such as, shock acceleration model, which suggests that the knee may be arise from the maximum energy that can be achieved through shock waves produced by supernova explosions, extragalactic sources model, which suggests that the ankle may be arise from the extremely energetic astrophysical sources outside our galaxy, and the propagation models, that we focus on in this research. Cosmic ray propagation has usually been assumed to be in a form of normal diffusion, which is a diffusion process with a linear relationship to time. But, in anomalous diffusion, the mean squared displacement of a particle has a non-linear relationship to time. In this research, we investigate the propagation of cosmic rays in the galactic medium. First, we simulate the trajectory of cosmic rays with the energy of 1017eV from the galactic center in two models of diffusion to show the differences between propagation in the homogeneous and fractal galactic medium. Simulations show that cosmic ray propagation in the galactic medium gives a greater galactic residence time and energy density for normal diffusion particles compared to anomalous diffusion particles. Here, the program, that is applied in this research, presents the results of a simulation using a model of the galactic magnetic field appropriate to the related medium. It uses the technique described in Clay et al. (2000) and Clay (2002). Normal cosmic ray diffusion assumes very simple properties of the structure of cosmic magnetic fields. A better approximation is to assume that the magnetic structure has fractal properties when modelling the propagation. Later, residence times of cosmic rays on a wide range of energy spectrum in the anomalous diffusion model are found. Results can correspond to Lagutin’s point of view saying that the “knee” in the cosmic ray spectrum is the consequence of anomalous diffusion of the particles in the fractal galactic medium (Lagutin et al., 2001b). In other words, the “knee” may be caused by the extensive distances that cosmic ray particles can travel between inhomogeneities of magnetic fields and from the fact that a particle stays in a magnetic trap for a long time. Our study is useful for understanding the possibility that some spectral features (the knee and the ankle) of the spectrum of cosmic rays observed at the Earth are induced by the fractal nature of the galactic medium.

کلیدواژه‌ها [English]

  • Normal diffusion
  • Anomalous diffusion
  • Cosmic rays
  • Fractal galactic medium
  • Galactic magnetic field
Abu-Zayyad, T., Belov, K., Bird, D. J., Boyer, J., Cao, Z., Catanese, M., Chen, G. F., Clay, R. W., Covault, C. E., Dai, H. Y., & Dawson, B. R. (2001). Measurement of the cosmic-ray energy spectrum and composition from 1017 to 1018.3 eV using a hybrid technique. The Astrophysical Journal, 557(2), 686.
Allard, D., Parizot, E., Olinto, A. V., Khan, E., & Goriely, S. (2005). UHE nuclei propagation and the interpretation of the ankle in the cosmic-ray spectrum. Astronomy & Astrophysics, 443(3), L29-L32.
Allard, D., Parizot, E., & Olinto, A. V. (2007). On the transition from galactic to extragalactic cosmic-rays: Spectral and composition features from two opposite scenarios. Astroparticle Physics, 27(1), 61-75.
Berezinsky, V. S., Ginzburg, V. L., Bulanov, S. V., & Dogiel, V. (1990). PTUSKIN, VS. Astrophysics of cosmic rays. North-Holland, Amsterdam, Netherlands.
Bykov, A. M., & Toptygin, I. N. (2001). A model of particle acceleration to high energies by multiple supernova explosions in OB associations. Astronomy Letters, 27, 625-633.
Castellina, A. (2001). Cosmic ray composition and energy spectrum above 1 TeV: direct and EAS measurements. Nuclear Physics B-Proceedings Supplements, 97(1-3), 35-47.
Chappell, D., & Scalo, J. (2001). Multifractal scaling, geometrical diversity, and hierarchical structure in the cool interstellar medium. The Astrophysical Journal, 551(2), 712.
Clay, R. W., Dawson, B. R., Bowen, J., & Debes, M. (2000). Cosmic rays from the galactic center. Astroparticle Physics, 12(4), 249-254.
Clay, R. W. (2002). The source energy spectrum of cosmic rays. Publications of the Astronomical Society of Australia, 19(2), 228-232.
Dorman, L. (2006). Cosmic ray interactions, propagation, and acceleration in space plasmas (Vol. 339). Springer Science & Business Media.
Elmegreen, B. G., Kim, S., & Staveley-Smith, L. (2001). A fractal analysis of the HI emission from the Large Magellanic Cloud. The Astrophysical Journal, 548(2), 749.
Erlykin, A. D. (1995). Around and above the knee. Nuclear Physics B Proceedings Supplements, 39(1), 215-227.
