The propagation of galactic cosmic rays in the outer heliosphere

1Fedorov, YI
1Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
Kinemat. fiz. nebesnyh tel (Online) 2017, 33(2):37-59
Start Page: Space Physics
Language: Russian

The propagation of galactic cosmic ray in heliospheric magnetic fields is studied. The approximate solution of cosmic ray transport equation has been derived on the basis of method taking into account the small value of anisotropy of particle angular distribution. The energy and spatial distributions of cosmic ray intensity and anisotropy are investigated and estimates of cosmic ray energy flux were fulfilled.

Keywords: anisotropy, cosmic ray energy, galactic cosmic rays, heliospheric magnetic fields

1.V. S. Berezinskii, S. V. Bulanov, V. L. Ginzburg, et al., Astrophysics of Cosmic Rays (Nauka, Moscow, 1984; North Holland, Amsterdam, 1990).

2.J. C. Brandt, Introduction to the Solar Wind (Freeman, San Francisco, 1970; Mir, Moscow, 1973).

3.A. Z. Dolginov and I. N. Toptygin, “Multiple scattering of particles in a magnetic field with random inhomogeneities,” Sov. Phys. JETP 24, 1195–1202 (1967).

4.L. I. Dorman, Experimental and Theoretical Foundations of Cosmic Ray Astrophysics (Nauka, Moscow, 1975) [in Russian].

5.Yu. L. Kolesnik and B. A. Shakhov, “Effect of the heliosheath and standing termination shock on galactic cosmic ray propagation in a stationary heliosphere model,” Kinematics Phys. Celestial Bodies 28, 261–269 (2012).

6.I. N. Toptygin, Cosmic Rays in Interplanetary Magnetic Fields (Nauka, Moscow, 1983; Springer-Verlag, Dordrecht, 1985).

7.Yu. I. Fedorov, “Modulation of galactic cosmic ray intensity in the turbulent heliosphere,” Kinematics Phys. Celestial Bodies 31, 105–118 (2015).

8.B. A. Shakhov and Yu. L. Kolesnik, “Iterative method for solving boundary-value problems in the theory of cosmic ray propagation,” Kinematics Phys. Celestial Bodies 22, 75–80 (2006).

9.D. Bisschoff and M. S. Potgieter, “New local interstellar spectra for protons, helium and carbon derived from PAMELA and Voyager 1 observations,” Astrophys. Space Sci. 361, 48 (2016).

10.L. F. Burlaga, N. F. Ness, and E. C. Stone, “Magnetic field observations as Voyager 1 entered the heliosheath depletion region,” Science 341, 147–150 (2013).

11.A. C. Cummings, E. C. Stone, B. C. Heikkila, et al. “Voyager 1 observations of galactic cosmic rays in the local interstellar medium: Energy density and ionization rates,” in Proc. 34th Int. Cosmic Ray Conf., The Hague, Netherlands, July 30–Aug. 6, 2015 (SISSA, 2015), paper id. PoS(ICRC2015)318.

12.L. I. Dorman, M. E. Katz, Yu. I. Fedorov, and B. A. Shakhov, “Variations of cosmic-ray energy in interplanetary space,” Astrophys. Space Sci. 94, 43–95 (1983).

13.L. A. Fisk and W. I. Axford, “Anisotropies of solar cosmic rays,” Sol. Phys. 7, 486–498 (1969).

14.V. Florinski and N. V. Pogorelov, “Four-dimensional transport of galactic cosmic rays in the outer heliosphere and heliosheath,” Astrophys. J. 701, 642–651 (2009).

15.L. J. Gleeson and W. I. Axford, “Solar modulation of galactic cosmic rays,” Astrophys. J. 154, 1011–1026 (1968).

16.L. J. Gleeson and I. H. Urch, “A study of the force-field equation for the propagation of galactic cosmic rays,” Astrophys. Space Sci. 25, 387–404 (1973).

17.L. J. Gleeson and G. M. Webb, “Energy changes of cosmic rays in the interplanetary region,” Astrophys. Space Sci. 58, 21–39 (1987).

18.M. L. Goldstein, R. Ramaty, and L. A. Fisk, “Interstellar cosmic ray spectra from the nonthermal radio background from 0.4 to 400 MHz,” Phys. Rev. Lett. 24, 1193–1196 (1970).

