S. Della Torre1,2, P. Bobik5, G. Boella1,3, M.J. Boschini1,4, C. Consolandi1,

M. Gervasi1,3, D. Grandi1, K. Kudela5, F. Noventa1,3, S. Pensotti1,3, P.G. Rancoita1, D.Rozza1,2, M. Tacconi1

1 INFN Milano-Bicocca, Milano (Italy) 2 University of Insubria, Como (Italy)

3 University of Milano-Bicocca, Milano (Italy) 4 CILEA, Segrate (Milano, Italy)

5 Institute of Experimental Physics, Kosice (Slovak Republic).

OutlineOutline• Introduction to Solar modulation• Parker Equation • A Monte Carlo approach - HelMod

Code• Latititudinal intensity of Cosmic Rays • Our results • Conclusion

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Solar Modulation

Solar Activity

The Cosmic ray measured at Earth orbit is affected by Solar modulation at energy <10-30 GV

Solar Magnetic Polarity

Particle Charge

BESS data - Shikaze et al, 2007

+ -

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U Cosmic Rays number density per unit interval of kinetic energy

DiffusionSmall Scale Magnetic

Field irregoularity

ConvectionPresence of

the solar wind moving out from the

Sun

Energetic Loss

Due to adiabatic

expansion of the solar wind

Propagation in the heliosphere is decribed by Parker (1965) equation:

Parker transport equation

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Parker Equation Stochastic Differential

Equations (SDE)

The 2D Heliophere Modulation Monte Carlo Code:

Ito’s lemma,

see e.g. Gardiner, 1985

2-Dimensional set of SDEs

A Monte Carlo ApproachA Monte Carlo Approach

Details on HelMod modulation code, and how to compute the SDE, could be found in [Bobik et al. Ap.J. 2012, 745:132]

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The Inteplanetary Magnetic FieldThe Inteplanetary Magnetic Field

Parker Field

Jokipii & Kòta, 1989Langner, 2004

The Sun’s magnetic field is transported with the Solar wind into space, forming the so-called Heliospheric Magnetic Field (HMF)

Heaviside stepfunction

Field Polarity Neutral SheetRadial versor Azimutal versor

Polar versor

The Polar Correction BL is evaluated only For <30° and >150° of solar colatitude

BPBP +BL

[Bobik et al. Ap.J. 2012, 745:132]

see poster Rozza et al. ID: SH-489

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DiffusionDiffusion

In the magnetic field line reference the diffusion tensor is

K0(t) Is the modulation parameter obtained using cosmic ray flux >2 GV measured with neutron monitor at different latitudes

We apply modulation inside an effective spherical volume of 100 AU K0(t) takes into account the rough integrated effects on GCR modulation as seen at the Earth positionK0(t) is sensitive to GCR particles with rigidity > 2 GVwhere different LIS do not differ practically each other Changing Heliosphere dimensions (80 – 120 AU) modulated spectra do not differ significantly, for rigidity > 1 GV (> 400 MeV)

[Bobik et al. Ap.J. 2012, 745:132]

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We divide the Heliosphere in 15

regions. each one equivalent

to the average of solar activity in

periods before the experiment

Parameters in each region are

DiffusionDiffusionparameterparameter

Tilt angleTilt angleof the Neutral Sheetof the Neutral Sheet

Magnetic Field Magnetic Field Magnitude at EarthMagnitude at Earth

Solar Wind SpeedSolar Wind Speed

For further details on the modelsee poster Rozza et al. ID: SH-489

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The Bi-dimensional HeliosphereThe Bi-dimensional HeliosphereFrom ‘90s up to 2010 ESA/NASA Ulysses mission explore the heliophere outside the ecliptica plane

K.E.T. Instruments measured cosmic protons and electrons in energy range greater than 0.2 GeV.

[Heber et al. Ap.J. 2008, 689:1443]

The fast scan in 1995 (A>0) showed the presence of a latitudinal gradient of proton in the inner heliosphere. This gradient vanish during the 2007 (A<0) fast scan.Electrons show opposite behavior.

[see e.g. Heber et al. Ap.J. 2008, 689:1443 and reference therin]

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Drift effect on latitudinal gradientDrift effect on latitudinal gradientWe use HelMod Code with present model of to evaluate the latitudinal

gradient in both magnetic field polarity.

The presence (or not) of a latitudinal gradient is related to Drift mechanism in the heliosphere.

Since drift is related to the product of charge (q) and field Polarity (A), with electron opposite behaviors appears, in qualitatively agreement with Ulysses

analysis

T>2.1 GeVR>2.1GV

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Data comparisonData comparisonTo compare out results with Ulysses dataWe evaluate the Cosmic rays intensity during the both two fast scan at the same distance and latitude of Ulysses Spacescraft (IU)

To takes in to accout the time variation of the Cosmic rays intensity We evaluate also the intensity at the same time at 1AU on ecliptica (IE) and

renormalized the ratio IU/IE in order to have 1 at south pole (-90° -70°)

The same is done both for Proton and Electron

A<0 solar minimum Ulysses fast scan

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ResultsResultsA>0 Ulysses Fast Scan

A<0 Ulysses Fast Scan

R R

R R

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ConclusionConclusion

• We presented the 2-D HelMod Monte Carlo Code for the study of cosmic rays propagation in the inner Heliosphere (ApJ, 2011, arXiv:1110.4315);

• We use the Monte Carlo Code to explore the latitudinal intensity of the galactic cosmic ray

• We found an agreement with Ulysses data for both Magnetic field Polarity showing as Magnetic drift could explain the observed latitudinal gradient of proton during A>0 fast scan, the near isotropic intensity during A<0 fast scan and the simmetry of the behavior with Electron

Thank for your attention

Stefano.dellatorre@mib.infn.it