Cosmic Ray Generator for GLAST Geant4 Simulation
- BFEM Version Tsunefumi Mizuno(1), Yasushi Fukazawa(1), Katsuya Hirano(1), Tuneyoshi Kamae(2), Hirofumi
Mizushima(1), Sei Ogata(1), and Masanobu Ozaki(3)
(1) Hiroshima Univ., (2)SLAC, and (3)ISAS
--- update log of thid document --June 30, 2001 first written by T. Mizuno and T. Kamae.
1. Introduction
GLAST Large Area Telescope (LAT) is designed to trigger (Level-1 Trigger or L1T) whenever 3 contiguous
pairs of (x,y) silicon layers in one tower register one or more strip as being hit. Level-1 Trigger is predicted
to occur at a few kHz while the default day-average downlink bandwidth is about 30Hz [1]. Gamma-ray
signal from a strong extra-terrestrial source (e.g., Crab pulsar) is expected to be about one per minute [2]
while the sensitivity reach stated in the Science Requirement Document [1] allows only about two terrestrial
background events per minute for the entire LAT sky (11000cm**2 and 2.5sr). We have to develop a
“cosmic-ray-proof” instrument rejecting 99.999% of particle-induced backgrounds by an ultra-efficient data
acquisition electronic system and a fully optimized on-line/off-line filtering programs. All possible
background types need to be studied in details by computer simulations and by beam tests. The planned
balloon flight of Balloon Flight Engineering Model (BFEM) will be very important in this regard: it provides
us with direct measurements of possible background types. The Cosmic Ray Generator described here has
been developed to simulate the BFEM response to the cosmic ray protons, electrons, positrons, muons and
gamma rays on the Geant4 platform. It is readily adaptable to the GLASTsim on the GISMO platform.
In the program most parameters are fixed for the BFEM flight at Palestine Texas, as shown in Table 1. Solar
modulation potential (phi) is set at 1100 MV, a typical value for the solar maximum. Cutoff rigidity (Rcutoff)
is, by assuming the earth magnetic field to be the dipole shape, calculated as [3] [4]
Rcutoff (GV) = 14.9 * (1+h/Rearth)**-2 * (cos theta_m)**4 = 4.46 GV
where h is the balloon altitude (~35 km), Rearth means the earth radius (~6380 km), and theta_m is the
geomagnetic latitude (~0.735 radian).
The program has been debugged in many ways. The validity of various spectral shapes and their
normalizations have been calculated independently using Mathcad as shown in Appendices 1, 2, 3, and 4. As
of June 14, 2001, the positron, muon, and gamma ray generators are still being debugged and have not been
implemented. The solar modulation and geomagnetic cutoff parameters are fixed at Palestine Texas and at
the solar maximum (see Table 1). Generalization to the entire low-earth orbit and to the entire solar cycle
should be straightforward and will be done in near future.
Table 1 Parameters for National Scientific Balloon Facility in Palestine Texas in 2001 (GLAST Balloon
experiment). Geocentric latitude and longitude are obtained from http://tower.nsbf.nasa.gov/. Geomagnetic
latitude is calculated by the formula given at http://nssdc.gsfc.nasa.gov/space/cgm/cgm.html, and the cutoff
rigidity (Rcutoff) by assuming the earth magnetic field to be of the dipole shape (see text).
Latitude
Longitude
N31d46.85m =
31.78deg. North
W95d43.37m =
95.73deg. West
Geomagnetic
latitude
42.15 deg. North
(0.735 radian)
Balloon
altitude
35 km
Rcutoff
phi
4.46 GV
1100 MV
2. Composition of Cosmic Ray Generator in BalloonTestV13
In the current cosmic-ray generator, cosmic-ray proton and electron are implemented. Both spectral class
(CrProton and CrElectron) are derived from CrSpectrum, where Rcutoff and phi are calculated at a
constructor. Each component (primary/reentrant/splash) is included at the constructer of CrProton or
CrElectron, and has its own methods that define spectral property (energy, direction, flux, etc). A generation
of the spectrum is controlled by CosmicRayGeneratorAction. If you want to select proton, type “/gun/particle
proton” in Geant4 prompt. Then CosmicRayGeneratorAction chooses CrProton class (and please type
“/gun/particle e-” to select electron). Next, CosmicRayGeneratorAction selects component (primary, reentrant,
splash) by calling a selectComponent() method, get particle energy by calling an energySrc() method, and get
particle direction by calling a dir() method. The flow of the generator described above is summarized in
Figure 1.
