1. Primary Cosmic Ray Spectra in the Planet Atmospheres Marusja Buchvarova 1, Peter Velinov 2 (1) Space Research Institute – Bulgarian Academy of Sciences, BULGARIA (2) Solar-Terrestrial Influences Laboratory (STIL), Bulgarian Academy of Sciences, BULGARIA E-mail: marusjab@yahoo.com

2.  INTRODUCTION  MODELING COSMIC RAY DIFFERENTIAL SPECTRUM  MODELING COSMIC RAY INTEGRAL SPECTRUM IN OUTER PLANETS  COMPARISON OF THE MODELING COSMIC RAY SPECTRUM WITH THEORETICAL MODELS: THE FORCE FIELD APPROXIMATION 2D SOLUTIONS OF COSMIC RAY TRANSPORT EQUATION  APPLICATION FOR CALCULATION OF THE ELECTRON PRODUCTION RATE q(h) PROFILES DUE TO PARTICLES WITH ENERGY INTERVALS OF GALACTIC CR AND ANOMALOUS CR COMPONENT OUTLINE OF THE TALK:

3. PARTICLE POPULATIONS ARE DIVERSE: 1) Galactic CR (GCR), with energy range from ~ 10s MeV to 10 6 GeV, which are accelerated in the space of our Galaxy. 2) Metagalactic CR with energies 10 6 GeV - 10 12 GeV, accelerated in the Metagalaxy. 3) Solar CR, with energy range from ~ 10s of MeV to 100s of MeV, accelerated on the Sun 4) Anomalous CR, with energy from 1 MeV ~ 100 MeV, accelerated in the interplanetary space. CR are important for the Sun-Earth connections, because they possess maximal penetration capability in comparison with the other radiations. CR maintain ionization in ionosphere, atmosphere, hydrosphere, cryosphere and lithosphere of the Earth and planets. INTRODUCTION

4. The intensity of the GCR with E< 20 GeV shows an inverse relationship to the 11 – years solar cycle. Galactic cosmic ray particles - anti-correlated with SA Solar Activity Solar particles – correlated with SA INTRODUCTION This picture is from F. Nichitiu, CANADA

5. The expression for the differential spectrum (energy range E from ~ 30 MeV to 100 GeV) of the protons and other groups of cosmic ray nuclei on account of the anomalous cosmic rays (energy range E from 1 MeV to about 30 MeV) is (Velinov, 2000; Buchvarova, 2006): Here the first term presents the galactic CR, and the last term takes into account anomalous CR (Cummings and Stone, 1987). The members with tanh are smoothing functions (Velinov, 2002). Here we take K p =25.298 GeV 2.75 /(s.m 2 ster.MeV) and  p = 2.75 for protons. The used parameters for the alpha particles are K  = 1.145 GeV 2.68 /(s.m 2 ster.MeV) and   =2.68. The normalization constants K p and K  are chosen to match the modulated data near to 100 GeV/ /nucl, where the modulation effect is negligible. The parameters α, β, x and y are related with modulation levels in corresponding energy intervals. The dimensionless parameter = 100 is inversely proportional to the length of the smoothing interval between the two addends. The physical meaning of  (GeV) is the energy at which the differential spectrum of GCR crosses the differential spectrum of ACR (Buchvarova, 2006). The differential spectrum is given as the number of particles observed per (m 2 s.ster.MeV/n) [part/ m 2 s.ster.MeV/n]. The calculation of parameters α, β, x, y and  is performed by Levenberg-Marquardt algorithm (Press et al., 1991), applied to the special case of a least squares. The described programme is realized in algorithmic language C++. Experimental data (Ei, Di) for protons and helium nuclei was got from Hillas (1972) for 20 solar cycle. MODELING COSMIC RAY DIFFERENTIAL SPECTRUM

6. Fig.3.The modelled spectrum D(E) of CR protons for eleven levels of solar activity and measurements: period near to solar maximum - ■ IMAX92 and periods near to solar minimum – ●CAPRICE94 and ▲ AMS98. The results from the differential energy spectrum D(E) of primary protons and helium for solar minimum and maximum for the Earth. The modelled spectra are compared with the measurements for the period near to solar maximum - ■ IMAX92 (Menn et al., 2000) and periods near to solar minimum – ● CAPRICE94 (Boezio et al., 1999) and ▲ AMS98 (Alcaraz et al., 2000a, b). This data practically coincides with our results for these periods.

