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... La physique d'AMS, Annecy 9-10 March 2010

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

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

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

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

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

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

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 CR propagation in the heliosphere is decribed by: U is density number of CR for unit interval of energy La physique d'AMS, Annecy 9-10 March 2010

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

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 La physique d'AMS, Annecy 9-10 March 2010

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

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

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 La physique d'AMS, Annecy 9-10 March 2010

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 La physique d'AMS, Annecy 9-10 March 2010

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

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

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 La physique d'AMS, Annecy 9-10 March 2010

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 La physique d'AMS, Annecy 9-10 March 2010

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

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

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

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

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

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

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

Summary GCRs entering the Heliosphere undergo diffusion, convection, magnetic drift and adiabatic energy loss Parker in 1965 gave the first description of Solar Modulation with his famous FP like equation First simmetric approximation is called Force Field and depends on just one parameter, the modulation potenzial  The heliosphere is much more complex: polarity of the field changes every 11 years, magnetic drift plays an important role depending also on particle’s charge, and solar Wind is not constant Using a set of SDEs that solves Parker’s equation we realized a 2D Stochastic Montecarlo for GCRs modulation with JK modification for the polar field and the PM as NS Drift, for different solar conditions. With a dynamic approach we reproduced the proton CR flux for different experiments (AMS, Caprice, BESS and IMAX) and predicted the CR flux that AMS-02 will measure on the ISS We are working on a connection between tilt angle and solar activity and different particles (antiprotons, nuclei, electrons etc.)

Thank you for your attention!

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