Antiprotons of interstellar origin at balloon altitudes: Flux simulations U. B. Jayanthi, K. C. Talavera Instituto Nacional de Pesquisas Espaciais (INPE),

Antiprotons of interstellar origin Antiprotons of interstellar origin at balloon altitudes: at balloon altitudes:

Flux simulationsFlux simulations

U. B. Jayanthi , K. C. TalaveraU. B. Jayanthi , K. C. Talavera Instituto Nacional de Pesquisas Espaciais (INPE), Brasil.Instituto Nacional de Pesquisas Espaciais (INPE), Brasil.

A. A. GusevA. A. Gusev Space Research Institute (IKIRAS), Space Research Institute (IKIRAS), MoscowMoscow, , RussiaRussia..

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

INTRODUCTIONINTRODUCTION The interest of antimatter component in the cosmic radiation The interest of antimatter component in the cosmic radiation

ranges from the basics of cosmology .ranges from the basics of cosmology . The CR antiprotons are expected as secondary products of the The CR antiprotons are expected as secondary products of the

primary CR interactions with the interstellar medium that is primary CR interactions with the interstellar medium that is supported by observations in experiments (Asaoka, et al., 2002; supported by observations in experiments (Asaoka, et al., 2002; Boezio, et al., 2000; Grimani, et al., 2002; Wang, et al., 2002). Boezio, et al., 2000; Grimani, et al., 2002; Wang, et al., 2002).

Continuing simulations are made considering the solar Continuing simulations are made considering the solar modulation as initiated by Perko (1987) to explain the modulation as initiated by Perko (1987) to explain the observational result at ~0.2 GeV of Buffington et al. (1981) which observational result at ~0.2 GeV of Buffington et al. (1981) which indicated a possible excess at energies <1indicated a possible excess at energies <1GeVGeV. .

The recent experimental data from different balloon The recent experimental data from different balloon experiments at different solar activity phases, provided a experiments at different solar activity phases, provided a very good opportunity to understand the modulation very good opportunity to understand the modulation process as well as the similarity in the proton and process as well as the similarity in the proton and antiproton transport, inspite of fluctuations in data and the antiproton transport, inspite of fluctuations in data and the model approximations.model approximations.

2 Interstellar antiproton fluxes2 Interstellar antiproton fluxes In our simulation the antiproton LIS In our simulation the antiproton LIS FFpp ( (EEpp) was obtained ) was obtained

through the Leaky-box model as a solution of the integro-through the Leaky-box model as a solution of the integro-differential equation (Ginzburg, 1964): 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 (λesc) and interaction (λinel), and the energy losses <dE/dx> in the interstellar matter.

,

vogH,He,O

vogH,He,O

esc inel

,

3

b) (1)

a)( )

( ) ( ) ( ) ( ) (

( ) ( , ) ( ) , (

( ) ( ,

p th

jA

j j E

jA

j j

p p p pp p p pp p

p

jp p p n p p pp

p

jp p pp

p

p

F E F F d dEF E E Q E Q E

dE dx

dnQ E N E E F E dE

A dE

dnQ E N E E

A dE

2 3

2

0

c)) ( ) . (p p pF E dE

2.1 Antiproton production spectrum2.1 Antiproton production spectrum

The antiproton production spectrumThe antiproton production spectrum i.e. the source functioni.e. the source function Q Q 22 p p~~ + + Q Q 33 p p~ in Eq.(1) is a sum of~ in Eq.(1) is a sum of thethe contributions from interactions of contributions from interactions of the protons and antiprotons with the interstellar H, He and O the protons and antiprotons with the interstellar H, He and O nuclei in the interstellar matter. The corresponding densities nnuclei in the interstellar matter. The corresponding densities n jj are are 1, 0.1, 8·10-4 1, 0.1, 8·10-4 cm-3cm-3 (Simon, et al., 1998). (Simon, et al., 1998).