7. MODELING COSMIC RAY DIFFERENTIAL SPECTRUM Fig. 4. The modelled spectrum D(E) of CR helium nuclei for three levels of solar activity and measurements: period near to solar maximum - ■ IMAX92 and periods near to solar minimum – ● CAPRICE94 and ▲ AMS98. Curve 1 relates to solar maximum, 2 – to comparatively average level of the solar activity and 3 – to solar minimum.

8. COMPARISON OF THE MODELING COSMIC RAY SPECTRUM WITH THE FORCE FIELD APPROXIMATION AND 2D SOLUTIONS OF COSMIC RAY TRANSPORT EQUATION Under some simplifying assumption, CR transport equation can be reduced to Force Field approximation. The force field parameterization of cosmic ray nuclei at 1 AU is given as: D (E, Φ) is differential intensity of cosmic ray nuclei and D LIS (E+Φ) - LIS of cosmic ray nuclei (was taken from Burger et al., 2000 ). E is the kinetic energy (in MeV per nucleon) of cosmic nuclei with charge number Z and mass number A, Φ=(Ze/A) ϕ - modulation strength (in MeV), and Е 0 = 938 MeV is the proton’s rest mass energy. We calculate differential intensity of galactic protons and alpha particles from Eq.(2) at given values of the modulation potential ϕ. Received spectra are fitted to Eq. (1). On the base on the calculated coefficients from our model for the proton and alpha particles, D(E) is estimated for different values of modulation parameter ϕ. The results from the differential energy spectrum D(E) of primary protons for four values of modulation parameter:  = 400, 550, 700 and 1200 MV are shown in Fig.4. These results are given for helium nuclei In Fig. 5. The number ratio α/p = 0.05 in LIS (Usoskin et al., 2005) is used for alpha particles. COMPARISON WITH THE FORCE FIELD APPROXIMATION

9. Fig. 5. The differential spectra D(E) of GCR protons for modulation levels  = 400, 550, 700 and 1200 MV. Measurements with IMAX92 are in the vicinity of   700 MV, CAPRCE94 and AMS98 of   550 MV. Fig. 6. The differential spectra D(E) of GCR helium nuclei for modulation levels  = 400, 550, 700 and 1200 MV. Measurements with IMAX92 are in the vicinity of   700 MV and CAPRCE94 and AMS98 of   550 MV. Figs. 4 and 5 show that our empirical model (1) well agrees with the data from force field approximation (2) for the protons and alpha particles. The measurements with IMAX 92 are in the vicinity of   700 MV, while CAPRICE 94 and AMS 98 of   550 MV. On the fit the standard deviations for protons and alpha particles are in the range of 1.5%.

10. Comparison of modeling spectrum with two-dimensional model without drift of Potgieter and Moraal (Astroph.J., 1985) Fig.7. The modelled spectrum D(E) of CR protons for eleven levels of solar activity is compare with solutions (Potgieter, Moraal, Ap.J., 1985) of the cosmic ray transport equation without drift for nearly flat neutral sheet with parameters : (K ┴ ) 0 = 2x10 20 cm 2 s -1, r b = 50AU, (K II ) 0 = 2.28x10 22 cm 2 s -1 (near solar minimum) (K II ) 0 = 0.6 x10 22 cm 2 s -1 ) (near solar maximum )

11. r a, AU is planetary average distance of the planet from the Sun P EUV is parameter of decreasing of solar UV radiation, proportional to 1/ r a 2 P CR is parameter of CR increasing intensity because of solar modulation. For 1 AU, the energy flux with wave length below 100 nm is about 3.3 erg/cm 2.s Galactic CR energy flux is  2  10 -2 erg/cm 2.s The solar EUV radiation is weaker than the galactic cosmic ray intensity for Jupiter, Saturn, Uranus and Neptune. This comparison shows the importance of the galactic cosmic rays in the formation of outer planet ionospheres. We assume mean differential gradient of GCR in the interplanetary space as 3%/AU Values of planetary average distances r a from the Sun, parameter P EUV of decreasing of solar EUV radiation, and parameter P CR of increasing of galactic CR intensity

