Solar Modulation Davide Grandi AMS Group-INFN Milano-Bicocca.
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Transcript of Solar Modulation Davide Grandi AMS Group-INFN Milano-Bicocca.
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
e r
eg
ion
of
influ
en
ce o
f th
e s
ola
r m
ag
neti
c 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
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
11th ICATPP, Como 5-9 October 2009
Magnetic Drift
using the Guiding Center approximation
11th ICATPP, Como 5-9 October 2009
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
R22
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
11th ICATPP, Como 5-9 October 2009
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
11th ICATPP, Como 5-9 October 2009
Cosmic Rays moduated spectra -IMAX
11th ICATPP, Como 5-9 October 2009
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
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 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)