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Time-Dependent Modulation of Cosmic Rays in the Heliosphere

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Abstract

The time-dependent modulation of galactic cosmic rays in the heliosphere is studied by computing intensities using a time-dependent modulation model. By introducing recent theoretical advances in the transport coefficients in the model, computed intensities are compared with Voyager 1, International Monitoring Platform (IMP) 8, and Ulysses proton observations in search of compatibility. The effect of different modulation parameters on computed intensities is also illustrated. It is shown that this approach produces, on a global scale, realistic cosmic-ray proton intensities along the Voyager 1 spacecraft trajectory and at Earth up to ≈ 2004, whereafter the computed intensities recover much more slowly towards solar minimum than observed in the inner heliosphere. A modified time dependence in the diffusion coefficients is proposed to improve compatibility with the observations at Earth after ≈ 2004. This modified time dependence led to an improved compatibility between computed intensities and the observations along the Voyager 1 trajectory and at Earth even after ≈ 2004. An interesting result is that the cosmic-ray modulation during the current polarity cycle is not determined only by changes in the drift coefficient and tilt angle of the wavy current sheet, but is also largely dependent on changes in the diffusion coefficients.

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References

  • Bieber, J.W., Matthaeus, W.H., Smith, C.W., Wanner, W., Kallenrode, M.-B., Wibberenz, G.: 1994, Proton and electron mean free paths: The Palmer consensus revisited. Astrophys. J. 420, 294 – 306.

    Article  ADS  Google Scholar 

  • Burger, R.A., Potgieter, M.S., Heber, B.: 2000, Rigidity dependence of cosmic ray proton latitudinal gradients measured by the Ulysses spacecraft: Implications for the diffusion tensor. J. Geophys. Res. 105, 27447 – 27455.

    Article  ADS  Google Scholar 

  • Burlaga, L.F., McDonald, F.B., Ness, N.F.: 1993, Cosmic ray modulation and the distant heliospheric magnetic field – Voyager 1 and 2 observations from 1986 to 1989. J. Geophys. Res. 98(17), 1 – 11.

    Article  ADS  Google Scholar 

  • Burlaga, L.F., Ness, N.F., Acuña, M.H.: 2007, Magnetic fields in the heliosheath and distant heliosphere: Voyager 1 and 2 observations during 2005 and 2006. Astrophys. J. 668, 1246 – 1258.

    Article  ADS  Google Scholar 

  • Burlaga, L.F., Ness, N.F., Stone, E.C.: 2013, Magnetic field observations as Voyager 1 entered the heliosheath depletion region. Science 341, 147 – 150.

    Article  ADS  Google Scholar 

  • Burlaga, L.F., Ness, N.F., Acuña, M.H., Lepping, R.P., Connerney, J.E.P., Stone, E.C., McDonald, F.B.: 2005, Crossing the termination shock into the heliosheath: Magnetic fields. Science 309, 2027 – 2029.

    Article  ADS  Google Scholar 

  • Cane, H.V., Wibberenz, G., Richardson, I.G., von Rosenvinge, T.T.: 1999, Cosmic ray modulation and the solar magnetic field. Geophys. Res. Lett. 26, 565 – 568.

    Article  ADS  Google Scholar 

  • Ferreira, S.E.S., Potgieter, M.S.: 2003, Modulation over a 22-year cosmic ray cycle: On the tilt angles of the heliospheric current sheet. Adv. Space Res. 32(4), 657 – 662.

    Article  ADS  Google Scholar 

  • Ferreira, S.E.S., Potgieter, M.S.: 2004, Long-term cosmic-ray modulation in the heliosphere. Astrophys. J. 603, 744 – 752.

    Article  ADS  Google Scholar 

  • Ferreira, S.E.S., Potgieter, M.S., Scherer, K.: 2007a, Modeling of the heliospheric interface, magnetic field, and cosmic-ray transport. Astrophys. J. 659, 1777 – 1783.

