Solar Solar ModulationModulation

Davide GrandiAMS Group-INFN Milano-Bicocca

Outline The heliosphere

Sun’s Magnetic Field , Polarity and Activity

Solar Wind and Neutral SheetSolar 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 heliosphereth

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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

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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

The solar activity is related to: - Sunspot number

(<10 minimum; >100 maximum)- Wavy Neutral Sheet opening/tilt angle

(10° minimum ; >75° maximum)

A<0 A<0A>0 A>0 A<0A>0

11th ICATPP, Como 5-9 October 2009

Latitudinal Dependence

Solar Wind and Magnetic FieldWavy Neutral Sheet

11th ICATPP, Como 5-9 October 2009

Solar WindHigh Solar ActivityLow Solar Activity

)cos(10 VVSW

Modulazione solare dei RCG

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

Introduzione Mod. Parker Propag. RC Nostro Modello Risultati & Conclusioni

Modulazione SolareModulazione SolareIl 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 InterplanetarioCampo Magnetico InterplanetarioIl Sole Ruota Le linee di campo si deformano secondo una “spirale di

Archimede”

La rotazione del sole è differenzialeL’eliosfera si divide in due emisferi a

polarità opposta divisi a uno strato neutro di corrente

Introduzione Mod. Parker Propag. RC Nostro Modello Risultati & Conclusioni

Propagazione di RC in EliosferaPropagazione di RC in EliosferaForce Field

Nymmik

Risoluzione analitica dell’equazione di Parker monodimensionale.Ha come unico parametro il fattore di modulazione

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

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

Parker’s FP Equation

11th ICATPP, Como 5-9 October 2009

CR propagation in the heliosphere is decribed by:

Parker’s Equation

Is essentially a Fokker-Planck equation

Diffusive TermConvective/Drift

Term

U is density number of CR for unit interval of energy

31st ICRC Lodz 7-15 July 2009

Diffusione e Moti di DerivaInterazione della particella cosmica con il mezzo interplanetario

Continui URTI che causano una variazione del percorso

Processo di Random Walk

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

Diffusive termConvective/Drift term

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Magnetic Drift

using the Guiding Center approximation

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Introduzione Mod. Parker Propag. RC Nostro Modello Risultati & Conclusioni

Deriva MagneticaDeriva MagneticaLa deriva magnetica è legata alla componente anti-simmetrica del tensore di diffusione

Different Solar polarities....

11th ICATPP, Como 5-9 October 2009

Drift model: WNS vs. PM

Massimo Solare

Minimo Solare

Potgieter Moraal model (1985)

Wavy Neutral Sheet Model (1995)

Transition function, is 0 on the ecliptic plane and ± 1 at the poles

NS term, is maximum on the ecliptic

Magnetic drift equation is solved for the approximation

<<1 rad 30°

31st ICRC Lodz 7-15 July 2009

Neutral Sheet DriftPotgieter & Moraal (1985)

Burger & Potgieter (1989)

Wavy Neutral Sheet - Hattingh & Burger (1995)

Ordinary Drift

NS drift

Transition Function that emulate the effect of a wavy neutral sheet

2D Approximation

er

r

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N

S

Drift model: PM

Massimo Solare

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

where the term f(θ), is

11th ICATPP, Como 5-9 October 2009

Ulysses(orbita polare solare)

IMP8(1AU)

Cou

ntin

g ra

te (

1/s)

~16%

[Heber 1998]

Polar field corrections

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Polar field corrections

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Polar field corrections

31st ICRC Lodz 7-15 July 2009

Dynamic parameters

100 AU

Magnetic perturbations move with the solar wind

Sun magnetic field in not constant in the Heliosphere

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Dynamic parametersAt 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

The time needed for a magnetic perturbation to reach the external limit of the heliosphere (100AU) is roughly:

months

11th ICATPP, Como 5-9 October 2009

Cosmic Rays moduated spectra

30°

A>0 A<0

BESSHigh Solar Activity

AMS-01Low SOlar ACtivity

IMAXMedium Solar Activity

CAPRICELow Solar Activity

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Cosmic Rays moduated spectra -IMAX

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Menn et al. 2000

Cosmic Rays moduated spectra - BESS

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Shikaze et al.2007

Cosmic Rays moduated spectra - Caprice

11th ICATPP, Como 5-9 October 2009Boezio et. al. 1999

Cosmic Rays moduated spectra – AMS 01

11th ICATPP, Como 5-9 October 2009Alcaraz et. al. 1998

Cosmic Rays moduated spectra

31st ICRC Lodz 7-15 July 200911th ICATPP, Como 5-9 October 2009

Cosmic Rays moduated spectra

31st ICRC Lodz 7-15 July 200911th ICATPP, Como 5-9 October 2009

Cosmic Rays moduated spectra

31st ICRC Lodz 7-15 July 200911th ICATPP, Como 5-9 October 2009

Cosmic Rays moduated spectra

31st ICRC Lodz 7-15 July 200911th ICATPP, Como 5-9 October 2009

We estimated the expected GCR flux for the AMS-02 mission

Estimated Sunspot Numbers

A<0 A>0 A<0

AMS-02 measurements

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Predictions for AMS-02

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Relation between Solar Activity and Tilt angle

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Relation between Solar Activity and Tilt angle

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Conclusions We realized a 2D Stochastic Montecarlo to evaluate the CR

modulation in the HeliosphereWe introduced the JK modification for the polar field and used

the PM as NS Drift models, suitable for different solar conditionsWe 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 experimentsdifferent 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

Boella et. Al. 2001

Modulation

There is a strong dependence of the modulation from the polarity of the field

Variation between two consecutive minimum(it change the Field polarity)

Rate of flux in two consecutive period with similar solar activity

Raggi Cosmici in Eliosfera

Lo strato neutro di corrente oscilla entro un certo angolo con l’eclittica

Angolo di Tilt

La rotazione differenziale del Sole causa una divisione dell’eliosfera in 2 regioni divise da uno strato neutro di corrente

Raggi Cosmici in Eliosfera

Il modello comprende

Deriva magnetica dovuta a curvatura e gradiente dell’IMF

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)