Drift models and polar field

for cosmic rays propagation

Stefano Della Torre

11th ICATPP, Como 5-9 october 2009

Outline•Cosmic Rays propagation

in different period/polarity

•Drift Models

•Solar Wind

•Heliosphere

•Conclusions

Modulation

A>0 A<0

Tilt Angle from Wilcox Obs.

Shikaze et al. 2007

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

Boella et. Al. 2001

The Cosmic Rays propagation inside the heliosphere is described by the Parker equation

U Cosmic Rays number density per unit interval of kinetic energy

Cosmic Rays propagation

Diffusion

Small Scale Magnetic

Field irregoularity

ConvectionPresence of

the solar wind moving out

from the Sun

Energetic Loss

Due to adiabatic expansion of the

solar wind

Drift

Large Scale structure of

magnetic field(e.g. gradients)

Along the equatorial region, where the magnetic field invert his polarity, we have Neutral Sheet Drift

Neutral Sheet

Sheet with |B|=0

-> charge dependent

-> Magnetic polarity dependent

Magnetic Drift

Drift

This Effect is greater during solar minimum periods, when the Heliosferic Magnetic Field (HMF) have a regular

topology, and vanishing during Solar Maxima due to chaotic behavior of the field line

Potgieter et al. 1985

Neutral Sheet

Coronal Magnetic Field lines at Solar minimum Activity

The combination with the Solar Rotation cause a tilt of the Neutral Sheet; causing the so called “ballerina skirt”

effect around the Eclittica Plane

The amplitute of this oscillation is called Tilt Angle ()

And it depends of Solar activity: e.g. minimum activity -> 10°, maximum activity ->

>75°

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

during solar Minimum

AMS-01 (1998)

CAPRICE (1994)

Tilt Angle () < 30°

Solar WindHigh Solar ActivityLow Solar Activity

)cos(10 VVSWUlysses measurement

Agreement with dataAgreement with data

Modified Heliospheric Magnetic Field

A

We use a Simple

Parker’s Field

With a Polar modification as in Jokipii & Kòta 1989

Polar Cosmic Rays access reduced

Agreement with Agreement with datadata

A solar Magnetic perturbation generated TODAY on the Sun, will get the Heliopause in

Dynamic view of HMF

month

We divide the heliosphere in 14 region, with previous solar condition each

AMS-01 view of heliosphere

A Cosmic Particle in average will remain 1 month into heliosphere

Agreement with dataAgreement with data

In all simulation presented we use PM model

30°

A>0 A<0

BESSHigh Solar Activity

AMS-01Low Solar Activity

IMAXMiddle solar

activity

CAPRICELow Solar Activity

Experimental Data

NymmikEmpirical Model.One parameter model:

smoothed sunspot number in the months previous the oservations data.

For All NucleiActually the ISO

standard for space qualification.

Increase of precision compared with Nymmik model

Our Average variance = 5%Nymmik Average variance = 16%

Conclusions

• We develop a 2D - MonteCarlo Stochastic

program that reproduces Cosmic rays data in

different solar periods using a dynamic view of

HMF.

• We use a modified Magnetic field that reduces

the drift contribute in polar regions.

• We find that during solar minimum both

PM and WNS model reproduce data with

confidence; increasing solar activity only

PM model does that.

• The Solar wind latitudinal dependency is

relevant in order to reproduce data

Thanks for Yours Attention

Stefano.DellaTorre@mib.infn.it