    Article  ADS  Google Scholar 

  • Ferreira, S.E.S., Potgieter, M.S., Scherer, K.: 2007b, Transport and acceleration of anomalous cosmic rays in the inner heliosheath. J. Geophys. Res. 112, A11101, 1 – 11.

    Article  ADS  Google Scholar 

  • Ferreira, S.E.S., Potgieter, M.S., Webber, W.R.: 2004, Modulation of low-energy cosmicy ray electrons in the outer heliosphere. Adv. Space Res. 34, 126 – 131.

    Article  ADS  Google Scholar 

  • Ferreira, S.E.S., Scherer, K.: 2006, Time evolution of galactic and anomalous cosmic ray spectra in a dynamic heliosphere. Astrophys. J. 642, 1256 – 1266.

    Article  ADS  Google Scholar 

  • Florinski, V., Zank, G.P., Pogorelov, N.V.: 2003, Galactic cosmic ray transport in the global heliosphere. J. Geophys. Res. 108(A6), 1228, SSH 1: 1 – 16.

    Article  Google Scholar 

  • Giacalone, J., Jokipii, J.R.: 1999, The transport of cosmic rays across a turbulent magnetic field. Astrophys. J. 520, 204 – 214.

    Article  ADS  Google Scholar 

  • Heber, B., Kopp, A., Gieseler, J., Müller-Mellin, R., Fichtner, H., Scherer, K., Potgieter, M.S., Ferreira, S.E.S.: 2009, Modulation of galactic cosmic ray protons and electrons during an unusual solar minimum. Astrophys. J. 699, 1956 – 1963.

    Article  ADS  Google Scholar 

  • Hoeksema, J.T.: 1992, Large-scale structure of the heliospheric magnetic field: 1976 – 1991. In: Marsch, E., Schwenn, R. (eds.) Solar Wind Seven, Proc. Third COSPAR Coll., Elsevier, Amsterdam, 191 – 196.

    Chapter  Google Scholar 

  • Jokipii, J.R., Levy, E.H., Hubbard, W.B.: 1977, Effects of particle drift on cosmic-ray transport. I. General properties, application to solar modulation. Astrophys. J. 213(3), 861 – 868.

    Article  ADS  Google Scholar 

  • Krimigis, S.M., Roelof, E.C., Decker, R.B., Hill, M.E.: 2011, Zero outward flow velocity for plasma in a heliosheath transition layer. Nature 474, 359 – 361.

    Article  ADS  Google Scholar 

  • Langner, U.W., Potgieter, M.S., Webber, W.R.: 2004, Modelling of ‘barrier’ modulation for cosmic ray protons in the outer heliosphere. Adv. Space Res. 34, 138 – 143.

    Article  ADS  Google Scholar 

  • le Roux, J.A., Potgieter, M.S.: 1989, Episodic cosmic-ray modulation in the heliosphere. Adv. Space Res. 9(4), 225 – 228.

    Article  ADS  Google Scholar 

  • le Roux, J.A., Potgieter, M.S.: 1995, The simulation of complete 11 and 22 year modulation cycles for cosmic rays in the heliosphere using a drift model with global merged interaction regions. Astrophys. J. 442, 847 – 851.

    Article  ADS  Google Scholar 

  • le Roux, J.A., Zank, G.P., Ptuskin, V.S.: 1999, An evaluation of perpendicular diffusion models regarding cosmic ray modulation on the basis of a hydromagnetic description for solar wind turbulence. J. Geophys. Res. 104(A11), 24845 – 24862.

    Article  ADS  Google Scholar 

  • Manuel, R., Ferreira, S.E.S., Potgieter, M.S.: 2011, Cosmic ray modulation in the outer heliosphere: Predictions for cosmic ray intensities up to the heliopause along Voyager 1 and 2 trajectories. Adv. Space Res. 48, 874 – 883.

