CRflux_protonAlpha_ ppt 1 Proton/alpha background flux models October 14, 2003 Tsunefumi Mizuno Background flux model functions for proton/alpha in CRflux package are given here. The model is under construction and the function shown in this report could be modified in future.

CRflux_protonAlpha_ ppt 2 Plan overview The background flux depends on satellite position (due to geomagnetic cutoff) and year (due to solar activity). We need to take these two effect into account. We refer to the solar modulation theory to take the solar activity effect into account. We also plan to collect the reference data at various positions and model them with analytic function (i.e., model function). Particles implemented in CRflux package: protons (primary/secondary) alphas (primary) electrons/positrons (primary/secondary) gammas (primary/secondary); position dependence is not yet implemented

CRflux_protonAlpha_ ppt 3 Cutoff rigidity and solar modulation potential To calculate the cutoff rigidity (Rc), we assume that the earth magnetic field is the dipole shape and calculate Rc as Rc(GV)=14.9*(1+h/Rearth)^-2*(cos theta_M)^4, where h is the satellite altitude, Rearth is the earth radius (6380 km) and theta_M is the geomagnetic latitude (see Zombeck “Handbook of space astronomy and astrophysics” 2 nd edition (1990) p225; Longair “High Energy Astrophysics” 2 nd edition (1992) p ). Typical value of solar modulation potential phi (see formula in the next page) is ~550 MV and ~1100 MV for solar activity minimum and maximum, respectively (e.g., Seo et al. 1991, ApJ 378, 763; Boezio et al. 1999, ApJ 518, 457; Menn et al. 2000, ApJ 533, 281). It is difficult to predict the value in advance. Instead, we could use the Climax Neutron Monitor count ( to derive phi of the day of observation, for the neutron monitor count is a good indicator of the solar activity.

CRflux_protonAlpha_ ppt 4 Model functions: Primary: Power-law with solar modulation effect (Gleeson and Axford 1968) and geomagnetic cutoff (introduced by T. Kamae and M. Ozaki to reproduce low geomag. lat. data of AMS). A similar formula is used for alphas, electrons and positrons. Secondary: Simple analytic functions such as power-law. Model functions are determined to reproduce the AMS data. Below 100 MeV, we do not have AMS data. Therefore, we just extrapolate the spectrum down to 10 MeV with E^-1. To keep the model simple, we use the same function to express the reentrant (downward) and splash (upward) spectra. proton spectrum model function Reference: AMS data (J. Alcaraz et al. 2000, Phys. Let. B 472, 215 and Phys. Let. B 490, 27) BESS data (T. Sanuki et al. 2000, ApJ 545, 1135) Solar modulation theory (L. J. Gleeson and W. I. Axford 1968, ApJ 154, 1011) Etc. [c/s/m^2/sr/MeV]

CRflux_protonAlpha_ ppt 5 proton primary spectra phi=650 MV phi=800 MV phi=1100MV (Rc=0 GV) Rc=0.5GV in the formula given in the previous page. Proton primary spectra obtained by various balloon and satellite experiments at high geomagnetic latitude are given with our model functions. Please note that our formula of geomagnetic cutoff, 1/(1+(R/Rc)^-12.0), gives lower flux in low energy region. Except for this, our model function reproduces the observed spectra very well. references; J. Alcaraz et al. 2000, Phys. Let. B 490, 27 T. Sanuki et al. 2000, ApJ 545, 1135 Set et al. 1991, ApJ 378, 763 Boezio et al. 1999, ApJ 518, 457 Menn et al. 2000, ApJ 533, 281

CRflux_protonAlpha_ ppt 6 proton models (1) Vertically downward/upward going proton flux data by AMS (geomagnetic latitude theta_M<0.2; geomagnetic equator) and model functions. AMS provides us with data of 0<theta_M<1.0 (from geomagnetic equator to polar). phi=650 MV Rc=13.0 GV Ek^-1 (below 100 MeV) primary secondary (100 MeV-10 GeV)

CRflux_protonAlpha_ ppt 7 proton models (2) Vertically downward/upward going proton flux data by AMS (0.2<theta_M<0.3) and model functions. AMS provides us with data of 0<theta_M<1.0 (from geomagnetic equator to polar). phi=650 MV Rc=11.7 GV Ek^-1 (<=100 MeV) primary secondary Ek^-0.86 ( MeV) Ek^-2.4 ( GeV)

CRflux_protonAlpha_ ppt 8 proton models (3) Vertically downward/upward going proton flux data by AMS (0.3<theta_M<0.4) and model functions. AMS provides us with data of 0<theta_M<1.0 (from geomagnetic equator to polar). phi=650 MV Rc=10.3 GV Ek^-1 (<=600 MeV) primary secondary Ek^-2.4 ( GeV)

