Study of the effects of water properties on Monte Carlo simulation of the
atmospheric muon flux
Annarita Margiotta
Dipartimento di Fisica - Università di Bologna and Sezione INFN di Bologna
margiotta@bo.infn.it
Introduction
An extensive study has been carried out to evaluate possible effects that water properties could have
on Monte Carlo (MC) simulation of the atmospheric muon flux.
The number and the angular distribution of photons reaching a photomultiplier (PMT), given a
certain distance from the emission point, depend on the optical properties of water. A direct effect is
produced, in particular, by the absorption length, the scattering length and the volume scattering
function.
In the MC program chain used to simulate the response of the ANTARES detector to the passage of
atmospheric muons, Cherenkov light production, its propagation to the optical modules and the
response of PMTs are treated in the program called KM3 [1].
Single photons are not followed from their emission point to PMTs. Specific sections of the
program (GEN and HIT codes [1]) are devoted to create tables where the probability to produce a
signal, when a photon hits a PMT, is stored as a function of the distance from the emission point to
the PMT and of the emitting particle energy. Different sets of tables corresponding to different
water properties have been compiled to perform a comparison.
Details on definitions and models of water properties can be found in [2].
Water models
Absorption (abs) and attenuation (att) lengths were measured at the ANTARES site during several
campaigns. A summary of results is shown in fig. 1 together with measurements performed at Capo
Passero and Catania sites [3].
Fig.1 – (left) absorption length; (right) attenuation length. Points refer to measurements performed at Toulon, Capo
Passero and Catania sites [3]. The parameterization of Smith and Baker for pure sea water is shown for comparison [4].
The scattering length (scat) can be derived using the relation 1/att = 1/abs + 1/scat, while its
dependence on wavelength is described by the Kopelevich parameterization [5]:
b  0.0017  (550 /  ) 4.3  1.34v s  (550 /  )1.7  0.312vl  (550 /  ) 0.3 m 1
(1)
where b = 1/scat is the scattering coefficient. In fig. 2 the dependence of the scattering length on
light wavelength is plotted.
1
vs=vl=0.0
222
vs=vl=0.0075
partic
m
o
d
e
l
medsea
mo
del
Fig.2 – Dependence of scattering length on
light wavelength according to the Kopelevich
parameterization. The 2 lines refer to 2 values
of vs and vl and correspond to different
concentrations of scattering centres.
Fig.3 – Scattering phase functions.
The scattering effect depends also on a phase scattering function (.
Some experimental measurements were performed in the past to evaluate both the scattering length
and the phase function. Details on the experimental procedure, setup and on the analysis can be
found in [2].
The phase scattering function can be described as a linear combination of 2 terms (see fig.3) which
take into account the effect of the scattering on water molecules (Rayleigh component) and on
particulate matter (Mie component):
Ray) + (1 – ) part()
(2)
where represents their relative contributions. Its value was obtained using a fit to experimental
measurements and set equal to 0.17 [2]. The particulate component has a strongly forward peaked
scattering distribution.
The water model described by eq.(2) is usually called partic model, in KM3 tables nomenclature.
An alternative definition, referred to as medsea model, is shown in fig. 3.
It can be described as a linear combination of 2 Henyey-Greenstein functions:

medsea(,g1,g2,) =  HG(g1,)+(1-)HG(g2,)
(3)
The values of the parameters are:  = 0.985, g1 = 0.72, g2 = -0.6, where g1,2 are the average cosine
of the scattering angles and  is the relative contribution of the 2 functions.
It includes an important contribution from the particulate scattering and a small component with a
backscattering effect. A detailed description of the models can be found in [2].
The analysis carried out in [2] led to assume, as water model for ANTARES simulations, the so
called partic-0.0075 model for the scattering function, where 0.0075 is the value of vs = vl in the
Kopelevich parameterization, eq. (1). The absorption length dependence on light wavelength is
shown in fig. 4.