Figure 1: Flow chart of the Geant4 cosmic-ray generator for the balloon flight. Spectral class of each particle
(proton, electron, gamma, etc) is derived from CrSpectrum class, where Rcutoff and phi are calculated. A
generation of particle in the simulator is controlled by CosmicRayGeneratorAction class.
3. Effect of Solar Activity and Earth Magnetism on Primary Particle Fluxes
The primary charged particle fluxes are known to have a uniform angular distribution pointing downward
from above the earth horizon except for the east-west effect (yet to be implemented in this program). Its
spectral shape and normalization is calculated from the universal power-law spectrum outside of the solar
system in the following manner.
A) The unmodulated uniform spectrum (Unmod (E)) is first modulated by the solar wind. The effect is
represented by an effective shift (solar potential “phi” in units of MeV) in the spectrum as [5]
Mod(E) = Unmod (E+0.001 phi) ((E+M)**2-M**2)/((E+M+0.001 phi)**2-M**2) ,
Where E is the kinetic energy [GeV] and M means the rest mass of the particle [GeV].
B) The second and much bigger modulation is due to the earth magnetism. This effect is represented by a
reduction factor and highly dependent on the geomagnetic latitude of the instrument. The reduction
factor can be calculated by assuming a dipole magnetic field and neglecting interaction in atmosphere
(e.g., in CHIME model [6]). In BalloonTestV13 we didn’t adopt this model because it fails to reproduce
the measurements by the AMS experiments [7] in the low energy region where the geomagnetic cutoff
effect is quite high. We have eye-ball fitted the AMS measurements and defined the reduction factor as
(1+(R/Rcutoff)**(-12)), where R is the magnetic rigidity of particles [GV] and Rcutoff is the cutoff
rigidity [GV]. For unit-charge particles (i.e.,. proton and electron), R [GV] becomes momentum (P)
[GeV] and Rcutoff [GV] becomes Pcutoff [GeV], because rigidity is defined as R=P/Z|e|
The reduction factor used in this program is compared with that of the CHIME model [6] in Appendix 1 in
their functional form as well as in a figure.
4. Proton Fluxes
The cosmic ray proton flux is simulated in 3 components, the primary flux, the reentrant secondary flux and
the splash secondary flux.
Primary proton flux at Palestine
The BESS experiment (BESS 1998 [8]) provides the most accurate proton spectrum near the geomagnetic
north pole and its spectral shape probably represents best the primary proton spectrum before the geomagnetic
cutoff. The AMS experiment [7] have measured the proton flux at many different geomagnetic latitudes and
provide us with the most accurate spectra on the downward moving and upward moving proton spectra above
and below the geomagnetic cutoff. According to Sanuki et al. 2000 [8] difference between the AMS data [7]
and the BESS data [8] is small for protons below 15 GeV where the flux is highest. At higher energies the
difference becomes noticeable: in the 15-40 GeV and 80-100 GeV ranges, the AMS flux is 10-15% lower
than BESS flux. Our model is based on the AMS data because they include measurements at several
geomagnetic cutoffs. The difference between the two primary particle number fluxes is a few % when
integrated over the energy.
The relevant fluxes from above the earth horizon are described below. In Appendices 2 and 4, algebraic
formulae and their normalizations are verified.
