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Solar Modulation

Solar Modulation. Davide Grandi AMS Group-INFN Milano-Bicocca. Outline. The heliosphere Sun’s Magnetic Field , Polarity and Activity Solar Wind and Neutral Sheet Solar modulation of GCR Diffusion, Convection, Energy Loss, Drift The basic: Parker Model Force Field Approx.

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Solar Modulation

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  1. Solar Modulation Davide Grandi AMS Group-INFN Milano-Bicocca

  2. Outline • The heliosphere • Sun’s Magnetic Field , Polarity and Activity • Solar Wind and Neutral Sheet • Solar modulation of GCR • Diffusion, Convection, Energy Loss, Drift • The basic: Parker Model • Force Field Approx. • Our 2D Stochastic Monte Carlo • JK modif. of polar field • Drift model: WNS & PM • Dynamic parameters • Comparison with data & Prediction for AMS-02 • Conclusions La physique d'AMS, Annecy 9-10 March 2010

  3. The heliosphere the region of influence of the solar magnetic field... La physique d'AMS, Annecy 9-10 March 2010

  4. Magnetic field generated from the Sun Field lines “frozen” in the plasma created by the solar corona adiabatic expansion La physique d'AMS, Annecy 9-10 March 2010

  5. Field polarity Configuration for A>0 Configuration for A<0 Archimedean Spiral La physique d'AMS, Annecy 9-10 March 2010

  6. Solar Activity A>0 A<0 A<0 A<0 A>0 A>0 • The solar activity is related to: • - Sunspot number (<10 minimum; >100 maximum) - Wavy Neutral Sheet opening/tilt angle (10° minimum ; >75° maximum) La physique d'AMS, Annecy 9-10 March 2010

  7. Wavy Neutral Sheet Solar Wind and Magnetic Field Latitudinal Dependence La physique d'AMS, Annecy 9-10 March 2010

  8. Low Solar Activity High Solar Activity Solar Wind La physique d'AMS, Annecy 9-10 March 2010

  9. Solar Modulation Cr transport effect is a flux DECREASE moving from the outer to the inner Heliosphere La physique d'AMS, Annecy 9-10 March 2010

  10. Parker’s FP Equation Magnetic irregularities on a small scale Diffusion Magnetic field gradients on larger domains Magnetic Drift Solar Wind expansion Convection CR propagation in the heliosphere is decribed by: The global effect on CR si given by: U is density number of CR for unit interval of energy La physique d'AMS, Annecy 9-10 March 2010

  11. Force Field Analitical solution of Parker’s equation in the monodimensional approx. The only parameter is the modulation potential  • Assumptions: • V constant with r • K constant with r • Steady state (no sources) • No convection • No drift (K simmetric) La physique d'AMS, Annecy 9-10 March 2010

  12. Stochastic 2D Montecarlo Parker’s equation, in the 2D (radius and co-latitude) approximation, is mathematically equivalent to the following set of stochastic differential equations Convective/Drift term Diffusive term La physique d'AMS, Annecy 9-10 March 2010

  13. Diffusion and Drift Particles generated at 100 AU Interact with the Interplanetary Medium Random Walk Process Down to 1 AU La physique d'AMS, Annecy 9-10 March 2010

  14. Magnetic Drift using the Guiding Center approximation La physique d'AMS, Annecy 9-10 March 2010

  15. N Ordinary Drift er NS drift Transition Function that emulate the effect of a wavy neutral sheet S Neutral Sheet Drift 2D Approximation Potgieter & Moraal (1985) Burger & Potgieter (1989) Wavy Neutral Sheet - Hattingh & Burger (1995) La physique d'AMS, Annecy 9-10 March 2010

  16. Drift model: PM Minimo Solare Potgieter Moraal model (1985) Transition function, is 0 on the ecliptic plane and ± 1 at the poles NS term, is maximum on the ecliptic Massimo Solare where the term f(θ), is La physique d'AMS, Annecy 9-10 March 2010

  17. Ulysses (orbita polare solare) Counting rate (1/s) IMP8 (1AU) Polar Field corrections ~16% [Heber 1998] La physique d'AMS, Annecy 9-10 March 2010

  18. Polar Field corrections La physique d'AMS, Annecy 9-10 March 2010

  19. Dynamic parameters Sun magnetic field in not constant in the Heliosphere 100 AU Magnetic perturbations move with the solar wind La physique d'AMS, Annecy 9-10 March 2010

  20. The time needed for a magnetic perturbation to reach the external limit of the heliosphere (100AU) is roughly: months Dynamic parameters At a first approximation we can divide the heliosphere in different regions In every sector we consider solar condition of a period x-months before the data taking La physique d'AMS, Annecy 9-10 March 2010

  21. Cosmic Rays moduated spectra La physique d'AMS, Annecy 9-10 March 2010 31st ICRC Lodz 7-15 July 2009

  22. Cosmic Rays moduated spectra La physique d'AMS, Annecy 9-10 March 2010 31st ICRC Lodz 7-15 July 2009

  23. Cosmic Rays moduated spectra La physique d'AMS, Annecy 9-10 March 2010 31st ICRC Lodz 7-15 July 2009

  24. Cosmic Rays moduated spectra La physique d'AMS, Annecy 9-10 March 2010

  25. Cosmic Rays moduated spectra La physique d'AMS, Annecy 9-10 March 2010

  26. A<0 A>0 A<0 AMS-02 measurements We estimated the expected GCR flux for the AMS-02 mission Estimated Sunspot Numbers La physique d'AMS, Annecy 9-10 March 2010

  27. Predictions for AMS-02 La physique d'AMS, Annecy 9-10 March 2010

  28. Relation between Solar Activity and Tilt angle La physique d'AMS, Annecy 9-10 March 2010

  29. Summary • GCRsentering the Heliosphereundergodiffusion, convection, magneticdrift and adiabaticenergy loss • Parker in 1965 gave the first descriptionofSolarModulationwithhisfamous FP likeequation • First simmetricapproximationiscalledForceField and depends on just oneparameter, the modulationpotenzial • The heliosphereismuch more complex: polarityof the fieldchangesevery 11 years, magneticdriftplaysanimportantroledependingalso on particle’s charge, and solar Wind isnotconstant • Using a set ofSDEsthatsolvesParker’s equationwerealizeda 2D Stochastic MontecarloforGCRsmodulationwith JK modificationfor the polarfield and the PM as NS Drift, fordifferentsolarconditions.With a dynamicapproachwereproducedthe proton CR fluxfordifferentexperiments (AMS, Caprice, BESS and IMAX) and predictedthe CRfluxthat AMS-02 willmeasure on the ISS • Weare investigatingalso a more strict connectionbetween the tilt angle and the solaractivity

  30. Thank you for your attention!

  31. Modulation Boella et. Al. 2001 Rate of flux in two consecutive period with similar solar activity Variation between two consecutive minimum (it change the Field polarity) There is a strong dependence of the modulation from the polarity of the field

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