Proton/alpha background flux models

1
Proton/alpha background flux models
October 14, 2003 Tsunefumi Mizuno mizuno_at_SLAC.Stan
ford.EDU
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.
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

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(1h/Rearth)-2(c
  os 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
  2nd edition (1990) p225 Longair High Energy
  Astrophysics 2nd edition (1992) p325-330).
• 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
  (http//ulysses.sr.unh.edu/NeutronMonitor) to
  derive phi of the day of observation, for the
  neutron monitor count is a good indicator of the
  solar activity.

4
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.

• 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.

c/s/m2/sr/MeV
5
proton primary spectra
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.
phi650 MV phi800 MV phi1100MV (Rc0 GV)
Rc0.5GV in the formula given in the previous
page.
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
6
proton models (1)
Vertically downward/upward going proton flux data
by AMS (geomagnetic latitude theta_Mlt0.2
geomagnetic equator) and model functions. AMS
provides us with data of 0lttheta_Mlt1.0 (from
geomagnetic equator to polar).
Ek-1 (below 100 MeV)
phi650 MV Rc13.0 GV
(100 MeV-10 GeV)
primary
secondary
7
proton models (2)

• Vertically downward/upward going proton flux data
  by AMS (0.2lttheta_Mlt0.3) and model functions. AMS
  provides us with data of 0lttheta_Mlt1.0 (from
  geomagnetic equator to polar).

Ek-1 (lt100 MeV)
phi650 MV Rc11.7 GV
Ek-0.86 (100-600 MeV)
Ek-2.4 (0.6-10 GeV)
primary
secondary
8
proton models (3)

• Vertically downward/upward going proton flux data
  by AMS (0.3lttheta_Mlt0.4) and model functions. AMS
  provides us with data of 0lttheta_Mlt1.0 (from
  geomagnetic equator to polar).

Ek-1 (lt600 MeV)
phi650 MV Rc10.3 GV
Ek-2.4 (0.6-10 GeV)
primary
secondary
9
proton models (4)

• Vertically downward/upward going proton flux data
  by AMS (0.4lttheta_Mlt0.5) and model functions. AMS
  provides us with data of 0lttheta_Mlt1.0 (from
  geomagnetic equator to polar).

Ek-1 (lt100 MeV)
phi650 MV Rc8.7 GV
Ek-1.3 (100-600 MeV)
Ek-2.4 (0.6-10 GeV)
primary
secondary
10
proton models (5)

• Vertically downward/upward going proton flux data
  by AMS (0.5lttheta_Mlt0.6) and model functions. AMS
  provides us with data of 0lttheta_Mlt1.0 (from
  geomagnetic equator to polar).

Ek-1 (lt100 MeV)
phi650 MV Rc7.0 GV
Ek-1.2 (100-400 MeV)
Ek-2.4 (0.4-10 GeV)
primary
secondary
11
proton models (6)

• Vertically downward/upward going proton flux data
  by AMS (0.6lttheta_Mlt0.7) and model functions. AMS
  provides us with data of 0lttheta_Mlt1.0 (from
  geomagnetic equator to polar).

Ek-1 (lt300 MeV)
phi650 MV Rc5.3 GV
Ek-2.3 (0.3-10 GeV)
primary
secondary
12
proton models (7)

• Vertically downward/upward going proton flux data
  by AMS (0.7lttheta_Mlt0.8) and model functions. AMS
  provides us with data of 0lttheta_Mlt1.0 (from
  geomagnetic equator to polar).

Ek-1 (below 100 MeV)
phi650 MV Rc3.8 GV
(100 MeV-10 GeV)
secondary
primary
13
proton models (8)

• Vertically downward/upward going proton flux data
  by AMS (0.8lttheta_Mlt0.9) and model functions. AMS
  provides us with data of 0lttheta_Mlt1.0 (from
  geomagnetic equator to polar).

Ek-1 (below 100 MeV)
phi650 MV Rc2.5 GV
(100 MeV-10 GeV)
secondary
primary
14
proton models (9)

• Vertically downward/upward going proton flux data
  by AMS (0.9lttheta_Mlt1.0) and model functions. AMS
  provides us with data of 0lttheta_Mlt1.0 (from
  geomagnetic equator to polar).

Ek-1 (below 100 MeV)
phi650 MV Rc1.5 GV
(100 MeV-10 GeV)
secondary
primary
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 10.6sin(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.

• Zenith angle dependence of protons at Pelestine,
  Texas and solar activity maximum, generated by
  the program.

primary
secondary upward
secondary downward
downward
upward
16
alpha models (1)
Primary Power-law with solar modulation effect
and geomagnetic cutoff.
c/s/m2/sr/MeV
Secondary Could be negligible. (e.g., Fig. 1 in
Alcaraz et al. 2000, Phys. Let. B 494, 193)
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.
phi650 MV phi1100MV (Rc0 GV)
Rc0.5GV in the formula given in the previous
page.
18
alpha models (3)
Alpha primary spectra obtained by AMS in various
geomagnetic latitude are given below. Our model
for intermediate region (0.4lttheta_Mlt0.8)
somewhat differs from the data. This could be
because the corresponding region of Rc is too
broad (Rc9.6 and 3.1 GV for theta_M0.4 and 0.8,
respectively) to reproduce the spectrum with
single value of Rc. For other region, our formula
reproduces the data very well.
data above COR Model Rc0 GV
data0.4lttheta_Mlt0.8 Model Rc6.2 GV
(theta_M0.6)
data0lttheta_Mlt0.4 Model Rc12.2 GV (theta_M0.2)