Primary proton spectrum before solar modulation: Unmod (E) = A P**(-a) [1/MeV/m**2/s/sr]
where E is kinetic energy [GeV], P is momentum [GeV], A=16.9 [1/MeV/m**2/s/sr], and a=2.79
Primary proton spectrum after solar modulation:
Mod (E) = Unmod (E+0.001 phi) ((E+M)**2-M**2)/((E+M+0.001 phi)**2-M**2)
where phi is 1100 [MV] for the solar maximum and M is the proton mass (0.938 [GeV] )
Primary proton spectrum after the geomagnetic cutoff:
Primary(E) = Mod(E) * 1/(1+(P/Pcutoff)**(-12)) * v/c [1/MeV/m**2/s/sr]
where Pcutoff is the cutoff momentum [GeV] due to the geomagnetism. The spectrum is measured as
the number of particles that passed the detector per unit time. To represent this fact, v/c is needed.
The angular distribution is uniform and independent of the angle (theta) relative to the zenith-nadir axis for
theta<90 degree and zero for theta > 90 degree. Here, we define that theta=0 means particle going to nadir.
The above proton primary spectrum is generated using uniform random numbers. Since the spectrum
diminishes rapidly like a exponential function, the method known as the Transformation Method (e.g., p. 214
of [9]) speeds up generation of our probability distribution by orders of magnitude. For this method to work,
the indefinite integral of the probability distribution or the spectrum must be invertible. Because of the solar
modulation factor, the cosmic ray primary spectra of any charged particle do not have invertible integral. We
define another function (“the envelope function” given in Appendix 2) that is slightly larger everywhere than
the real one and has an invertible integral. Thus generated probability function (that of the envelope function)
is trimmed down by eliminating a fraction of randomly chosen particle energies corresponding to the
difference between the two functions.
Reentrant and splash proton fluxes at Palestine:
Reentrant protons point downward and splash protons point upward, both covering a hemisphere, respectively.
They are collectively called as the “secondary” or “albedo” flux. For simplicity, we assume the reentrant and
the splash protons to have an identical spectrum and normalization. This assumption is basically correct [7],
but gives somewhat larger flux for splash proton in high geomagnetic latitude region; See Figure 2 and 3.
The implemented fluxes are given below and verified in Appendix 3 and 4. Here we define theta=0 pointing
the Nadir for the reentrant and the Zenith for the splash. This notation is different from that used in the
program.
Reentrant (E, theta=0) = Splash(E, theta=0) = A E**(-a) exp(-Ecutoff/E) [1/MeV/m**2/s/sr]
where A=0.003 [1/MeV/m**2/s/sr], a=2.5, and Ecutoff=0.16 [GeV].
The angular distribution of Reentrant (E, theta) and Splash (E, theta) [1/MeV/m**2/s/sr] is again identical, (1
+ 0.6 sin(theta)) except the directions.
The downward flux and upward proton fluxes generated by our program are given in Figure 2 and 3. The
combined angular distribution is given in Fig.4.
The secondary flux has been measured in several balloon and rocket experiments [10][11] and in the AMS
experiment [7]. The AMS experiment did not measure fluxes at large zenith angles and hence did not detect
the angular dependence of the flux [7], whereas many other experiments have detected build up of the
secondary flux near the earth horizon. We take the spectral shape from the AMS data and the angular
dependence from old measurements [10][11]. See also an unpublished summary of old measurements on the
albedo flux by Tylka [12].
Measurements below 100 MeV are scarce at high geomagnetic cutoffs. Our model function cuts off sharply
below Ecutoff=0.16 GeV. Those protons have only negligible chance of producing gamma-rays to trigger
GLAST-LAT.
Figure 2: Downward moving proton (primary + reentrant) flux along the Zenith-Nadir axis at Palestine
Unfilled squares are measurments by BESS (Rcutoff<0.5 GV, geomagnetic lat. ~1.2 [rad]) [8], while circles
are from AMS measurements (0.6 < geomag. Lat. < 0.7 and 0.7 < geomag. lat < 0.8 [rad]) [7]. For
comparison, upward fluxes measured by AMS are plotted as triangles. Note that upward and downward
secondary fluxes measured by AMS are somewhat different with each other, although we assume identical
spectra between the reentrant (downward) and splash (upward) protons. Crosses represent G4 model
prediction for the total downward proton (primary + reentrant) flux at Palestine Texas (geomag. lat.=0.735).