12. COSMIC RAY INTEGRAL SPECTRA Using the values of the parameters P GCR of increasing of galactic CR intensity for outer planets and the received values of coefficients from Eq.(1) for the Earth the integral spectra of the outer planets are obtained. At integration we use equation (3): D(E) - differential spectrum of galactic and anomalous CR. D(>E) - integral spectrum, expressed by the number of particles per unit solid angle, square centimetre, and second, with total energies at least E. The integration on E begins from the energy, corresponding to the geomagnetic cut-off rigidity in the point of measurements. (The low’energy part of the spectrum (below some tens of GeV) is dependent of the geographycal position). In our model integral spectra are computed only in first approximation. We assume mean differential gradient of GCR as 3%/AU for all rigidity, irrespectively of the distance in the heliosphere or solar activity level. The measurements give radial gradient ~1.5%/AU at solar minimum and 3%/AU at solar maximum in inner heliosphere.

13. Fig. 8. The modeled integral spectra D(>E) of CR protons for maximum and minimum levels of solar activity for Earth and Jupiter. The computations are compared with data: - Schopper (1967) for Earth, ▼ - Voyager 2 (5 July 1979 – near to solar maximum) for Jupiter and theoretical results of 2D stochastic model built from Bobik et al., (ECRS, 2007). It is seen from Fig. 8 that in Bobik model, the integral spectrum of the Earth almost tally with Jupiter’s integral spectrum at solar minimum. It is due to lower average values of integral radial gradient in this model. Actually at high K radial gradient has lower values in the inner heliosphere. (The radial intensity gradient has lower values in higher energy also). In Bobik model for positive solar period (A > 0) are used the following values (K II ) 0 = 2x10 22 cm 2 s -1, tilt angle ϑ = 30 0 and the ratio between the parallel and the perpendicular diffusion coefficient is (K ┴ ) 0 = 0.025. Burgers’s model (Burger et al., J. Geophys. Res., 2000) is used as local spectrum of protons. The model with these parameters reproduces the spectrum measured by AMS – 01 (corresponding to a modulation strength   510 - 550 MV (in agreement with independent estimation)). COSMIC RAY INTEGRAL SPECTRA

14. Fig. 9. The modeled integral spectra D(>E) of CR protons for maximum and minimum levels of solar activity for Saturn, Uranus and Neptune. The results are compared with computations of Bobik et al., (ECRS, 2006) for 2D transport model with drift.

15. The observed CR spectrum in the energy interval from 30 MeV/n to 3.10 2 GeV/n has important contribution for the physical processes in the ionospheric CR-layers of the planetary ionospheres. The GCR modulation is essential in this energy interval. The energy interval E = 1 – 30 MeV/n is related to the polar cap region in Earth’s ionosphere. The particles from this interval can penetrate directly in the cusp regions, where they cause enhanced ionization, heating and excitation of the upper and middle atmosphere. Application of the model for calculation of the electron production rate q(h) profiles in energy intervals of galactic CR and anomalous CR component Picture: (Mikhail Panasyuk, ECRS, 2006)

16. The differential D(E) spectra (1) of galactic and anomalous CR are used for computation of the electron production rate profiles in the atmospheres and ionospheres, at which the ACR component is also taken (Mateev L., Bul. Geophys.J, 1997; Velinov et al., JASR, 2008). In Fig. 10 electron production rate q(h) profiles are presented. The computational data present the ionization by galactic CR and their anomalous CR component, which has significant influence above 80 km. The profile with maximal values refers to the polar cap region, the one with minimal values presents the electron production rate at the equator. The positive deviation in the upper part of the polar cap profile shows clearly the contribution of the anomalous CR component Application of the model for calculation of the electron production rate q(h) profiles due to particles of energy intervals of galactic CR and anomalous CR component.

17. The relative electron production rate profiles (for elliptical per spherical geometry) in Kronian ionosphere for latitudes: 0 o - equator, 40 o - middle latitudes, and 90 o - polar regions The lowest value for electron production rate profiles are obtained in case of spherical geometry. The observed difference is the smallest for the equator and the biggest for the polar regions.

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