2
absorption length
(m)
Smith & Baker standard model
Antares MC
(from NESTOR old
measurements)
Antares measurements
wavelength (nm)
Fig.4 – Dependence of abs on light wavength.
Green points are ANTARES measurements,
while yellow line is the parameterization in
ANTARES MC simulation.
Using this model, a comparison between data and CORSIKA simulation of atmospheric muon flux
was performed.
All details on Monte Carlo production will be summarized in a dedicated internal note.
In the present analysis a small subsample of the full CORSIKA simulation was considered. It was
processed with the full chain of programs simulating the real data stream: MonteCarloEventWriter,
SummaryTimeSliceWriter, TriggerEfficiency and Calibrate [6]. The background was taken from
run 25920 (baseline ~ 54 kHz).
The reconstruction was performed using strategies available in the Real program [6].
As a comparison, a couple of real data runs were analysed (Run 25920 and 25921).
Results of comparison
The influence of the absorption length was studied using KM3 table sets prepared for the
ANTARES and Capo Passero sites. The 2-lines detector was considered. The reconstruction
strategy used both for data and MC is the strategy 2 of Real program. In figs. 5 – 7 the red lines
refer to data and the black ones to MC.
 partic-0.0075 model + ANTARES absorption length
As starting point of the comparison between data and MC, the standard set of KM3 tables was
used. The ratio between data and MC trigger rates is about 5, while the ratio for the
reconstructed track rates is ~ 4.
Results are shown in fig.5: the red line shows the angular distribution of reconstructed real
events, while the black one is the MC distribution, multiplied by 4.
 partic-0.0075 model + Capo Passero absorption length
To evaluate the influence of absorption length, the KM3 tables produced to describe the Capo
Passero site were used. As can be seen from fig. 1, the Capo Passero absorption length is very
close to what expected for pure sea water according to Smith and Baker parameterization [4].
The "partic-0.0075" model for scattering function and scattering length is used.
Result is shown in fig. 6. As expected the number of MC triggers and reconstructed events
increase (the ratios with data are about 3.5 and 3, respectively), but the peak of the angular
distribution seems to be slightly moved wrt data. This could be ascribed to an increased
sensitivity to inclined events due to a larger absorption length.
 no scattering model + Capo Passero absorption length
The NEMO Collaboration prepared a set of tables using the Capo Passero absorption length and
no scattering effect (scattering length = 1000 m). The result of the comparison between MC
simulation with these tables and data is shown in fig. 7.
3
The ratio between data and MC increased (around 7 for trigger rate and 5 for reconstructed track
rate), as the suppression of photon scattering disfavour light collection for downward muons.
The angular distribution shape for MC is significantly different from data.
Fig. 5 - Comparison between data (red line) and MC
simulation (black line) obtained using KM3 tables
with the ANTARES water model (partic-0.0075).
Fig. 6 - Comparison between data (red line) and MC
simulation (black line) obtained using KM3 tables
with the ANTARES scattering model (partic-0.0075)
and the Capo Passero absorption length.
Fig. 7- Comparison between data (red line) and MC
simulation (black line) obtained using KM3 tables
with a no scattering model and the Capo
Passero absorption length.
A further analysis was performed to compare the influence of different models for the scattering
function.
For the medsea model, 2 different values for vs and vl in eq. (1) were used, corresponding to
different concentrations of the scattering centres. Data collected with the 5-line ANTARES detector
were considered, together with the corresponding MC simulation. Note that in figs. 8 – 10 the red
lines refer to MC and the black lines to the data.
