1. Solar Modulation: A Theoretical Perspective Modeling of cosmic ray charge-sign dependence in the heliosphere Marius Potgieter Unit for Space Physics North-West University Potchefstroom, South Africa PAMELA Workshop May 2009 Colaborators: Stefan Ferreira, Bernd Heber Students: DuToit Strauss, Etienne Vos, Driaan Bisschoff, Rex Manuel, Edwin Mogadimisha

2. Cosmic Rays from the Galaxy Inside the heliosphere Charged Particle Populations

3. Bow Shocks 500 AU 250 AU Heliospace The heliosphere Voyager 1: Dec 2004 Voyager 2: Aug 2007

4. Cosmic ray transport part Hydrodynamic part > describe the balance of mass, momentum and energy of the protons in solar wind and LISM, neutral hydrogen, pickup ions, and additional is GCR’s and ACR’s > mass density , velocity u, pressure P and Q sources related to the interaction between the various species. A 5 fluid model based on the Kausch (1998) model : > including all major modulation mechanisms : diffusion, drifts, convection and energy changes Realistic heliospheric geometry and solar wind flow profile Magnetic part > Magnetized flow is calculated by solving Faraday’s law assuming ideal MHD Magnetic field Cosmic ray transport and acceleration calculated by Parker (1965) TPE :

5. How is the heliosphere formed ? Allow the physics to tell us !

6. TS 93AU HP 140 AU TS 155 AU HP 245 AU TS 205 AU Scherer, K., & Ferreira, S. E. S. 2005, ASTRA, 1, 17 Ferreira, S. E. S., & Scherer, K. 2004, ApJ, 616, 1215 Hydrodynamic modeling of major heliospheric structures

7. r Predictions of TS crossing for V1 and V2 AU Time (years) Termination shock changes position over a solar cycle V1 & V2 launched in 1977 V1 is presently at 107 AU, 34°N V2 is presently at 86 AU, 28°S V1 crossed the TS in Dec. 2004 at 94 AU V2 crossed the TS end of Aug. 2007 at 84 AU

8. Cosmic rays are excellent indicators of solar cycle variations Modulation of galactic cosmic rays at Neutron Monitor energies

9. Time-dependent, pitch-angle-averaged distribution function Diffusion Convection with solar wind Particle Drifts Adiabatic energy changes Any local source Parker (Planet. Space Science, 13, 9,1965) Transport equation for the modulation and acceleration of cosmic rays in the heliosphere Modulation-Acceleration Model Second order Fermi acceleration

10. Heliospheric CR Modulation Processes As for electrons

11. The wavy current sheet (HCS) Heliosphere & Cosmic Ray Modulation Mechanisms

12. Tilt angle of the HCS: proxy for solar activity Maximum solar activity Minimum solar activity The wavy heliospheric current sheet (HCS) Moderate solar activity Extreme solar activity

13. Moskalenko and Strong, 2002. Langner, 2002, 2005; Computed Galactic Spectra (LIS?)

14. Webber et al. (AIP-IGPP-2006) Solar modulation of galactic carbon

15. Major features of cosmic rays near Earth Langner, Potgieter & Webber, JGR, 2003; ASR, 2004 Observed spectra crossings at Earth, from A > 0 and A < 0 solar minima polarity cycles… Observed small latitudinal gradients, especially at low energies; compared to Ulysses-KET observations; for A > 0, solar minimum to maximum…

16. Effects of gradient and curvature drifts in the heliosheath-nose Langner, Potgieter & Webber, JGR, 2003 200 MeV GCR protons Solar minimum conditions Conclusions: GC&CS-drifts may play a significant role in the HS….? Without drifts the TS seems insignificant for GCRs … The HP is more important to GCR modulation than the TS

17. Drifts during a complete solar activity cycle

18. Long term modulation: charge-sign dependence Long-term modulation of 1.2 GV electrons and helium at Earth over 22 years. Electron measurements form ISEE/ICE (Clem et al., 1996; Evenson, 1998). He measurements form IMP (McDonald, 1998; McDonald et al., 2001).

19. Computed radial gradients for galactic protons At Earth 50 AU TS = 91 AU During solar minimum modulation; A > 0; A < 0

20. Computed proton polar gradients Earth 50 AU 91 AU During solar minimum modulation; A > 0; A < 0

21. Modulation of galactic protons and anti-protons at solar minimum

22. Modulation of galactic electrons and positrons at solar minimum

23. Ratio of Electrons to Positrons At Earth Solar minimum modulation Two concecutive magnetic field polarities Ratio of Electrons to Positrons At Earth Solar maximum modulation Two concecutive magnetic field polarities

24. Ratio of Electrons to Positrons At Earth vs. LIS Solar minimum modulation Two concecutive magnetic field polarities Ratio of Protons to Anti-protons At Earth vs. LIS Solar minimum modulation Two concecutive magnetic field polarities

25. The Wonders of Heliospace Profile of the Latitudinal Solar Wind

26. Contribution of Jovian Electrons Electron Spectra at Earth and at increasing radial distances

27. Modulation of Jovian Electrons Jupiter is a strong source of low-energy electrons at 5 AU Illustration of electrons following the HMF spiral structure; paralllel and perpendicular diffusion

28. Charged-sign Dependent Modulation over two Solar Maxima Electron measurements form ISEE/ICE (Clem et al., 1996; Evenson, 1998) and KET (Heber et al, this conference). He measurements from IMP (McDonald, 1998; McDonald et al., 2001).