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  • Open Access

Cosmic-ray interactions with the Sun using the fluka code

M. N. Mazziotta, P. De La Torre Luque, L. Di Venere, A. Fassò, A. Ferrari, F. Loparco, P. R. Sala, and D. Serini
Phys. Rev. D 101, 083011 – Published 8 April 2020

Abstract

The interactions of cosmic rays with the solar atmosphere produce secondary particles which can reach the Earth. In this work, we present a comprehensive calculation of the yields of secondary particles such as gamma-rays, electrons, positrons, neutrons, and neutrinos performed with the fluka code. We also estimate the intensity at the Sun and the fluxes at the Earth of these secondary particles by folding their yields with the intensities of cosmic rays impinging on the solar surface. The results are sensitive to the assumptions on the magnetic field nearby the Sun and to the cosmic-ray transport in the magnetic field in the inner Solar System.

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  • Received 29 January 2020
  • Accepted 2 March 2020
  • Corrected 27 October 2020

DOI:https://doi.org/10.1103/PhysRevD.101.083011

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Corrections

27 October 2020

Correction: The top left panel of the previously published Figure 12 contained a plotting error and has been replaced.

Authors & Affiliations

M. N. Mazziotta1,*, P. De La Torre Luque1,2, L. Di Venere3, A. Fassò4, A. Ferrari5, F. Loparco1,2, P. R. Sala6, and D. Serini1,2

  • 1Istituto Nazionale di Fisica Nucleare, Sezione di Bari, via Orabona 4, I-70126 Bari, Italy
  • 2Dipartimento di Fisica “M. Merlin” dell’Università e del Politecnico di Bari, via Amendola 173, I-70126 Bari, Italy
  • 3Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari, Italy
  • 413 Passage Hamo, CH-1262 EYSINS, Switzerland
  • 5CERN, the European Organization for Nuclear Research, Esplanade des Particules 1, 1211 Geneva, Switzerland
  • 6Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria,16, 20133 Milano, Italy

  • *mazziotta@ba.infn.it;

Article Text

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Vol. 101, Iss. 8 — 15 April 2020

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Images

  • Figure 1
    Figure 1

    Mass fractions in the gs98 model as a function of the distance from the center of the Sun in units of R. Only atoms with mass fractions above 104 at the surface are shown. The data are taken from Ref. [27].

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  • Figure 2
    Figure 2

    Density (top panel), pressure (middle panel), and temperature (bottom panel) as a function of the radial distance from the Sun center in units of R. The black dots indicate the model S [28]; the blue line is the model gs98 [27]; the red line is the present extrapolation. The inset shows a zoom near the Sun radius.

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  • Figure 3
    Figure 3

    Magnetic field intensity as a function of the Carrington longitude and latitude angles at r=R for the CR 2111.

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  • Figure 4
    Figure 4

    Time evolution of B0 (black line), of the solar wind speed vSW (red line), and of the tilt angle α (blue line). The upper horizontal timescale shows the CR numbers. The values of the tilt angle α and its polarity are taken from the Wilcox Solar Observatory public website [41]. The magnetic field at the Earth B0 and the velocity of the solar wind vSW are taken from the observations of the ACE satellite extracted from the NASA/GSFC’s OMNI dataset [42, 43].

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  • Figure 5
    Figure 5

    Gamma-ray yields from protons (top panel), helium nuclei (middle panel), and electrons (bottom panel) as a function of the primary kinetic energy (or kinetic energy per nucleon in the case of helium primaries) (x axis) and of the gamma-ray energy (y axis). The color scale (z axis) indicates the yields.

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  • Figure 6
    Figure 6

    Gamma-ray yields as a function of the gamma-ray energy for three different primary proton energies: 1 TeV (blue line), 100 GeV (red line), 10 GeV (black line).

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  • Figure 7
    Figure 7

    Proton [49], helium [50, 51], and electron intensities [52, 56] as functions of the kinetic energy (kinetic energy per nucleon in the case of helium). The full circles correspond to the experimental data measured by AMS-02 at Earth during CR 2111; the solid lines indicate the results of the fits; the open circles with dashed lines indicate the intensities near the Sun at RSS=2.5×R, evaluated by scaling the intensities at Earth with the survival probabilities obtained from HelioProp [44].

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  • Figure 8
    Figure 8

    Gamma-ray fluxes at the Earth for four different CRs. Top left panel: CR 2111; top right panel: CR 2125 and CR 2138; bottom right panel: CR 2152. Black line: total emission; blue line: gamma rays from protons; red line: gamma rays from He4 nuclei; magenta line: gamma rays from electrons. Light blue shadow region: Seckel et al. model [5]; gray points: 1.5 years Fermi-LAT data [4]; dark red points: 9 years Fermi-LAT data [57].

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  • Figure 9
    Figure 9

    Gamma-ray flux at the Earth evaluated as the average of the fluxes of the four different Carrington rotations shown in Fig. 8. Color lines and data points have the same meanings as those in Fig. 8.

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  • Figure 10
    Figure 10

    Left panels: gamma-ray fluxes at the Earth as a function of the angle of sight. Right panels: spatial map of the solar gamma-ray emission built with the healpix pixelization with Nside=2048. Two different energy bins are considered: [0.1, 0.133] (top row) and [1,1.33] GeV (bottom row).

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  • Figure 11
    Figure 11

    Average intensity at the Sun of νμ+ν¯μ (black line), νe+ν¯e (red line), neutrons (blue line), e++e (magenta line) for CRs 2111, 2125, 2138, and 2152.

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  • Figure 12
    Figure 12

    Gamma-ray fluxes at the Earth for the four different magnetic field configurations. Top left panel: no B field; top right panel: B reduced by a factor 10 with respect to the nominal PFSS configuration; bottom left panel: PFSS configuration; bottom right panel: enhanced magnetic field according to the bifrost model. Color lines and data points have the same meanings as in Fig. 8.

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  • Figure 13
    Figure 13

    Gamma-ray and neutrino fluxes at the Earth calculated for the Carrington rotation 2111 with two models for the Sun magnetic field: PFSS (continuous line) and enhanced model according to the bifrost prediction (dashed line). Black line: gamma-ray; red line: νμ+ν¯μ; blue line: νe+ν¯e. The prediction of neutrinos by Ref. [9] is also shown. In addition, we include results from gamma-ray observations from Fermi-LAT [4, 57], gamma-ray HAWC’s 95% limit [65], and neutrinos IceCube’s 90% limit [66].

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