Measurement errors are typically less than 5 % for the primary component (<80 GeV) and 10-20% for the
secondary component above 1 GeV.
Figure3: Upward moving proton flux (splash) along the Zenith-Nadir axis at Palestine from AMS (0.6 <
geomag. latitude < 0.7 [rad] and 0.7 < geomag. latitude < 0.8 [rad] [7]. Crosses represent G4 model
prediction for the splash proton flux at Palestine Texas (geomag latitude=0.735 [rad]). Note that splash proton
is assumed to have the same spectral shape and normalization with those of reentrant proton in our program,
but gives somewhat smaller normalization in the real data.
Figure 4: Angular distribution of the total proton flux (primary + reentrant + splash) at Palestine. Histograms
represent G4 model prediction at Palestine Texas (geomag. latitude=0.735[rad]). There are not enough
measurements to cover the entire solid angle. The AMS measurement [7] on the reentrant and splash proton
fluxes have not detected the sin(theta) dependent component. We have adopted a fit to old measurements
(mostly from balloon experiments) given in Refs. [10][11].
4. Electron Flux
The cosmic ray electron flux is also simulated in 3 components, the primary flux, the reentrant secondary flux
and the splash secondary flux.
Primary electron flux at Palestine
No single experiment has measure the primary cosmic electron energy over a wide energy range yet. We
used a data compilation of measurements [13] and took the power-law fit given in there (Figure5). This is in
agreement with the AMS data on electron fluxes [14]. A recent measurement at higher magnetic latitude by
the Caprice experiment [15] gives a primary flux lower by about a factor of 2 (Figure 6). We regard
systematic errors in measurements on the primary and secondary fluxes be worse for electrons and about
100%.
The electron primary spectrum is generated in the same manner as for the proton primary spectrum. I. e., the
spectrum is also assumed to have a universal power-law spectrum outside of the solar system, which is
distorted by the solar wind and the earth magnetism. The relevant fluxes along any direction from above the
earth horizon are as follows (see Appendix 2 about the functional forms and Appendix 4 about the
normalization):
Primary electron spectrum before solar modulation:
Unmod (E) = A P**(-a) [1/MeV/m**2/s/sr]
where E is kinetic energy [GV], P is momentum [GeV], A=0.723 [1/MeV/m**2/s/sr] and a=3.33
Primary electron spectrum after solar modulation:
Mod (E) = Unmod (E+0.001 phi) ((E+M)**2-M**2)/((E+M+0.001 phi)**2-M**2)
where phi is 1100 [MV] for the solar maximum and M is the electron mass (0.000511 [GeV] )
Primary electron spectrum after the geomagnetic cutoff:
Primary (E) = Mod (E) * 1/(1+(P/Pcutoff)**(-12)) *v/c [1/MeV/m**2/s/sr]
where Pcutoff is the cutoff momentum [GeV] due to the geomagnetism, and v/c is introduced because
the flux is measured as the number of particles that passed the detector per unit time.
The angular distribution is uniform and independent of angle (theta) relative to the zenith-nadir axis for
theta<90 degree and zero for theta > 90 degree (theta=0 degree means particle goes to nadir).
Figure 5: Compilation of measured downward-moving electron fluxes along the Zenith-Nadir axis (multiplied
by E**3 in GeV) by Komori et al. [13] (The same data points are also given in Kobayashi et al. [13]). The
fitted function shown as an inset has been adopted as the primary flux in our simulator. This function form is
consistent with measurements by the AMS low earth orbit experiment [14] at higher energies but not with
those of the Caprice experiment [15]
.
