1. electron/positron background flux models
October 14, 2003
Tsunefumi Mizuno
Background flux model functions for e-/e+ in CRflux package are given here. The model is under construction and the function shown in this report could be modified in future.
CRflux_electronPositron_ ppt

2. Plan overview
The background flux depends on satellite position (due to geomagnetic cutoff) and year (due to solar activity). To take these effects into account for primary component, we utilize the formula similar to those of proton and alpha. There, solar modulation potential and cutoff rigidity are included in the function explicitly.
We refer to the AMS data (Alcaraz et al. 2000, Phys. Let. B 484, 10) and model the flux spectra with analytic functions.
CRflux_electronPositron_ ppt

3. electron model functions
Reference:
Data compilation in Komori et al. 1999, proceeding of large balloon symposium at ISAS, p33. (The same data points are also given in Kobayashi et al. 1999, proceeding of 26th ICRC 3, p61). Spectrum for all electrons(e- + e+) is given here.
Golden et al. 1996, ApJL 457, 103; assume that positron fraction is 0.078
Solar modulation theory (L. J. Gleeson and W. I. Axford 1968, ApJ 154, 1011)
Etc.
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. proton data of AMS).
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 and 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.
[c/s/m^2/sr/MeV]
CRflux_electronPositron_ ppt

4. positron model functions
Reference:
Model functions for electron primary.
Golden et al. 1996, ApJL 457, 103
Etc.
Model functions:
Primary: We adopted the results of Golden et al. (1996) and assume that a fraction fraction is (energy indepent).
Secondary: Like for electrons, we utilize Simple analytic functions such as power-law.
[c/s/m^2/sr/MeV]
CRflux_electronPositron_ ppt

5. Note for primary spectra
We have utilized the data compilation in high energy region (100 GeV-10 TeV) and modeled the interstellar electron spectra as 0.667*E^ This function givse a slightly higher flux in relatively low energy region (around 10 GeV), as shown in figure below. We can also see that the interstellar spectrum of primary electron could not be a single power-law, but suffers a small cutoff in low energy region (below 2-3 GeV).
Interstellar spectrum of primary electron. Three observations shown here were in similar solar activity, and we demodulated their data according to equation in page 3 with phi=650 MV.
Unmod=0.667*E^-3.33
references;
J. Alcaraz et al. 2000, Phys. Let. B 484, 10
Boezio et al. 200, ApJ 532, 653
Golden et al. 1994, ApJ 436, 769
CRflux_electronPositron_ ppt

6. e-/e+ models (1) 2ndary electron 2ndary positron phi=650 MV Rc=12.7 GV
Vertically downward going e-/e+ flux data by AMS (geomagnetic latitude theta_M<0.3; geomagnetic equator) and model functions.
phi=650 MV
Rc=12.7 GV
2ndary electron
2ndary positron
(E<100 MeV)
(E<100 MeV)
(E=0.1-2 GeV)
(E=2-20 GeV)
(E= GeV)
CRflux_electronPositron_ ppt

7. e-/e+ models (2) 2ndary electron 2ndary positron phi=650 MV Rc=8.7 GV
Vertically downward going e-/e+ flux data by AMS (0.3<theta_M<0.6) and model functions.
phi=650 MV
Rc=8.7 GV
2ndary electron
2ndary positron
(E<100 MeV)
(E<100 MeV)
(E= GeV)
(E= GeV)
CRflux_electronPositron_ ppt

8. e-/e+ models (3) 2ndary e-/e+ phi=650 MV Rc=4.5 GV (E<100 MeV)
Vertically downward going e-/e+ flux data by AMS (0.6<theta_M<0.8) and model functions.
phi=650 MV
Rc=4.5 GV
2ndary e-/e+
(E<100 MeV)
(E= GeV)
CRflux_electronPositron_ ppt

9. e-/e+ models (4) 2ndary e-/e+ phi=650 MV Rc=2.5 GV (E<100 MeV)
Vertically downward going e-/e+ flux data by AMS (0.8<theta_M<0.9) and model functions.
phi=650 MV
Rc=2.5 GV
2ndary e-/e+
(E<100 MeV)
(E= GeV)
CRflux_electronPositron_ ppt

10. e-/e+ models (5) 2ndary e-/e+ phi=650 MV Rc=1.5 GV (E<100 MeV)
Vertically downward going e-/e+ flux data by AMS (0.9<theta_M<1.0) and model functions.
phi=650 MV
Rc=1.5 GV
2ndary e-/e+
(E<100 MeV)
(E= MeV)
(E= GeV)
CRflux_electronPositron_ ppt

11. e-/e+ models (6) 2ndary e-/e+ phi=650 MV Rc=0.8 GV (E<100 MeV)
Vertically downward going e-/e+ flux data by AMS (1.0<theta_M<1.1) and model functions.
phi=650 MV
Rc=0.8 GV
2ndary e-/e+
(E<100 MeV)
(E= GeV)
CRflux_electronPositron_ ppt