    Article  ADS  Google Scholar 

  • Manuel, R., Ferreira, S.E.S., Potgieter, M.S., Strauss, R.D., Engelbrecht, N.E.: 2011, Time-dependent cosmic ray modulation. Adv. Space Res. 47, 1529 – 1537.

    Article  ADS  Google Scholar 

  • Minnie, J., Bieber, J.W., Matthaeus, W.H., Burger, R.A.: 2007, Suppression of particle drifts by turbulence. Astrophys. J. 670, 1149 – 1158.

    Article  ADS  Google Scholar 

  • Moeketsi, D.M., Potgieter, M.S., Ferreira, S.E.S., Heber, B., Fichtner, H., Henize, V.K.: 2005, The heliospheric modulation of 3 – 10 MeV electrons: Modeling of changes in the solar wind speed in relation to perpendicular polar diffusion. Adv. Space Res. 35, 597 – 604.

    Article  ADS  Google Scholar 

  • Moskalenko, I.V., Strong, A.W., Ormes, J.F., Potgieter, M.S.: 2002, Secondary antiprotons and propagation of cosmic rays in the galaxy and heliosphere. Astrophys. J. 565, 280 – 296.

    Article  ADS  Google Scholar 

  • Ndiitwani, D.C., Ferreira, S.E.S., Potgieter, M.S., Heber, B.: 2005, Modelling cosmic ray intensities along the Ulysses trajectory. Ann. Geophys. 23, 1061 – 1070.

    Article  ADS  Google Scholar 

  • Ngobeni, M.D., Potgieter, M.S.: 2010, The heliospheric modulation of cosmic rays: Effects of a latitude dependent solar wind termination shock. Adv. Space Res. 46, 391 – 401.

    Article  ADS  Google Scholar 

  • Ngobeni, M.D., Potgieter, M.S.: 2011, Modulation of galactic cosmic rays in a north-south asymmetrical heliosphere. Adv. Space Res. 48, 300 – 307.

    Article  ADS  Google Scholar 

  • Parker, E.N.: 1965, The passage of energetic charged particles through interplanetary space. Planet. Space Sci. 13, 9 – 49.

    Article  ADS  Google Scholar 

  • Perko, J.S., Fisk, L.A.: 1983, Solar modulation of galactic cosmic rays. 5 – time-dependent modulation. J. Geophys. Res. 88(A11), 9033 – 9036.

    Article  ADS  Google Scholar 

  • Potgieter, M.S.: 1993, Time-dependent cosmic-ray modulation – role of drifts and interaction regions. Adv. Space Res. 13, 239 – 249.

    Article  ADS  Google Scholar 

  • Potgieter, M.S.: 1997, The heliospheric modulation of galactic cosmic rays at solar minimum. Adv. Space Res. 19, 883 – 892.

    Article  ADS  Google Scholar 

  • Potgieter, M.S.: 2000, Heliospheric modulation of cosmic ray protons: Role of enhanced perpendicular diffusion during periods of minimum solar modulation. J. Geophys. Res. 105(A8), 18295 – 18303.

    Article  ADS  Google Scholar 

  • Potgieter, M.S.: 2013a, Solar modulation of cosmic rays. Liv. Rev. Solar Phys. 10(3). doi: 10.12942/lrsp-2013-3 .

  • Potgieter, M.S.: 2013b, The modulation of galactic cosmic rays in the heliosphere: Theory and models. Space Sci. Rev. 176, 165 – 176.

    Article  ADS  Google Scholar 

  • Potgieter, M.S., le Roux, J.A.: 1989, A numerical model for a cosmic ray modulation barrier in the outer heliosphere. Astron. Astrophys. 209, 406 – 410.

    ADS  Google Scholar 

  • Potgieter, M.S., Moraal, H.: 1985, A drift model for the modulation of galactic cosmic rays. Astrophys. J. 294, 425 – 440.