Figure 6: Electron spectrum multiplied by E**3 [GeV] measured by the Caprice experiment [15] and other
balloon-borne experiments. The solid line labeled as IS is the calculated interstellar electron spectrum by
Moskalenko and Strong [16]. The dashed line is the same spectrum with a solar modulation parameter phi =
600 MV, the value at the time of the experiment.
Reentrant and splash electron fluxes at Palestine
Secondary cosmic ray electrons are simulated in two categories, the downward moving component (the
reentrant flux) and the upward moving component (the splash flux). Old measurements by balloon
experiments gave their crude spectral shapes and normalizations at isolated locations and solar cycles [17].
They were often inconsistent to each other. The recent measurement by AMS gives a broader picture of the
secondary flux [14]. According to the measurement, the splash flux has a similar spectral shape for protons
and electrons (Figure 7) but not the reentrant flux (Figure 8). For the reentrant electrons, the valley between
the cutoff primary spectrum and the power-law secondary spectrum is filled by a new component at high
geomagnetic latitudes (the upper panels of Figure 8). In the program, this third component is modeled as a
hump (see Figure 9 and Appendix 3). The normalizations for the reentrant and splash components are
calculated in Appendix 4.
Splash (E, theta=0) = A E**(-a) [1/MeV/m**2/s/sr]
where A=0.000133 [1/MeV/m**2/s/sr] and a=3.53, and E is in units of GeV.
The angular distribution of Splash (E, theta) [1/MeV/m**2/s/sr] is (1 + 0.6 sin(theta))
Reentrant (E, theta=0) =
A E**(-a)
[1/MeV/m**2/s/sr] for ElowA<E<ElowB and E>EhighB
A E**(-a) + B E**(b) exp(-(E/EcutoffB)**(b+1)) for ElowB<E<EhighB
where A and a are the same as those for the splash component, B=0.0002 [1/MeV/m**2/s/sr], b=2,
EcutoffB = 3.2 [GeV], ElowA = 0.1 [GeV], ElowB = 0.6 [GeV], EhighB = 6.0 [GeV], and EhighA = 10.0
[GeV].
The angular distribution of Reentrant (E, theta) [1/MeV/m**2/s/sr] is (1 + 0.6 sin(theta))
We note here that the AMS measurement did not detect significant sin(theta) component in their limited
angular coverage [14]. The measurement by the Caprice experiment [15] is in general agreement with the
AMS measurement at around kinetic energy of 1 GeV. However some old measurements give much higher
secondary fluxes [17] than those given by AMS or Caprice or this program. The downward flux and upward
electron fluxes generated by our program are given in Figure 10 and 11. The combined angular distribution is
given in Figure 12.
Figure 7: Upward moving electron and positron fluxes (open circles) are compared with downward moving
fluxes (filled circles) in the AMS experiment [14]. Note that the downward fluxes include the primary fluxes.
Note also that the spectrum for upward (splash) electrons can be approximated by a simple power-law. The
AMS experiment has plotted the fluxes assuming a uniform angular distribution
Figure 8: Downward moving electron and positron fluxes measured by the AMS experiment [14]. Note
that the downward fluxes include the primary fluxes. Note also that the valley in the upper right spectrum
(due to the geomagnetic cutoff) is partially filled. The AMS experiment has plotted the fluxes assuming a
uniform angular distribution
Figure 9: Comparison of the upward moving (continuous blue line) and downward moving (thick broken
line in red) secondary electron fluxes (both along the Zenith-Nadir axis) implemented in the program.
The bump in the reentrant electron flux is added to reproduce the spectrum in Fig.8 (0.6 < geomag.
latitude < 0.8 [rad] in the upper left panel) by the AMS experiment.
Figure 10: Downward moving electron (primary + reentrant) flux along the Zenith-Nadir axis at Palestine
in BalloonTestV13 compared with the data by the AMS experiment [10].
Figure 11: Upward moving electron flux (splash) along the Zenith-Nadir axis at Palestine.