CRflux_protonAlpha_ ppt 9 proton models (4) Vertically downward/upward going proton flux data by AMS (0.4<theta_M<0.5) and model functions. AMS provides us with data of 0<theta_M<1.0 (from geomagnetic equator to polar). phi=650 MV Rc=8.7 GV Ek^-1 (<=100 MeV) primary secondary Ek^-1.3 ( MeV) Ek^-2.4 ( GeV)

CRflux_protonAlpha_ ppt 10 proton models (5) Vertically downward/upward going proton flux data by AMS (0.5<theta_M<0.6) and model functions. AMS provides us with data of 0<theta_M<1.0 (from geomagnetic equator to polar). phi=650 MV Rc=7.0 GV Ek^-1 (<=100 MeV) primary secondary Ek^-1.2 ( MeV) Ek^-2.4 ( GeV)

CRflux_protonAlpha_ ppt 11 proton models (6) Vertically downward/upward going proton flux data by AMS (0.6<theta_M<0.7) and model functions. AMS provides us with data of 0<theta_M<1.0 (from geomagnetic equator to polar). phi=650 MV Rc=5.3 GV Ek^-1 (<=300 MeV) primary secondary Ek^-2.3 ( GeV)

CRflux_protonAlpha_ ppt 12 proton models (7) Vertically downward/upward going proton flux data by AMS (0.7<theta_M<0.8) and model functions. AMS provides us with data of 0<theta_M<1.0 (from geomagnetic equator to polar). phi=650 MV Rc=3.8 GV Ek^-1 (below 100 MeV) primary secondary (100 MeV-10 GeV)

CRflux_protonAlpha_ ppt 13 proton models (8) Vertically downward/upward going proton flux data by AMS (0.8<theta_M<0.9) and model functions. AMS provides us with data of 0<theta_M<1.0 (from geomagnetic equator to polar). phi=650 MV Rc=2.5 GV Ek^-1 (below 100 MeV) primary secondary (100 MeV-10 GeV)

CRflux_protonAlpha_ ppt 14 proton models (9) Vertically downward/upward going proton flux data by AMS (0.9<theta_M<1.0) and model functions. AMS provides us with data of 0<theta_M<1.0 (from geomagnetic equator to polar). phi=650 MV Rc=1.5 GV Ek^-1 (below 100 MeV) primary secondary (100 MeV-10 GeV)

CRflux_protonAlpha_ ppt 15 proton models (10) Based on old rocket measurements (e.g., J.A.Van Allen and A.V. Gangnes 1950, Phys. Rev. 78, 50; S.F. Singer 1950, Phys. Rev. 77, 729), we adopt the zenith angle dependence of 1+0.6sin(theta) for secondaries. For primaries, we assume uniform distribution from cos(theta)=1.0 (vertically downward) to -0.4 (blocking by earth). The same angular dependence is used for alpha primaries and electron/positron primaries and secondaries. primary secondary upward secondary downward upward Zenith angle dependence of protons at Pelestine, Texas and solar activity maximum, generated by the program.

CRflux_protonAlpha_ ppt 16 alpha models (1) [c/s/m^2/sr/MeV] Primary: Power-law with solar modulation effect and geomagnetic cutoff. Secondary: Could be negligible. (e.g., Fig. 1 in Alcaraz et al. 2000, Phys. Let. B 494, 193)

CRflux_protonAlpha_ ppt 17 alpha models (2) Alpha primary spectra obtained by various balloon and satellite experiments at high geomagnetic latitude with our model functions. Except for that the formula of geomagnetic cutoff gives lower flux in low energy region, our model function reproduces the observed spectra very well. Note that model is expressed as a function of kinetic energy but the figure is given in unit of kinetic energy per nucleon. phi=650 MV phi=1100MV (Rc=0 GV) Rc=0.5GV in the formula given in the previous page.

CRflux_protonAlpha_ ppt 18 alpha models (3) Alpha primary spectra obtained by AMS in various geomagnetic latitude are given below. Our model for intermediate region (0.4<theta_M<0.8) somewhat differs from the data. This could be because the corresponding region of Rc is too broad (Rc=9.6 and 3.1 GV for theta_M=0.4 and 0.8, respectively) to reproduce the spectrum with single value of Rc. For other region, our formula reproduces the data very well. data;0<theta_M<0.4 Model; Rc=12.2 GV (theta_M=0.2) data;0.4<theta_M<0.8 Model; Rc=6.2 GV (theta_M=0.6) data; above COR Model; Rc=0 GV