    Article  ADS  Google Scholar 

  • Potgieter, M.S., Nndanganeni, R.R.: 2013, The solar modulation of electrons in the heliosphere. Astrophys. Space Sci. 345(1), 33 – 40.

    Article  ADS  Google Scholar 

  • Potgieter, M.S., le Roux, J.A., Burlaga, L.F., McDonald, F.B.: 1993, The role of merged interaction regions and drifts in the heliospheric modulation of cosmic rays beyond 20 AU: A computer simulation. Astrophys. J. 403, 760 – 768.

    Article  ADS  Google Scholar 

  • Potgieter, M.S., Vos, E.E., Boezio, M., De Simone, N., Di Felice, V., Formato, V.: 2013, Modulation of galactic protons in the heliosphere during the unusual solar minimum of 2006 to 2009. Solar Phys. doi: 10.1007/s11207-013-0324-6 .

    MATH  Google Scholar 

  • Ptuskin, V.S., Moskalenko, I.V., Jones, F.C., Strong, A.W., Zirakashvili, V.N.: 2006, Dissipation of magnetohydrodynamic waves on energetic particles: Impact on interstellar turbulence and cosmic-ray transport. Astrophys. J. 642, 902 – 916.

    Article  ADS  Google Scholar 

  • Qin, G., Matthaeus, W.H., Bieber, J.W.: 2002, Subdiffusive transport of charged particles perpendicular to the large scale magnetic field. Geophys. Res. Lett. 29(4), 1048, 7: 1 – 4.

    Article  ADS  Google Scholar 

  • Reinecke, J.P., Moraal, H., McDonald, F.B.: 1996, The cosmic radiation in the heliosphere at successive solar minima 3. Steady state drift solutions of the transport equation. J. Geophys. Res. 101(A10), 21581 – 21588.

    Article  ADS  Google Scholar 

  • Richardson, J.D., Kasper, J.C., Wang, C., Belcher, J.W., Lazarus, A.J.: 2008, Cool heliosheath plasma and deceleration of the upstream solar wind at the termination shock. Nature 454, 63 – 66.

    Article  ADS  Google Scholar 

  • Scherer, K., Fahr, H.J.: 2003, Breathing of heliospheric structures triggered by the solar-cycle activity. Ann. Geophys. 21, 1303 – 1313.

    Article  ADS  Google Scholar 

  • Scherer, K., Ferreira, S.E.S.: 2005, A heliospheric hybrid model: Hydrodynamic plasma flow and kinetic cosmic ray transport. Astrophys. Space Sci. Trans. 1, 17 – 27.

    Article  ADS  Google Scholar 

  • Scherer, K., Fichtner, H., Strauss, R.D., Ferreira, S.E.S., Potgieter, M.S., Fahr, H.J.: 2011, On cosmic ray modulation beyond the heliopause: Where is the modulation boundary? Astrophys. J. 735(128), 1 – 5.

    Google Scholar 

  • Shalchi, A., Bieber, J.W., Matthaeus, W.H.: 2004, Analytic forms of the perpendicular diffusion coefficient in magnetostatic turbulence. Astrophys. J. 604, 675 – 686.

    Article  ADS  Google Scholar 

  • Stone, E.C., Cummings, A.C., McDonald, F.B., Heikkila, B.C., Lal, N., Webber, W.R.: 2005, Voyager 1 explores the termination shock region and the heliosheath beyond. Science 309, 2017 – 2020.

    Article  ADS  Google Scholar 

  • Stone, E.C., Cummings, A.C., McDonald, F.B., Heikkila, B.C., Lal, N., Webber, W.R.: 2008, An asymmetric solar wind termination shock. Nature 454, 71 – 74.

    Article  ADS  Google Scholar 

  • Stone, E.C., Cummings, A.C., McDonald, F.B., Heikkila, B.C., Lal, N., Webber, W.R.: 2013, Voyager 1 observes low-energy galactic cosmic rays in a region depleted of heliospheric ions. Science 341, 150 – 153.

