G. La Vacca

Solution of Heliospheric Propagation: Unveiling the Local Interstellar Spectra of Cosmic-ray Species

Local interstellar spectra (LIS) for protons, helium, and antiprotons are built using the most recent experimental results combined with state-of-the-art models for propagation in the Galaxy and he ...

HelMod in the works: from direct observations to the local interstellar spectrum of cosmic-ray electrons

The local interstellar spectrum (LIS) of cosmic-ray (CR) electrons for the energy range 1 MeV to 1 TeV is derived using the most recent experimental results combined with the state-of-the-art models for CR propagation in the Galaxy and in the heliosphere. Two propagation packages, GALPROP and HelMod, are combined to provide a single framework that is run to reproduce direct measurements of CR species at different modulation levels, and at both polarities of the solar magnetic field. An iterative maximum-likelihood method is developed that uses GALPROP-predicted LIS as input to HelMod, which provides the modulated spectra for specific time periods of the selected experiments for model-data comparison. The optimized HelMod parameters are then used to adjust GALPROP parameters to predict a refined LIS with the procedure repeated subject to a convergence criterion. The parameter optimization uses an extensive data set of proton spectra from 1997-2015. The proposed CR electron LIS accommodates both the low-energy interstellar spectra measured by Voyager 1 as well as the high-energy observations by PAMELA and AMS-02 that are made deep in the heliosphere; it also accounts for Ulysses counting rate features measured out of the ecliptic plane. The interstellar and heliospheric propagation parameters derived in this study agree well with our earlier results for CR protons, helium nuclei, and anti-protons propagation and LIS obtained in the same framework.

Deciphering the local Interstellar spectra of primary cosmic ray species with HelMod

Local interstellar spectra (LIS) of primary cosmic ray (CR) nuclei, such as helium, oxygen, and mostly primary carbon are derived for the rigidity range from 10 MV to ~200 TV using the most recent experimental results combined with the state-of-the-art models for CR propagation in the Galaxy and in the heliosphere. Two propagation packages, GALPROP and HelMod, are combined into a single framework that is used to reproduce direct measurements of CR species at different modulation levels, and at both polarities of the solar magnetic field. The developed iterative maximum-likelihood method uses GALPROP-predicted LIS as input to HelMod, which provides the modulated spectra for specific time periods of the selected experiments for model-data comparison. The interstellar and heliospheric propagation parameters derived in this study are consistent with our prior analyses using the same methodology for propagation of CR protons, helium, antiprotons, and electrons. The resulting LIS accommodate a variety of measurements made in the local interstellar space (Voyager 1) and deep inside the heliosphere at low (ACE/CRIS, HEAO-3) and high energies (PAMELA, AMS-02).

Cosmic Rays Propagation with HelMod: Difference between forward-in-time and backward-in-time approaches

The cosmic rays modulation inside the heliosphere is well described by a transport equation introduced by Parker in 1965. To solve this equation several approaches were followed in the past. Recently the Monte Carlo approach becomes widely used in force of his advantages with respect to other numerical methods. In the Monte Carlo approach, the transport equation is associated to a fully equivalent set of Stochastic Differential Equations. This set is used to describe the stochastic path of a quasi-particle from a source, e.g., the interstellar medium, to a specific target, e.g., a detector at Earth. In this work, we present both the Forward-in-Time and Backward-in-Time Monte Carlo solutions. We present an implementation of both algorithms in the framework of HelMod Code showing that the difference between the two approach is below 5\% that can be quoted as the systematic uncertain of the Method itself.

Solar Modulation along last solar minimum

Universita di Milano Bicocca, I-20126 Milano, Italy * Corresponding Author: stefano.dellatorre@mib.infn.it The effects of cosmic rays modulation on proton spectrum was studied using the HelMod - 2-D Monte Carlo code, that includes a general description of the diffusion tensor, and polar magnetic-field. The Numerical Approach used in this work is based on a set of Stochastic Differential Equations fully equivalent to the well know Parker Equation for the transport of Cosmic Rays. The model description was updated using Proton spectras measured by PAMELA during the last solar minimum. Keywords: Cosmic rays; Solar Modulation.

Cosmic Rays in the Earth Magnetosphere: the importance of the External Field models in trajectory reconstruction with AMS-02 data

We developed a backtracing code for Cosmic Rays trajectory reconstruction in the Earth Magnetosphere with last models of Internal (IGRF-11) and External (Tsyganenko 1996 and 2005) field components. Particles can be reconstructed, in case of allowed trajectory, as Primary Cosmic Rays if they reach the outer boundary (magnetopause) or, in case of forbidden trajectory, as Secondary particles if they go back to the inner boundary. During the last solar active period (2011 and 2012) we compared backtracing results on AMS-02 proton and electron data with and without external field model. Using TS05, specifically designed for storm events, we confirmed the well known East-West effect. Moreover we clearly found the day night effect related to the asymmetric shape of the Magnetosphere if considering the External Field, in comparison with the Internal Field only.

Transport of cosmic rays in magnetosphere and heliosphere: GeoMag and HelMod webmodels

1 INFN Milano BicoccaPiazza della Scienza 3, 20126 Milano, Italy, 2 Institute of experimental Physics, K osice Slovakia, 3 CINECA-Sede di Milano, Via R. Sanzio 4, 20090 Segrate (MI), Italy, 4 University of Milano BicoccaPiazza della Scienza 3, 20126 Milano, Italy, 5 University of Insubria Como, Italy, 6 CERN Geneve, Switzerland, *E-mail: massimo.gervasi@mib.infn.it www.mib.infn.it; www.unimib.it