Erlykin, A. D., & Wolfendale, A. W. (2001). Structure in the cosmic ray spectrum: an update. Journal of Physics G: Nuclear and Particle Physics, 27(5), 1005.
Falgarone, E., Phillips, T. G., & Walker, C. K. (1991). The edges of molecular clouds-Fractal boundaries and density structure. Astrophysical Journal, Part 1 (ISSN 0004-637X), 378(1), 186-201.
Gaggero, D. (2012). Cosmic Ray Diffusion in the Galaxy. Cosmic Ray Diffusion in the Galaxy and Diffuse Gamma Emission, 7-28.
Ginzburg, V. L., & Syrovatskii, S. I. (1964). The secondary electron component of cosmic rays and the spectrum of general galactic radio emission. Soviet Astronomy, Vol. 8, p. 342, 8, 342.
Greisen, K. (1966). End to the cosmic-ray spectrum?. Physical Review Letters, 16(17), 748.
Kachelriess, M. (2008). Lecture notes on high energy cosmic rays. arXiv preprint arXiv:0801.4376.
Kaplan, S., & Pikelner, S. (1979). The physics of the interstellar medium (Russian book). Moscow, Izdatel'stvo Nauka, 1979. 592.
Lagutin, A. A., Makarov, V. V., & Tyumentsev, A. G. (2001a). Anomalous diffusion of the cosmic rays: steady-state solution. arXiv preprint astro-ph/0107253.
Lagutin, A. A., Nikulin, Y. A., & Uchaikin, V. V. (2001b). The “knee” in the primary cosmic ray spectrum as consequence of the anomalous diffusion of the particles in the fractal interstellar medium. Nuclear Physics B-Proceedings Supplements, 97(1-3), 267-270.
Lagutin, A. A., & Uchaikin, V. V. (2001). Fractional diffusion of cosmic rays. arXiv preprint astro-ph/0107230.
Lagutin, A. A., & Uchaikin, V. V. (2003). Anomalous diffusion equation: Application to cosmic ray transport. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 201(1), 212-216.
Lee, A. A., & Clay, R. W. (1993). Effects of Galactic Magnetic Field Turbulence on EHE Cosmic Ray Propagation. In 23rd International Cosmic Ray Conference (ICRC23), Volume 2 (Vol. 2, p. 77).
Lee, A. A., & Clay, R. W. (1995). The anisotropy of EHE cosmic rays. Journal of Physics G: Nuclear and Particle Physics, 21(12), 1743.
Lee, L. C., & Jokipii, J. R. (1976). The irregularity spectrum in interstellar space. Astrophysical Journal, vol. 206, June 15, 1976, pt. 1, p. 735-743., 206, 735-743.
Maurin, D., Donato, F., Taillet, R., & Salati, P. (2001). Cosmic rays below z= 30 in a diffusion model: new constraints on propagation parameters. The Astrophysical Journal, 555(2), 585.
Nagano, M., Teshima, M., Matsubara, Y., Dai, H. Y., Hara, T., Hayashida, N., Honda, M., Ohoka, H., & Yoshida, S. (1992). Energy spectrum of primary cosmic rays above 1017.0 eV determined from extensive air shower experiments at Akeno. Journal of Physics G: Nuclear and Particle Physics, 18(2), 423.
Ogio, S., & Kakimoto, F. (2003). Advective diffusion propagation model for galactic cosmic rays above 1012 eV. In International Cosmic Ray Conference (Vol. 1, p. 315).
Ptuskin, V. S., Rogovaya, S. I., Zirakashvili, V. N., Chuvilgin, L. G., Khristiansen, G. B., Klepach, E. G., & Kulikov, G. V. (1993). Diffusion and drift of very high energy cosmic rays in galactic magnetic fields. Astronomy and Astrophysics (ISSN 0004-6361), vol. 268, no. 2, p. 726-735., 268, 726-735.
Ptuskin, V. S., & Zirakashvili, V. N. (2005). On the spectrum of high-energy cosmic rays produced by supernova remnants in the presence of strong cosmic-ray streaming instability and wave dissipation. Astronomy & Astrophysics, 429(3), 755-765.
Ptuskin, V. (2006). Cosmic ray transport in the Galaxy. In Journal of Physics: Conference Series (Vol. 47, No. 1). IOP Publishing.
Roulet, E. (2004). Astroparticle theory: Some new insights into high energy cosmic rays. International Journal of Modern Physics A, 19(07), 1133-1141.
Vainshtein, S. I., Bykov, A. M., & Toptygin, I. N. (1989). Turbulence, stream layers and shock wave in cosmic plasm. M.: Nauka.