The production of antiprotons and antineutrons was simulated The production of antiprotons and antineutrons was simulated with a Multi Stage Dynamical Model (MSDM) Monte Carlo code with a Multi Stage Dynamical Model (MSDM) Monte Carlo code (Dementyev and Sobolevsky, 1999). The code simulates yield from (Dementyev and Sobolevsky, 1999). The code simulates yield from a nuclear reaction (a nuclear reaction (x,Ax,A) of an incident particle ) of an incident particle xx with a target with a target nucleus nucleus A.A. The projectile can be a hadron ( The projectile can be a hadron (nn, , nn ~ , ~ , p, pp, p~ ) or a ~ ) or a meson (meson (+,+,-,-, 0, 0, KK+, +, KK-, -, K K 00 ) with kinetic energies from 10 ) with kinetic energies from 10 MeVMeV up to 1 up to 1 TeVTeV. The target can be any nucleus with the atomic mass . The target can be any nucleus with the atomic mass AA≥1. The code simulates all the stages of hadron-nucleus and ≥1. The code simulates all the stages of hadron-nucleus and nucleus-nucleus interactions inside the target using the exclusive nucleus-nucleus interactions inside the target using the exclusive approach on the basis of models described by Botvina et al. approach on the basis of models described by Botvina et al. (1997). (1997).

The code produces energy spectra and angular distributions of the The code produces energy spectra and angular distributions of the reaction products together with total and inelastic cross sections reaction products together with total and inelastic cross sections and multiplicities.and multiplicities.

Fig. 1: Antiproton and antineutron production cross section for Fig. 1: Antiproton and antineutron production cross section for pp++HH reaction. Symbols mark the MSDM results; thick solid lines represents reaction. Symbols mark the MSDM results; thick solid lines represents

the Tan and Ng (1983) approximation.the Tan and Ng (1983) approximation.

Fig. 2. Antiproton and antineutron production cross section Fig. 2. Antiproton and antineutron production cross section

of of p p ++HH reaction simulated with the MSDM code reaction simulated with the MSDM code..

2.2 Antiproton LIS2.2 Antiproton LIS For our solution, the rigidity (For our solution, the rigidity (RR) dependent escape path ) dependent escape path

length for antiprotons in the Galaxylength for antiprotons in the Galaxy

is from Jones et al. (2000), the interaction length is from Jones et al. (2000), the interaction length λλinel of inel of antiprotons including annihilationantiprotons including annihilation is simulated with the is simulated with the MSDM and the stopping power MSDM and the stopping power <dE/dx<dE/dx> is calculated > is calculated utilizing standard procedureutilizing standard procedure (e.g. (e.g. PSTAR-NISTPSTAR-NIST).).The Eq.1 is solved through an iteration procedure using The Eq.1 is solved through an iteration procedure using the “Mathematica”the “Mathematica” package. The solution readily package. The solution readily converges in the third iteration.converges in the third iteration.

0.54

esc esc11.8 for 4.9 and 11.8 / 4.9 for 4.9R GV R R GV

The MSDM cross section provides about two times larger tertiary outputThe MSDM cross section provides about two times larger tertiary output Q Q3 3 pp~ in the range of 0.3-3 ~ in the range of 0.3-3 GeVGeV as compared to the uniform distribution. In as compared to the uniform distribution. In the energy range of 0.04-2 the energy range of 0.04-2 GeV GeV the LIS obtained with MSDM slightly the LIS obtained with MSDM slightly exceeds that obtained with the Tan and Ng (1983) approximation and the exceeds that obtained with the Tan and Ng (1983) approximation and the maximum deviations are ≤ 40% at maximum deviations are ≤ 40% at EEp p =0.2 =0.2 GeVGeV

Fig. 3. The interstellar secondary antiproton production spectra Fig. 3. The interstellar secondary antiproton production spectra simulated using the MSDM and Tan&Ng (1983) cross sections.simulated using the MSDM and Tan&Ng (1983) cross sections.

