Antiprotons of interstellar origin at balloon altitudes: Flux simulations

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Antiprotons of interstellar origin at balloon
altitudes Flux simulations

• U. B. Jayanthi , K. C. Talavera
• Instituto Nacional de Pesquisas Espaciais (INPE),
  Brasil.
• A. A. Gusev
• Space Research Institute (IKIRAS), Moscow,
  Russia.

21st European Cosmic Ray Symposium, Koice,
Slovakia, 9-12 September 2008
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INTRODUCTION

• The interest of antimatter component in the
  cosmic radiation ranges from the basics of
  cosmology .
• The CR antiprotons are expected as secondary
  products of the primary CR interactions with the
  interstellar medium that is supported by
  observations in experiments (Asaoka, et al.,
  2002 Boezio, et al., 2000 Grimani, et al.,
  2002 Wang, et al., 2002).
• Continuing simulations are made considering the
  solar modulation as initiated by Perko (1987) to
  explain the observational result at 0.2 GeV of
  Buffington et al. (1981) which indicated a
  possible excess at energies lt1GeV.
• The recent experimental data from different
  balloon experiments at different solar activity
  phases, provided a very good opportunity to
  understand the modulation process as well as the
  similarity in the proton and antiproton
  transport, inspite of fluctuations in data and
  the model approximations.

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2 Interstellar antiproton fluxes

• In our simulation the antiproton LIS F?p (E?p)
  was obtained through the Leaky-box model as a
  solution of the integro-differential equation
  (Ginzburg, 1964)

This considers the production of the secondary
antiprotons Q2 p by CR proton flux Fp(Ep) and
the subsequent tertiary antiprotons Q3 p , and
includes the flux decreases due to escape (?esc)
and interaction (?inel), and the energy losses
ltdE/dxgt in the interstellar matter.
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2.1 Antiproton production spectrum

• The antiproton production spectrum i.e. the
  source function Q 2 p Q 3 p in Eq.(1) is a
  sum of the contributions from interactions of the
  protons and antiprotons with the interstellar H,
  He and O nuclei in the interstellar matter. The
  corresponding densities nj are 1, 0.1, 810-4
  cm-3 (Simon, et al., 1998).
• The production of antiprotons and antineutrons
  was simulated with a Multi Stage Dynamical Model
  (MSDM) Monte Carlo code (Dementyev and
  Sobolevsky, 1999). The code simulates yield from
  a nuclear reaction (x,A) of an incident particle
  x with a target nucleus A. The projectile can be
  a hadron (n, n , p, p ) or a meson (?,?-,?
  0, K, K-, K 0 ) with kinetic energies from 10
  MeV up to 1 TeV. The target can be any nucleus
  with the atomic mass A1. The code simulates all
  the stages of hadron-nucleus and nucleus-nucleus
  interactions inside the target using the
  exclusive approach on the basis of models
  described by Botvina et al. (1997).
• The code produces energy spectra and angular
  distributions of the reaction products together
  with total and inelastic cross sections and
  multiplicities.

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Fig. 1 Antiproton and antineutron production
cross section for pH reaction. Symbols mark the
MSDM results thick solid lines represents the
Tan and Ng (1983) approximation.
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Fig. 2. Antiproton and antineutron production
cross section of ?p H reaction simulated with
the MSDM code.
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2.2 Antiproton LIS

• For our solution, the rigidity (R) dependent
  escape path length for antiprotons in the Galaxy
• is from Jones et al. (2000), the interaction
  length ?inel of antiprotons including
  annihilation is simulated with the MSDM and the
  stopping power ltdE/dxgt is calculated utilizing
  standard procedure (e.g. PSTAR-NIST).
• The Eq.1 is solved through an iteration
  procedure using the Mathematica package. The
  solution readily converges in the third iteration.

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The MSDM cross section provides about two times
larger tertiary output Q3 p in the range of
0.3-3 GeV as compared to the uniform
distribution. In the energy range of 0.04-2 GeV
the LIS obtained with MSDM slightly exceeds that
obtained with the Tan and Ng (1983) approximation
and the maximum deviations are 40 at E?p
0.2 GeV
Fig. 3. The interstellar secondary antiproton
production spectra simulated using the MSDM and
TanNg (1983) cross sections.
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2.3 Solar modulation of the LIS

• The LIS modulation in the heliosphere is
  considered on the basis of transport equation for
  the spherically-symmetric case (Gleeson and
  Axford, 1968 Fisk et al., 1973). The force
  field approximation inherently neglects the
  heliospheric gradient and curvature drifts but
  considers the diffusion, convection and adiabatic
  deceleration

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• FHB, EHB, PHB , and F1AU, E1AU, P1AU, are the
  antiproton flux, total energy in GeV, momentum in
  GV at heliospheric boundary (HB) and at the
  Earths orbit (1AU) respectively, m0 is the
  proton rest mass in GeV. V is the average solar
  wind speed in 103 km/hr. Physical sense of the
  solution implies a conservation of the
  distribution function F/P2 for particle energy
  decreases from EHB down to E1AU in travel from
  heliosphere RHB to the Earth at 1AU.
• The heliospheric conditions are described by the
  force field parameter F determined by the solar
  wind speed V and the heliospheric boundary
  distance RHB. In our simulation we used A17,
  Pc1.015 GV (Perko, 1987) who showed that for the
  energies 0.02 GeV the Eq.2 approximates the
  exact solution of the equation of Gleeson and
  Axford (1968) for the proton spectrum ??EHB-?
  (where ?PHB/EHB is the proton speed) and also
  consistent with the solar flare proton
  observations.
• The F magnitude is determined from the best fit
  approximation with the Eq.2 of the observed
  proton spectrum F1AU assuming the interstellar
  spectrum as FHB (EHB) 16470?EHB-2.76 protons/m s
  sr GeV. The fits furnish Fmax0.964 GeV and Fmin
  0.368 GeV corresponding to solar maximum and
  minimum epochs.

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Fig. 4 Simulated LIS and the modulated spectra
compared with experimental observations.
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The results of our simulated spectrum

• In fig 4 .Also antiproton fluxes obtained in
  different experiments conducted at different
  solar minimum and maximum periods. The increases
  in the low energy fluxes are provided by the
  higher fluxes of more energetic particles
  enriching the lt1 GeV region due to adiabatic
  energy losses. The steeper the low energy branch
  of the LIS spectrum the more pronounced is the
  above mentioned increases (Boella et al., 1998).
  The results of the simulations provided flux
  values of 4x10-3 to 10-2 and 10-2 to 1.7 x
  10-2 antiprotons/m2 s sr GeV at energies of 0.2
  and 1 GeV respectively, corresponding to the
  solar maximum and minimum epochs. The curve for
  F1.5 is the lower limit for all the experimental
  data. It may correspond for example to V 103
  km/hour and RHB70 AU.

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4 Conclusions

• A simulation of the expected fluxes of
  interstellar origin incorporating solar
  modulation is attempted to explain the recent
  measurements of antiprotons at solar maximum and
  minimum in balloon experiments. Particularly for
  the possible excess of the lt 1GeV interstellar
  antiproton observations, initially the simulation
  considered the tertiary and antineutron decay
  antiprotons of the LIS source. The interaction
  cross sections by the MSDM Monte Carlo code
  provided a slightly larger antiproton flux in the
  energy range of 0.1-1 GeV compared to the Tan and
  Ng (1983) approximation. Then the force field
  solution for the solar modulation with rigidity
  dependence in compliance with the LIS and the 1AU
  spectra showed satisfactory agreement between the
  simulations and the balloon results at the solar
  maximum and minimum periods..