Figure 12: Angular distribution of the total electron flux (primary+reentrant+splash) at Palestine
implemented in BallonTestV13
4. To Do List
1.
2.
3.
Dependence on the geomagnetic cutoff (and probably on the solar modulation cycle) is evident
in the AMS proton secondary flux [4] (see Figure 13). Similar complication exists in the AMS
electron data [14] (see Figure 8). We have to implement this for the low earth orbit.
Implement the azimuth dependency (east-west effect).
Implement atmospheric gamma-ray (upward moving), muon, positron, and He fluxes.
Figure 13: Dependence of the secondary proton fluxes on geomagnetic cutoff measured by the AMS
experiment.
5. References
[1] GLAST Science Requirements Document (SRD) (September 2000) states the background after the
full reconstruction to be less than 10% of 1.5x10**(-5)/cm**2/s/sr or 4.13x10**(-2)/s for E>100MeV for
the entire LAT (11000cm**2, 2.5sr) under several kHz of protons and nearly 1kHz of electrons.
[2] Response to NASA’s AO 99-055-03: “GLAST Large Area Telescope Flight Investigation: A ParticleAstrophysics Partnership to Explore the High-Energy Universe” (November 1999)
[3] Zombeck; "Handbook of space astronomy and astrophysics" 2nd edition (1990) p225, Cambridge
University Press
[4] M.S. Longair; "High Energy Astrophysics" 2nd edition (1992) p325-330, Cambridge University Press
[5] L.J. Gleeson and W.I. Axford; “Solar Modulation of Galactic Cosmic Rays”, Astroprysical Journal
154 (1968) p1011
[6] CHIME
[7] J. Alcaraz et al. (AMS Collaboration); "Cosmic Protons", Physics Letters B490 (2000) p27, "Protons
in near earth orbit", Physics Letters B472 (2000) p215
[8] T. Sanuki et al; "Precise Measurement of Cosmic-Ray Proton and Helium Spectra with the BESS
Spectrometer", astro-ph/0002481 (2000).
[9] W. H. Press, B. P. Fiannery, S. A. Teukolsky, and W. T. Vetterling; “Numerical Recipes in C” (1988)
Cambridge Univ. Press.
[10] J.A.Van Allen and A.V. Gangnes; “The Cosmic-Ray Intensity Above the Atmosphere at the
Geomagnetic Equator”, Physical Review 78 (1950) p50, “On the Azimuthal Asymmetry of Cosmic-Ray
Intensity above the Atmosphere at the Geomagnetic Equator”, Physical Review 79 (1950) p51
[11] S.F. Singer; “The Zenith Angle Dependence of the Cosmic Radiation above the Atmosphere at
lamda = 41 degree N”, Physical Review 77 (1950) p729
[12] A.J. Tylka; "A Review of Cosmic-Ray Albedo Studies: 1949-1970", Unpublished memo (May 2000).
[13] Y. Komori et al.; Proceeding of Dai-Kikyuu (large balloon) Symposium at ISAS (1999) p33,
T. Kobayasi et al.; “High Energy Cosmic-Ray Electrons Beyond 100 GeV”, Proceeding of 26th
International CosmicRay Conference 3 (1999) p61.
[14] J. Alcaraz et al. (AMS Collaboration); “Leptons in near earth orbit”.Physics Letters B484 (2000) p10
[15] M. Boezio et al.; “The Cosmic-Ray Electron and Positron Spectra Measured at 1 AU During Solar
Minimum Activity” Astrophys. J. 532 (2000) p653,
[16] I.V. Moskalenko, A.W. Strong and O. Reimer; “Diffuse galactic gamma rays, cosmic-ray nucleons
and antiprotons” Astronomy and Astorophysics 338 (1998) L75
[17]S.W. Barwick et al. “Cosmic ray reentrant electron albedo; High Energy Antimatter Telescope
balloon measurements from Fort Summer, New Mexico”, Journal of Geophsical research 103 (1998)
p4817 and references therein.