2.3 Solar modulation of the LIS2.3 Solar modulation of the LIS

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

1AU 1AU HB HB2 2

1AU HB

1AU 1AU1AU

1AU HB

HB

2 2 2 2 2 21AU 1AU 0 HB HB 0

( ) ( )

ln for

for

( 1 )

3

, .

c c cc c

c

F E F E

P P

P EE P E P P

P E

E E P P

R AUV

A

E P m E P m

FFHB,HB, E EHB,HB, P PHB , andHB , and F F1AU,1AU, E E1AU, 1AU, PP1AU1AU, , are the antiproton flux, are the antiproton flux, total energy in total energy in GeVGeV, momentum in , momentum in GVGV at heliospheric boundary (HB) at heliospheric boundary (HB) and at the Earth’s orbit (1and at the Earth’s orbit (1AUAU) respectively,) respectively, m m00 is the proton rest is the proton rest mass inmass in GeV GeV. . VV is the average solar wind speed is the average solar wind speed in 103 km/hr. in 103 km/hr. Physical sense of the solution implies a conservation of the Physical sense of the solution implies a conservation of the distribution function distribution function F/PF/P22 for particle energy decreases from for particle energy decreases from EEHB HB down to down to EE1AU in travel from heliosphere 1AU in travel from heliosphere RRHB to the Earth at 1HB to the Earth at 1AUAU..

The heliospheric conditions are described by the “force field” The heliospheric conditions are described by the “force field” parameter Φ determined by the solar wind speed parameter Φ determined by the solar wind speed V V and the and the heliospheric boundary distance heliospheric boundary distance RRHB. In ourHB. In our simulation we simulation we used used AA=17, =17, PPc=1.015 c=1.015 GVGV (Perko, 1987) who showed that for (Perko, 1987) who showed that for the energies ≥0.02 the energies ≥0.02 GeVGeV the Eq.2 approximates the exact the Eq.2 approximates the exact solution of the equation of Gleeson and Axford (1968) for the solution of the equation of Gleeson and Axford (1968) for the proton spectrum proton spectrum EEHBHB-γ -γ (where (where =P=PHBHB/E/EHB is the proton HB is the proton speed) and also consistent with the solar flare proton speed) and also consistent with the solar flare proton observations.observations.

The Φ magnitude is determined from the best fit The Φ magnitude is determined from the best fit approximation with the Eq.2 of the observed proton spectrum approximation with the Eq.2 of the observed proton spectrum FF1AU assuming the interstellar spectrum as 1AU assuming the interstellar spectrum as FFHB (HB (EEHB) HB) =16470=16470EEHB-2.76 protons/HB-2.76 protons/m s sr GeVm s sr GeV.. The fits furnish The fits furnish Φmax=0.964 Φmax=0.964 GeVGeV and Φmin =0.368 and Φmin =0.368 GeVGeV corresponding to corresponding to solar maximum and minimum epochs. solar maximum and minimum epochs.

Fig. 4: Simulated LIS and the modulated spectra compared Fig. 4: Simulated LIS and the modulated spectra compared with experimental observationswith experimental observations..

The results of our simulated spectrumThe results of our simulated spectrum

In fig 4 .Also antiproton fluxes obtained in In fig 4 .Also antiproton fluxes obtained in different experiments conducted at different solar different experiments conducted at different solar minimum and maximum periods. The increases in minimum and maximum periods. The increases in the low energy fluxes are provided by the higher the low energy fluxes are provided by the higher fluxes of more energetic particles enriching the fluxes of more energetic particles enriching the <1 <1 GeVGeV region due to adiabatic energy losses. region due to adiabatic energy losses. The steeper the low energy branch of the LIS The steeper the low energy branch of the LIS spectrum the more pronounced is the above spectrum the more pronounced is the above mentioned increases (Boella et al., 1998). The mentioned increases (Boella et al., 1998). The results of the simulations provided flux values of results of the simulations provided flux values of ~ 4x10-3 to 10-2 and ~ 10-2 to 1.7 x 10-2 ~ 4x10-3 to 10-2 and ~ 10-2 to 1.7 x 10-2 antiprotons/m2 s sr antiprotons/m2 s sr GeVGeV at energies of 0.2 and 1 at energies of 0.2 and 1 GeVGeV respectively, corresponding to the solar respectively, corresponding to the solar maximum and minimum epochs. The curve for maximum and minimum epochs. The curve for Φ=1.5 is the lower limit for all the experimental Φ=1.5 is the lower limit for all the experimental data. It may correspond for example to data. It may correspond for example to VV = 103 = 103 km/hourkm/hour and and RRHB=HB=70 70 AUAU. .

4 Conclusions4 Conclusions A simulation of the expected fluxes of interstellar A simulation of the expected fluxes of interstellar

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