Modeling high-energy cosmic ray induced terrestrial muon flux: A lookup table
Dimitra Atri∗and Adrian L. Melott
Department of Physics and Astronomy, University of Kansas,
1251 Wescoe Dr. # 1082, Lawrence, KS 66045, United States of America
(Dated: November 23, 2010)
On geological timescales, the Earth is likely to be exposed to an increased flux of high energy
cosmic rays (HECRs) from astrophysical sources such as nearby supernovae, gamma ray bursts
or by galactic shocks. Typical cosmic ray energies may be much higher than the ≤ 1 GeV flux
which normally dominates. These high-energy particles strike the Earth’s atmosphere initiating an
extensive air shower. As the air shower propagates deeper, it ionizes the atmosphere by producing
charged secondary particles. Secondary particles such as muons and thermal neutrons produced as
a result of nuclear interactions are able to reach the ground, enhancing the radiation dose. Muons
contribute 85% to the radiation dose from cosmic rays. This enhanced dose could be potentially
harmful to the biosphere. This mechanism has been discussed extensively in literature but has
never been quantified. Here, we have developed a lookup table that can be used to quantify this
effect by modeling terrestrial muon flux from any arbitrary cosmic ray spectra with 10 GeV - 1
PeV primaries. This will enable us to compute the radiation dose on terrestrial planetary surfaces
from a number of astrophysical sources and provide an important constraint on the habitability of
PACS numbers: 96.50.sd, 91.62.Xy, 91.62.Fc, 96.55.+z
There is a non-trivial probability of high-energy astro-
physical events such as nearby supernovae  and gamma
ray bursts  (GRBs) to expose the Earth to an en-
hanced flux of radiation over Gyr timescales. Along with
higher flux, the peak of energy spectrum of primaries is
also shifted toward higher energies. This radiation con-
sists of both photons and charged nuclei, also known as
cosmic rays. Periodic motion of the Sun perpendicular to
the galactic plane can also expose us to an enhanced level
of HECRs generated by the galactic shock . Detailed
modeling of the effects of photons hitting the Earths at-
mosphere exists  and will not be discussed further. We
focus on the effects of the cosmic ray component of this
radiation in this paper, which are of primary importance
to the biosphere. Cosmic ray primaries interact with the
nuclei of the atmosphere, initiating a series of reactions
propagating deeper into the atmosphere, known as ex-
tensive air showers.The shower propagates down to-
wards the ground with the shower-front shaped like a
pancake. Most of the energy of the primary particle is
used up in ionizing the atmosphere.
ionizing the atmosphere consists of charged particles and
photons, also referred to as the electromagnetic compo-
nent of the shower. This electromagnetic component is
mostly absorbed within first 1000 g cm−2of atmosphere
and mostly the hard component (muons) of the shower
is able to reach the ground. Other particles and pho-
tons reaching the ground are not biologically effective.
This atmospheric ionization induced by HECR primaries
has already been modeled for energies up to 1 PeV .
Along with ionizing the atmosphere, secondary particles
reach ground level. Depending on their energy, they have
the ability to penetrate deep underground and into wa-
ter. Enhanced levels of secondary particle flux could be
harmful to living organisms  by increased mutation
rates, cancer and birth defects .
Muons are generated by the decay of charged pions
and have a very small interaction cross section. Also,
their cross section is a very weak function of energy and
the ionization energy loss is a very small fraction of the
primary energy, even at very high energies. As a result,
high energy muons hit the ground practically unhindered,
generated by high energy primaries. But since muons
are charged particles, they are easy to detect and give
a dominant signal deep in the atmosphere and under-
ground. They are usually detected with detectors buried
under a meter or more underground in order to absorb
the electromagnetic component.
The muon component dominates the flux of particles
on the ground at energies above 100 MeV . Its contribu-
tion is about 85% of the total equivalent biological dose
by cosmic rays . At lower energies, the muon flux
decreases because of their short lifetime of 2 µs. Muons
with higher energy travel with higher velocities and hence
travel longer distances due to the time dilation effects.
They lose energy due to ionization at a rate of about 2
MeV per g cm−2. Since the column density of our at-
mosphere is about 1000 g cm−2, a muon loses around 2
GeV of energy, on an average, upon reaching the ground
Analytical models  can approximate muon flux re-
sulting from vertical GCR primaries and vast amount of
data  is available from detectors around the world.
