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A Monte Carlo study for 2-D Heliospheric modulation effects. S. Della Torre 1,2 , P. Bobik 5 , G. Boella 1,3 , M.J. Boschini 1,4 , C. Consolandi 1 , M . Gervasi 1,3 , D. Grandi 1 , K. Kudela 5 , F. Noventa 1,3 , S . Pensotti 1,3 , P.G. Rancoita 1 , D.Rozza 1,2 , M. Tacconi 1

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## S. Della Torre 1,2 , P. Bobik 5 , G. Boella 1,3 , M.J. Boschini 1,4 , C. Consolandi 1 ,

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**A Monte Carlo study for 2-D Heliospheric modulation effects**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).**Outline**• Introduction to Solar modulation • Parker Equation • A Monte Carlo approach - HelMod Code • Latititudinal intensity of Cosmic Rays • Our results • Conclusion S. Della Torre**Solar Modulation**The Cosmic ray measured at Earth orbit is affected by Solar modulation at energy <10-30 GV Solar Activity Particle Charge Solar Magnetic Polarity +- BESS data - Shikaze et al, 2007 S. Della Torre**Diffusion**Drift Large Scale structure of magnetic field (e.g. gradients) Small Scale Magnetic Field irregoularity Convection Energetic Loss Presence of the solar wind moving out from the Sun Due to adiabatic expansion of the solar wind Parker transport equation Propagation in the heliosphere is decribed by Parker (1965) equation: U Cosmic Rays number density per unit interval of kinetic energy S. Della Torre**A Monte Carlo Approach**The 2D Heliophere Modulation Monte Carlo Code: Parker Equation Stochastic Differential Equations (SDE) Ito’s lemma, see e.g. Gardiner, 1985 2-Dimensional set of SDEs Details on HelMod modulation code, and how to compute the SDE, could be found in [Bobik et al. Ap.J. 2012, 745:132] S. Della Torre**The Inteplanetary Magnetic Field**The Sun’s magnetic field is transported with the Solar wind into space, forming the so-called Heliospheric Magnetic Field (HMF) Heaviside step function Radial versor Field Polarity Azimutal versor Neutral Sheet Parker Field Jokipii & Kòta, 1989 Langner, 2004 Polar versor The Polar Correction BL is evaluated only For <30° and >150° of solar colatitude BP +BL BP [Bobik et al. Ap.J. 2012, 745:132] see poster Rozza et al. ID: SH-489 S. Della Torre**Diffusion**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 position K0(t) is sensitive to GCR particles with rigidity > 2 GV where 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] S. Della Torre**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 Tilt angle of the Neutral Sheet Magnetic Field Magnitude at Earth Diffusion parameter Solar Wind Speed For further details on the model see poster Rozza et al. ID: SH-489 S. Della Torre**The Bi-dimensional Heliosphere**From ‘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. 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] S. Della Torre [Heber et al. Ap.J. 2008, 689:1443]**Drift effect on latitudinal gradient**We use HelMod Code with present model of to evaluate the latitudinal gradient in both magnetic field polarity. R>2.1GV T>2.1 GeV 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 S. Della Torre**Data comparison**To compare out results with Ulysses data We evaluate the Cosmic rays intensity during the both two fast scan at the same distance and latitude of Ulysses Spacescraft (IU) A<0 solar minimum Ulysses fast scan 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 S. Della Torre**Results**A>0 Ulysses Fast Scan R R A<0 Ulysses Fast Scan R R S. Della Torre**Conclusion**• 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 S. Della Torre

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