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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... 11th ICATPP, Como 5-9 October 2009

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

  5. Field polarity Configuration for A>0 Configuration for A<0 Solar cycle period is approx 11 years 11th ICATPP, Como 5-9 October 2009

  6. Magnetic field generated from the Sun Field lines “frozen” in the plasma created by the solar corona adiabatic expansion 11th ICATPP, Como 5-9 October 2009

  7. 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) 11th ICATPP, Como 5-9 October 2009

  8. Wavy Neutral Sheet Solar Wind and Magnetic Field Latitudinal Dependence 11th ICATPP, Como 5-9 October 2009

  9. Low Solar Activity High Solar Activity Solar Wind

  10. Modulazione solare dei RCG L’effetto del trasporto dei RC è una DIMINUZIONE del flusso di RC dall’esterno verso l’interno della eliosfera

  11. Modulazione Solare Mod. Parker Propag. RC Nostro Modello Risultati & Conclusioni Introduzione Il Flusso Integrale dei Raggi Comici diminuisce avvicinandosi al Sole Flusso integrale misurato dalle sonde Voyager 1 (V1) Voyager 2 (V2) e Pioneer 10 (P10)

  12. Campo Magnetico Interplanetario Mod. Parker Propag. RC Nostro Modello Risultati & Conclusioni Introduzione Le linee di campo si deformano secondo una “spirale di Archimede” Il Sole Ruota L’eliosfera si divide in due emisferi a polarità opposta divisi a uno strato neutro di corrente La rotazione del sole è differenziale

  13. Propagazione di RC in Eliosfera Mod. Parker Propag. RC Nostro Modello Risultati & Conclusioni Introduzione Risoluzione analitica dell’equazione di Parker monodimensionale. Ha come unico parametro il fattore di modulazione Force Field Nymmik Modello empirico, richiede come unico parametro il numero di smoothed sunspot number per calcolare il potenziale effettivo modulazione nei mesi precedenti la data di osservazione

  14. Parker’s FP Equation Magnetic irregularities on a small scale Diffusion Magnetic field gradients on larger domains Magnetic Drift Solar Wind expansion Convection The global effect on CR si given by: 11th ICATPP, Como 5-9 October 2009

  15. Parker’s Equation CR propagation in the heliosphere is decribed by: U is density number of CR for unit interval of energy Is essentially a Fokker-Planck equation Convective/Drift Term Diffusive Term 31st ICRC Lodz 7-15 July 2009

  16. Diffusione e Moti di Deriva Interazione della particella cosmica con il mezzo interplanetario Continui URTI che causano una variazione del percorso Processo di Random Walk

  17. 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 11th ICATPP, Como 5-9 October 2009

  18. Magnetic Drift using the Guiding Center approximation 11th ICATPP, Como 5-9 October 2009

  19. Deriva Magnetica Mod. Parker Propag. RC Nostro Modello Risultati & Conclusioni Introduzione La deriva magnetica è legata alla componente anti-simmetrica del tensore di diffusione

  20. Different Solar polarities.... 11th ICATPP, Como 5-9 October 2009

  21. Magnetic drift equation is solved for the approximation <<1 rad  30° Drift model: WNS vs. 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 Wavy Neutral Sheet Model (1995) 31st ICRC Lodz 7-15 July 2009

  22. 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)

  23. 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 11th ICATPP, Como 5-9 October 2009

  24. Ulysses (orbita polare solare) Counting rate (1/s) IMP8 (1AU) Polar field corrections ~16% [Heber 1998] 11th ICATPP, Como 5-9 October 2009

  25. Polar field corrections 11th ICATPP, Como 5-9 October 2009

  26. Polar field corrections 31st ICRC Lodz 7-15 July 2009

  27. Dynamic parameters Sun magnetic field in not constant in the Heliosphere 100 AU Magnetic perturbations move with the solar wind 11th ICATPP, Como 5-9 October 2009

  28. 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 11th ICATPP, Como 5-9 October 2009

  29. Cosmic Rays moduated spectra BESS High Solar Activity A<0 A>0 IMAX Medium Solar Activity CAPRICE Low Solar Activity 30° AMS-01 Low SOlar ACtivity 11th ICATPP, Como 5-9 October 2009

  30. Cosmic Rays moduated spectra -IMAX Menn et al. 2000 11th ICATPP, Como 5-9 October 2009

  31. Cosmic Rays moduated spectra - BESS Shikaze et al.2007 11th ICATPP, Como 5-9 October 2009

  32. Cosmic Rays moduated spectra - Caprice 11th ICATPP, Como 5-9 October 2009 Boezio et. al. 1999

  33. Cosmic Rays moduated spectra – AMS 01 11th ICATPP, Como 5-9 October 2009 Alcaraz et. al. 1998

  34. Cosmic Rays moduated spectra 11th ICATPP, Como 5-9 October 2009 31st ICRC Lodz 7-15 July 2009

  35. Cosmic Rays moduated spectra 11th ICATPP, Como 5-9 October 2009 31st ICRC Lodz 7-15 July 2009

  36. Cosmic Rays moduated spectra 11th ICATPP, Como 5-9 October 2009 31st ICRC Lodz 7-15 July 2009

  37. Cosmic Rays moduated spectra 11th ICATPP, Como 5-9 October 2009 31st ICRC Lodz 7-15 July 2009

  38. A<0 A>0 A<0 AMS-02 measurements We estimated the expected GCR flux for the AMS-02 mission Estimated Sunspot Numbers 11th ICATPP, Como 5-9 October 2009

  39. Predictions for AMS-02 11th ICATPP, Como 5-9 October 2009

  40. Relation between Solar Activity and Tilt angle 11th ICATPP, Como 5-9 October 2009

  41. Relation between Solar Activity and Tilt angle 11th ICATPP, Como 5-9 October 2009

  42. Conclusions • We realized a 2D Stochastic Montecarlo to evaluate the CR modulation in the Heliosphere • We introduced the JK modification for the polar field and used the PM as NS Drift models, suitable for different solar conditions • We introduced a dynamic approach to the use of parameters in order to reproduce the real physical process • We reproduced the proton CR flux for different experiments (AMS, Caprice, BESS and IMAX) in different solar polarities for medium, high and low solar activity • We used our 2D Montecarlo to predict the CR flux that AMS-02 will measure on the ISS from 2010 to 2012 (maximum), this will also help a better tuning and small corrections • We are able to modulate different kind of particles (antiprotons, nuclei, electrons etc.) • We are investigating also a more strict connection between the tilt angle and the solar activity

  43. Thank you for your attention!

  44. Polarity/Charge dependence 31st ICRC Lodz 7-15 July 2009

  45. 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

  46. Raggi Cosmici in Eliosfera La rotazione differenziale del Sole causa una divisione dell’eliosfera in 2 regioni divise da uno strato neutro di corrente Lo strato neutro di corrente oscilla entro un certo angolo con l’eclittica Angolo di Tilt

  47. Raggi Cosmici in Eliosfera Deriva magnetica dovuta a curvatura e gradiente dell’IMF Il modello comprende Deriva dovuta a allo strato neutro di corrente Il modello dipende dalla polarità del campo magnetico solare e dalla carica delle particelle (in figura positive)

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