    Article  ADS  Google Scholar 

  • Strauss, R.D., Potgieter, M.S., Ferreira, S.E.S., Hill, M.E.: 2010, Modelling anomalous cosmic ray oxygen in the heliosheath. Astron. Astrophys. 522(A35), 1 – 8.

    Google Scholar 

  • Strauss, R.D., Potgieter, M.S., Ferreira, S.E.S., Fichtner, H., Scherer, K.: 2013, Cosmic ray modulation beyond the heliopause: A hybrid modelling approach. Astrophys. J. Lett. 765, L18.

    Article  ADS  Google Scholar 

  • Teufel, A., Schlickeiser, R.: 2002, Analytic calculation of the parallel mean free path of heliospheric cosmic rays. I. Dynamical magnetic slab turbulence and random sweeping slab turbulence. Astron. Astrophys. 393, 703 – 715.

    Article  ADS  Google Scholar 

  • Teufel, A., Schlickeiser, R.: 2003, Analytic calculation of the parallel mean free path of heliospheric cosmic rays. II. Dynamical magnetic slab turbulence and random sweeping slab turbulence with finite wave power at small wavenumbers. Astron. Astrophys. 397, 15 – 25.

    Article  ADS  MATH  Google Scholar 

  • Webber, W.R., Higbie, P.R.: 2009, Galactic propagation of cosmic ray nuclei in a model with an increasing diffusion coefficient at low rigidities: A comparison of the new interstellar spectra with Voyager data in the outer heliosphere. J. Geophys. Res. 114, A02103, 1 – 6.

    ADS  Google Scholar 

  • Webber, W.R., Intriligator, D.S.: 2011, Voyagers 1 and 2 in a shrunken and squashed heliosphere. J. Geophys. Res. 116, A06105, 1 – 8.

    Article  ADS  Google Scholar 

  • Webber, W.R., Lockwood, J.A.: 1995, Intensity variations of > 70-MeV cosmic rays measured by Pioneer 10, Voyager 1 & 2 and IMP in the heliosphere during the recovery period from 1992 – 1995. Geophys. Res. Lett. 22, 2669 – 2672.

    Article  ADS  Google Scholar 

  • Webber, W.R., McDonald, F.B.: 2013, 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.

    Article  ADS  Google Scholar 

  • Wibberenz, G., Richardson, I.G., Cane, H.V.: 2002, A simple concept for modeling cosmic ray modulation in the inner heliosphere during solar cycles 20 – 23. J. Geophys. Res. 107(A11), SSH 5: 1 – 15.

    Google Scholar 

  • Zhang, M.: 2006, Acceleration of galactic and anomalous cosmic rays in the heliosheath. In: Heerikhuisen, J., Florinski, V., Zank, G.P., Pogorelov, N.V. (eds.) Physics of the Inner Heliosheath CP-858, AIP, New York, 226 – 232.

    Google Scholar 

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Acknowledgements

This work is partially supported by the South African National Research Foundation (NRF). The authors wish to thank du Toit Strauss and Eugene Engelbrecht for valuable discussions and the referee for the constructive comments. We used data from the Wilcox Solar Observatory ( wso.stanford.edu ), NASA COHOWeb ( cohoweb.gsfc.nasa.gov ), W.R. Webber ( astro.nmsu.edu ), and Manuel et al. (2011).

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  1. Centre for Space Research, North-West University, Potchefstroom, 2520, South Africa

    R. Manuel, S. E. S. Ferreira & M. S. Potgieter

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  1. R. Manuel
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Correspondence to R. Manuel.

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Manuel, R., Ferreira, S.E.S. & Potgieter, M.S. Time-Dependent Modulation of Cosmic Rays in the Heliosphere. Sol Phys 289, 2207–2231 (2014). https://doi.org/10.1007/s11207-013-0445-y

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