19.X. Guo and V. Florinski, “Galactic cosmic-ray modulation near the heliopause,” Astrophys. J. 793, 18 (2014).

20.K. Herbst, B. Heber, A. Kopp, et al., “The local interstellar spectrum beyond the heliopause: what can be learned from Voyager in the inner heliosheath?,” Astrophys. J. 761, 17 (2012).

21.J. Kóta and J. R. Jokipii, “Are cosmic rays modulated beyond the heliopause?,” Astrophys. J. 782, 24 (2014).

22.S. M. Krimigis, R. B. Decker, E. C. Roelof, et al., “Search for the exit: Voyager 1 at heliosphere’s border with the galaxy,” Science 341, 144–147 (2013).

23.R. Manuel, S. E. S. Ferreira, and M. S. Potgieter, “Time-dependent modulation of cosmic rays in the heliosphere,” Sol. Phys. 289, 2207–2231 (2014).

24.H. Moraal, “Cosmic-ray modulation equations,” Space Sci. Rev. 176, 299–319 (2013).

25.E. N. Parker, “The passage of energetic charged particles through interplanetary space,” Planet Space Sci. 13, 9–49 (1965).

26.J. S. Perko, “Solar modulation of galactic antiprotons,” Astron. Astrophys. 184, 119–121 (1987).

27.M. S. Potgieter, “Solar modulation of cosmic rays,” Living Rev. Sol. Phys. 10, 3 (2013).

28.M. S. Potgieter, “Very local interstellar spectra for galactic electrons, protons and helium,” Braz. J. Phys. 44, 581 (2014).

29.M. S. Potgieter and R. T. Strauss, “At what rigidity does the solar modulation of galactic cosmic rays begin?” in Proc. 33rd Int. Cosmic Ray Conf. (ICRC2013), Rio de Janeiro, July 2–9, 2013 (Braz. Phys. Soc., 2013), paper id. ICRC2013-0156.

30.V. S. Ptuskin, H. J. Völk, V. N. Zirakashvili, and D. Breitschwerdt, “Transport of relativistic nucleons in a galactic wind driven by cosmic rays,” Astron. Astrophys. 321, 434–443 (1997).

31.J. D. Richardson and L. F. Burlaga, “The solar wind in the outer heliosphere and heliosheath,” Space Sci. Rev. 176, 217–235 (2013).

32.K. Scherer, H. Fichtner, R. D. Strauss, et al., “On cosmic ray modulation beyond the heliopause: Where is the modulation boundary?,” Astrophys. J. 735, 128 (2011).

33.R. Schlickeiser, Cosmic Ray Astrophysics (Springer-Verlag, Berlin, 2002).

34.E. C. Stone, A. C. Cummings, F. B. McDonald, et al., “Voyager 1 observes low-energy galactic cosmic rays in a region depleted of heliospheric ions,” Science 341, 150–153 (2013).

35.R. D. Strauss and H. Fichtner, “Cosmic ray anisotropies near the heliopause,” Astron. Astrophys., Lett. 572, L3 (2014).

36.I. H. Urch and L. J. Gleeson, “Galactic cosmic ray modulation from 1965–1970,” Astrophys. Space Sci. 17, 426–446 (1972).

37.H. J. Völk, “Cosmic ray propagation in interplanetary space,” Rev. Geophys. Space Phys. 13, 547–566 (1975).

38.W. R. Webber, P. R. Higbie, and F. B. McDonald, “The unfolding of the spectra of low energy galactic cosmic ray H and He nuclei as the Voyager 1 spacecraft exits the region of heliospheric modulation” (2013).

39.W. R. Webber and F. B. McDonald, “Recent Voyager 1 data indicate that on 25 August 2012 at a distance of 121.7 AU from the Sun, sudden and unprecedented intensity changes were observed in anomalous and galactic cosmic rays,” Geophys. Res. Lett. 40, 1665–1668 (2013).

40.M. Zhang, X. Luo, and N. Pogorelov, “Where is the cosmic-ray modulation boundary of the heliosphere?,” Phys. Plasmas 22, 091501 (2015).