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. 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

The heliosphere the region of influence of the solar magnetic field... 11th ICATPP, Como 5-9 October 2009

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

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

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

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

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

Solar Wind High Solar Activity Low Solar Activity

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

Modulazione Solare 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) Introduzione Mod. Parker Propag. RC Nostro Modello Risultati & Conclusioni

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

Propagazione di RC in Eliosfera Force Field Risoluzione analitica dell’equazione di Parker monodimensionale. Ha come unico parametro il fattore di modulazione  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 Introduzione Mod. Parker Propag. RC Nostro Modello Risultati & Conclusioni

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

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

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

Convective/Drift term 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

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

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

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

Drift model: WNS vs. PM <<1 rad  30° 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) Magnetic drift equation is solved for the approximation <<1 rad  30° 31st ICRC Lodz 7-15 July 2009

Neutral Sheet Drift 2D Approximation Potgieter & Moraal (1985) Burger & Potgieter (1989) Wavy Neutral Sheet - Hattingh & Burger (1995) er N S Ordinary Drift NS drift Transition Function that emulate the effect of a wavy neutral sheet

Drift model: PM where the term f(θ), is Potgieter Moraal model (1985) 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

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

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

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

Sun magnetic field in not constant in the Heliosphere 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

Dynamic parameters At a first approximation we can divide the heliosphere in different regions The time needed for a magnetic perturbation to reach the external limit of the heliosphere (100AU) is roughly: months In every sector we consider solar condition of a period x-months before the data taking 11th ICATPP, Como 5-9 October 2009

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Thank you for your attention!

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

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

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

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)