1. Recurrent Cosmic Ray Variations in 2007-2008 József Kόta & J.R. Jokipii University of Arizona, LPL Tucson, AZ 85721-0092, USA 23 rd ECRS, Moscow, Russia, July 5, 2012 kota@lpl.arizona.edu ● V-1

2. - Outline - 200-2008 was a Year of Recurrent Variations: the quiet Sun, moderate tilt angle, & stable CIRs* led to 27-day CR variations (Leske et al, Modzelewska et al., 2011). We present numerical simulations using our re-vitalized 3-D CR code assuming stable co-rotation. We discuss qualitative, general features of simulation results Briefly discuss numerical simulations of Jovian electrons, which also showed remarkable recurrent variations (Kecskemėty et al., 2011) * CIR = Corotating Interaction Region

3. Formation of Corotating Interaction Region CIRs are the result of tilted magnetic dipole + solar rotation: later emitted fast wind overtakes the earlier emitted slow wind. CIRs form typically beyond 1 AU Equatorial cut Fast wind from coronal holes

4. Recurrent Variations in 2007-2008 Leske et al, ICRC, Beijing, 2011) Modzelewska et al, 2011 CR SW B

5. Interpretation of 27-day CR wave Cosmic ray intensity is higher where the solar wind is slower. Modzelewska et al., 2011 relates CR flux, J, to V*B (electric field) The rate of CR decrease (dJ/dt) is higher in the stronger magnetic field of compressed regions (Burlaga’s CR-B law) dJ/dt ~ - B implying non-local connection between CR & B

6. Example of Earlier Numerical Simulation o Assume perfect co- rotation. SW & B are specified near the Sun (caveat: V kept radial) o Global 3-D transport code solves Parker’s diffusive equation in co- rotating frame

7. Current Simulation & Implications o Take symmetric dipole configuration but place Earth off-equator o CR Intensity peaks at low speed (Modzelewska) o Intensity falls sharply at strong B (Burlaga-law, Kota & Jokipii, 1991) o Connection between CR flux and plasma parameters may not be local A<0 (blue) applies

8. Jovian Electrons Leske et al (2011) presented and interesting study using near-Earth and Stereo A & B observations. Electron fluxes did not show any clear correlation with CIR structures. In simulations Jupiter is a moving source in the corotating frame. We expect combined effect of CIR + magnetic connection Earth/Jupiter go around in 27/26 days

9. Simulation of Jovian Electrons - 2

10. Simulation of Jovian Electrons - 4

11. Jovian Electons: Time dependence Note: fluxes at Earth & Stereos follow the flux near Jupiter which changes in 26-day wave according to CIRs. These results are in qualitative agreement with Kecskemėty et al. (2011) who find rather 26 than 27 day variations (non-local origin.)

12. Lesson ● “Make everything as simple as possible, but not simpler “ CR fluxes are not uniquely determined by local plasma & B

13. Summary/Conclusion The Sun was very quiet while its magnetic axis remained moderately high during 2007-2008, which lead to a remarkably stable CIR structure. Corresponding 27-day CR variations were clearly present (Leske et al., 2011; Modzelewska et al., 2011) We have re-vitalized our earlier 3-D CR transport/acceleration code to simulate these recurrent variations. Simulations results are qualitative agreement with observational findings: (e.g. CR max at slow wind, intensity decrease at strong B) While the mechanism cannot be definitely identified (there are alternative explanations), the connection between CR flux and B need not be local Jovian electrons tend to point to non-local origin of the recurrent CR variations as well.

14. The End

15. 2. Diffusive Particle Transport: Parker’s Equation (1965) Diffusive transport equation of energetic charged particles: - assumes near isotropic distribution Diffusion (anisotropic) Drift Convection Cooling/ Acceleration Source Related to regular gyro- motion Polarity/charge dependent Mixed system

16. Classic CIR-Calculation (Fisk & Lee, 1980) Fisk & Lee (1980) assume κ~r, which allows analytical approximation is but highly simplified Model results are in good qualitative agreement with observations. Harder spectrum at the reverse shock

17. Simulation of Jovian Electrons - 1

18. Simulation of Jovian Electrons - 3