But no model is available to compute muon flux when
the CR primary flux is different from the normal GCR
flux. In particular at higher energies, the hadronic inter-
action cross sections are only estimates, and reasonable
data can be obtained only by computational methods.
arXiv:1011.4522v1 [astro-ph.HE] 19 Nov 2010
We have developed a lookup table to compute terres-
trial flux of muons resulting from high energy cosmic rays
interaction with the atmosphere that can be used by con-
volving with the spectrum from any astrophysical source.
We use CORSIKA (COsmic Ray SImulations for KAs-
cade) , which is a Monte Carlo code used extensively
to study air showers generated by primaries up to 100
EeV .It is primarily calibrated by KASCADE data,
which is a detector used to study hadronic interactions
in the 1016to 1018eV energy range. We use the code
to simulate air showers for a flat spectrum of high-energy
primaries (protons) so that any arbitrary CR spectra can
be applied later on, to calculate the muon flux.
In order to obtain data that is independent of the
primary GCR spectrum and geographic location on the
Earth, we simulated showers at fixed primary energies.
The flux of muons at the ground level strongly depends
on the zenith angle of the primary; therefore we simu-
lated showers for a range of zenith angles. We compiled
data for primaries from 10 GeV up to 1 PeV in 0.1 log10
intervals. At each energy, simulations are performed at
zenith angles starting from 5, 15...up to 85 degrees. We
averaged 90,000 showers at each energy for 10 GeV - 1
TeV range, 9,000 for 1 TeV - 10 TeV , 900 for 10 TeV -
100 TeV and 180 showers for 100 TeV - 1 PeV . Overall,
the data is compiled from a large ensemble of 1.9 × 106
CORSIKA 6.960 was used for all the simulations. The
code was set up with EPOS as the high-energy hadronic
interaction model due to its compatibility with KAS-
CADE data. For low energies, the FLUKA hadronic in-
teraction model was chosen since it is the fastest and best
at tracking muons in our energy range . The code
was installed with the SLANT option to study the lon-
gitudinal shower development. It will be used for other
purposes, not discussed here. CURVED option was cho-
sen for primaries incident at large zenith angles and UP-
WARD option for albedo particles. The energy cut was
set at 300 MeV since it is adequate to get all the muons
and hadrons produced by photon interactions while sav-
ing a significant amount of computing time. Sea level
was set as the observation level.
CORSIKA outputs binary files, which record data on a
number of particle species hitting the ground level, which
were converted to ASCII format for analysis. Each file
contains momentum data of individual particles at the
sea level from a single air shower. Muon momentum is
extracted from each file generated by a primary at a fixed
energy and fixed zenith angle. The momentum data is
then compiled for all showers at a given energy and angle,
and is binned in logarithmic energy bins of 0.1 GeV in
log10intervals. It is then normalized by the total num-
ber of showers, giving the muon flux from a single pri-
mary. As a result we get the terrestrial muon spectrum
of a particular primary energy at a given zenith angle.
Data obtained from different angles at a given primary
energy is then averaged by sin theta weight resulting in
an isotropic muon spectrum at a particular primary en-
ergy. This is the data recorded in the data table. This
process is repeated for all 51 primary energies from 10
GeV - 1 PeV .
Muons have a lifetime of 2.2 µs. As the zenith angle
of the primary particle increases, so does the distance to
travel and therefore a lot of muons decay before reaching
FIG. 1: Differential muon flux for 10 TeV primaries at zenith
angles 5o(solid), 45o(dotted), and 85o(dashed). The flux
goes down with increasing zenith angles.
Therefore, as expected we get lesser muon flux at
higher zenith angles (Figures 1 and 2). Low energy pri-
maries are not efficient in producing muons of enough
energy so that they can reach the ground. A large num-
ber of primaries at lower energies produce fewer muons
at the ground level. The number of secondary particles
produced in the shower increases with the primary energy
and so does the number of muons hitting the ground (Fig-
ure 3). The contribution from larger zenith angle com-
ponent is very small for low energy primaries, and goes
up with energy. This is evident in Figure 3 where the
flux from 100 GeV primary falls very steeply compared
to primaries at higher energies.
