D. Rozza

ENERGY LOSS FOR ELECTRONS IN THE HELIOSPHERE AND LOCAL INTERSTELLAR SPECTRUM FOR SOLAR MODULATION

Galactic Cosmic Rays (GCR) entering the Heliosphere are affected by the solar modulation, which is a combination of diffusion, convection, magnetic drift, and adiabatic energy losses usually seen as a decrease of the flux at low energies (less than 10 GeV). We improved a quasi time-dependent 2D Stochastic Simulation code describing such effects. We focused our attention on the electron modulation, adding energy losses mechanisms in the Heliosphere that can be neglected for protons and ions: inverse Compton, ionization, synchrotron, and bremsstrahlung. These effects have been evaluated in the region affected by the solar magnetic field, up to 100 AU, where the environment conditions are not constant, especially the magnetic field intensity, and the photon density. In our calculation the inverse compton energy losses are dominant, but they contribute only a few percent in comparison with the adiabatic losses. We also compared the Local Interstellar Spectrum (LIS) of primary electrons with experimental data collected in the past years at energies 20 GeV. We found that, inside one standard deviation, LIS fits the data and can be used in a Monte carlo code reproducing CR propagation in the Heliosphere.

Latitudinal Dependence of Cosmic Rays Modulation at 1 AU and Interplanetary-Magnetic-Field Polar Correction

The cosmic rays differential intensity inside the heliosphere, for energy below 30 GeV/nuc, depends on solar activity and interplanetary magnetic field polarity. This variation, termed solar modulation, is described using a 2D (radius and colatitude) Monte Carlo approach for solving the Parker transport equation that includes diffusion, convection, magnetic drift, and adiabatic energy loss. Since the whole transport is strongly related to the interplanetary magnetic field (IMF) structure, a better understanding of his description is needed in order to reproduce the cosmic rays intensity at the Earth, as well as outside the ecliptic plane. In this work an interplanetary magnetic field model including the standard description on ecliptic region and a polar correction is presented. This treatment of the IMF, implemented in the HelMod Monte Carlo code (version 2.0), was used to determine the effects on the differential intensity of Proton at 1 AU and allowed one to investigate how latitudinal gradients of proton intensities, observed in the inner heliosphere with the Ulysses spacecraft during 1995, can be affected by the modification of the IMF in the polar regions.

Possible Contribution to Electron and Positron Fluxes from Pulsars and their Nebulae

The AMS-02 experiment confirms the excess of positrons in cosmic rays (CRs) for energy above 10 GeV with respect to the secondary production of positrons in the interstellar medium. This is interpreted as evidence of the existence of a primary source of these particles. Possible candidates are dark matter or astrophysical sources. In this work we discuss the possible contribution due to pulsars and their nebulae. Our key assumption is that the primary spectrum of electrons and positrons at the source is the same of the well known photon spectrum observed from gamma-rays telescopes. Using a diffusion model in the Galaxy we propagate the source spectra up to the Solar System. We compare our results with the recent experiments and with the LIS model.

Vela-X as main contributor to the electron and positron spectra for energy above 100 GeV

The precise measurements of the electron plus positron spectra, in the energy range from 0.5 GeV up to 1 TeV, were published by the AMS-02 collaboration. We focus the attention above 10 GeV where the solar modulation effects are negligible. The differences between these data and the “classical” Local Interstellar Spectra, obtained using optimized GALPROP parameters, show an extra contribution suggesting an equal amount for both electrons and positrons. Thus, they would be generated by a pair production process from the same source. We studied the contribution from Pulsar Wind Nebulae starting from the photon spectrum (due to synchrotron and inverse Compton processes) detected by gamma-ray telescopes. A diffusion model is applied from the source up to the Solar System and the propagated spectra are compared with the AMS-02 data. Above 100 GeV, Vela-X is the main candidate to contribute to the observed excess, while, below 100 GeV, more aged pulsars like Monogem give a higher contribution. An estimation on the degree of anisotropy from these sources is also presented.

HELIOSPHERE DIMENSION AND COSMIC RAY MODULATION

The differential intensities of Cosmic Rays at Earth were calculated using a 2D stochastic Montecarlo diffusion code and compared with observation data. We evaluated the effect of stretched and compressed heliospheres on the Cosmic Ray intensities at the Earth. This was studied introducing a dependence of the diffusion parameter on the heliospherical size. Then, we found that the optimum value of the heliospherical radius better accounting for experimental data. We also found that the obtained values depends on solar activity. Our results are compatible with Voyager observations and with models of heliospherical size modulation.

Inside out: unveiling 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 Heliosphere. Two propagation packages, GALPROP and HelMod, are combined to provide a single framework that is run to reproduce direct measurements of cosmic ray (CR) species at different modulation levels and at both polarities of the solar magnetic field. To do so in a self-consistent way, an iterative procedure was developed, where the GALPROP LIS output is fed into HelMod that provides modulated spectra for specific time periods of selected experiments to compare with the data. The parameters were tuned with a maximum likelihood procedure using an extensive data set of proton spectra from 1997-2015. The proposed LIS accommodate both the low energy interstellar CR spectra measured by Voyager 1 and the high energy observations by BESS, PAMELA, AMS-01, and AMS-02 made from the balloons and near-Earth payloads. The proton LIS also accounts for Ulysses counting rate features measured out of the ecliptic plane. The obtained solution is in a good agreement with proton, helium, and antiproton data by AMS-02, BESS, and PAMELA in the whole energy range.

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.

Trajectory reconstruction in the Earth Magnetosphere using TS05 model and evaluation of geomagnetic cutoff in AMS-02 data

D. Grandi∗1, B. Bertucci45, M.J. Boschini13, M. Crispoltoni45, S. Della Torre1, F. Donnini45, M. Duranti45, D. D’Urso56, E. Fiandrini45, V. Formato5, G. La Vacca1, M. Gervasi12, M. Graziani45, F. Nozzoli56, S. Pensotti12, C. Pizzolotto 56, P.G. Rancoita1, D. Rozza12, M. Tacconi1, V. Vitale 56, M. Zannoni12 1 INFN, Sezione di Milano Bicocca, I20126 Milano, Italy 2 Università di Milano Bicocca, I-20126 Milano, Italy 3 CINECA, I20090 Segrate (MI) ITALY 4 University of Perugia, I06124 Perugia, Italy 5 INFN Perugia, I06124 Perugia, Italy 6 ASDC, ASI Science Data Center, I-00133 Roma, Italy E-mail: davide.grandi@mib.infn.it

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.