Our primary energies are centered at 10 GeV , 101.1
GeV and so on with bin size of 0.1 in log10intervals. The
number of particles in a given energy bin (dN/dE) can
be calculated using the differential spectrum from any
astrophysical source. This number is then multiplied by
the data given in the table to get the corresponding muon
spectrum for each primary energy. The total muon spec-
trum can be obtained by summing over a given energy
range. Since the primaries higher than 17 GeV are unaf-
fected by the geomagnetic field, their flux is independent
of the geographic location. Large amount of literature
exists for muon flux for lower energies, both from experi-
FIG. 2: Differential muon flux for 1 PeV primaries at zenith
angles 5o(solid) and 85o(dotted).
FIG. 3: The muon flux averaged over the hemisphere from
100 GeV (solid), 10 TeV (dotted) and 1 PeV (dashed) pri-
maries. Flux for higher energy primaries does not fall sharply
compared to the lower energy primaries since the contribution
from higher zenith angles increases with increasing primary
ments  or using approximate analytical methods .
No simple method exists to calculate the terrestrial
muon flux induced by arbitrary cosmic ray spectra. We
have developed a lookup table that can be used for
primaries up to 1 PeV .
sponding to the increased muon flux can have signifi-
cant effects on the biosphere and can be quantified us-
ing this data. Data will be made freely available at
The radiation dose corre-
http : //kusmos.phsx.ku.edu/ melott/Astrobiology.htm
upon publication of this paper.
We thank Tanguy Pierog and Dieter Heck for their ad-
vice in using CORSIKA. The extensive computer simula-
tions were supported by the NSF via TeraGrid allocations
at the National Center for Supercomputing Applications,
Urbana, Illinois, TG-PHY090067T and TG-PHY090108.
∗Electronic address: email@example.com
 B.D. Fields, T. Athanassiadou, and S.R. Johnson, Super-
nova Collisions with the Heliosphere, Astrophys. J. 678,
 C.D. Dermer and J.M. Holmes, Cosmic Rays from
Gamma-Ray Bursts in the Galaxy, Astrophys. J. 628,
 C.D.Dermer, First Light
 A. Kusenko,Past Galactic
gin and composition of ultrahigh-energy cosmic rays,
 M.M. Medvedev and A.L. Melott, Do Extragalactic Cos-
mic Rays Induce Cycles in Fossil Diversity?, Astrophys.
J. 664, 879 (2007).
 B.C. Thomas, A.L. Melott, C.H. Jackman, C.M. Laird,
M.V. Medvedev, R.S. Stolarski, N. Gehrels, J.K. Can-
nizzo, D.P. Hogan, and L.M. Ejzak, Gamma-Ray Bursts
and the Earth: Exploration of Atmospheric, Biological,
Climatic, and Biogeochemical Effects, Astrophys. J. 634,
 D. Atri, A.L. Melott and B.C. Thomas, Lookup tables
to compute high energy cosmic ray induced atmospheric
ionization and changes in atmospheric chemistry, J. Cos-
mol. Astropart. P., 5 008 (2010).
 A. Dar, A. Laor, and N.J. Shaviv, Life Extinctions by
Cosmic Ray Jets, Phys. Rev. Lett. 80, 26 (1998)
 D.A. Juckett, A 17-year oscillation in cancer mortality
birth cohorts on three continents - synchrony to cosmic
ray modulations one generation earlier, Int. J. Biome-
terol. 53, 6 (2009).
 E.L. Alpen, Radiation Biophysics., Academic Press, San
 T.K. Gaisser, Cosmic rays and particle physics., Cam-
bridge University Press, Cambridge (1990).
 T. Hebbeker and C. Timmermans, A compilation of high
energy atmospheric muon data at sea level, Astropart.
Phys., 18 (2002).
 T. Pierog, D. Heck, and J. Knapp, CORSIKA (COsmic
Ray SImulations for KAscade) an air shower simulation
program homepage: http://www-ik.fzk.de/corsika/.
 T. Pierog, R. Engel, D. Heck, S. Ostapchenko,and K.
Werner, Prepared for 30th International Cosmic Ray
Conference, Latest Results from the Air Shower Simu-
lation Programs CORSIKA and CONEX, (ICRC 2007),
Merida, Yucatan, Mexico, arXiv:0802.1262v1 (2007).
on GRBswith Fermi,