4
 partic-0.0075 model + ANTARES absorption length
As a starting point the comparison between data and MC with the standard KM3 tables, for the
ANTARES 5-line detector is shown in fig. 8. No significant difference is evident with respect to
fig. 5, in particular for the agreement between the shapes of data and MC angular distribution.
 medsea-0.0075 model + ANTARES absorption length
Using the medsea model, with the same scattering length, a decrease of trigger and
reconstructed track rates in MC can be observed. This effect could be ascribed to a decrease of
the number of scattered photons due to the reduced component of large angle scattering.
 medsea-0.02 model + ANTARES absorption length
Increasing the number of scattering centres (vs=vl=0.02 in Kopelevich eq.(1)), an increase of
MC trigger rate and reconstructed tracks is seen, but the shape of the angular distribution is
significantly different with respect to data.
track rate (track/s)
Real strategy 3 – step 4
MC partic075 x 4.7
data (run 25921)
Fig. 8 - Comparison between data (black line) and MC
simulation (red line) obtained using KM3 tables
with the ANTARES water model (partic-0.0075).
5-line detector is used.
zenith angle
Fig. 9 - Comparison between data (black line) and MC
simulation (red line) obtained using KM3 tables
with the medsea-0.0075 water model.
5-line detector is used.
track rate (track/s)
Real strategy 3 – step 4
MC medsea02 x 4.4
data (run 25921)
Fig. 10 - Comparison between data (black line) and MC
simulation (red line) obtained using KM3 tables
with the medsea-0.02 water model.
5-line detector is used.
zenith angle
Finally, a preliminary plot obtained with an alternative parameterization for the OMs angular
acceptance [8] is shown in fig.11. A significant increase of trigger and reconstructed track rates and
a further improvement of the agreement of angular distribution shape is evident. A more detailed
analysis is in progress.
In Tab. 1 a summary of water properties used in this analysis, of the ratio between data and MC
reconstructed tracks and of the agreement in angular distribution shape is given.
5
Real strategy 3 – step 4
track rate (track/s)
MC partic075 (NT) x 1.5
data (run 25921)
zenith angle
Fig.11- Comparison between data (black line) and MC
simulation (red line) obtained using KM3 tables with a
new OM’s angular acceptance [7][8].
water
model
partic 0.0075
new tables
partic 0.0075
medsea 0.0075
medsea 0.02
partic 0.0075
Capo Passero
noscat
Capo Passero
abs(m)
scat(m)
@ 470nm @ 470nm
att (m)
@ 470nm
Data/MC
zenith shape
agreement
54.9
52.8
44
1.5
+++++
54.9
62.5
62.5
52.8
52.8
22.3
44
55
49
5
6
4
++++
++
-
70
52.8
54
3
+++
70
1000
70
5
-
Table 1 – Summary of water properties used in the analysis described in this note.
In the last column a qualitative evaluation of the agreement in shape between data
and MC angular distributions is given.
Conclusions
An extensive study on the influence of water properties on MC simulation of the atmospheric muon
flux was performed. The comparison between real data and MC events, using different absorption
lengths and scattering models, shows that the model presently adopted in our simulation chain
(partic-0.0075) is adequate to describe water optical properties of the Toulon site. In particular it is
able to reproduce satisfactorily the shape of the angular distribution of reconstructed tracks.
On the other hand, the choice of the water model does not affect significantly the trigger and the
reconstructed track rates, at least not enough to solve the discrepancy MC/data puzzle. A possible
way out is the use of KM3 tables obtained with a new parameterization for OM’s angular
acceptance, see [8] and fig. 11.
References
1- S. Navas and L. Thompson, ANTARES-SOFT-1999-011; D. Bailey, ANTARES-SOFT-2002-006.
2- N. Palanque-Delabrouille, ANTARES-SITE-1999-003; ANTARES-SITE-2000-002; ANTARES-SITE-2001002; ANTARES-SITE-2003-001; J. Aguilar et al., Astrop. Phys. 23 (2005)131.
3- G. Riccobene, Overview over Mediterranean water parameters, VLVnT Workshop Amsterdam, October 4-11
2003, http://www.vlvnt.nl
4- C.D.Mobley, Light and Water (Radiative Transfer in Natural Water), Academic Press (1994).
5- O.V.Kopelevich and E.M.Mezhericher, Izv. Akad. Nauk. SSSR, Fiz. Atmos. Okean., 19(2), 144(1983).
6- http://antares.in2p3.fr/users/becherin/internal/software/software.html
7- P. Kooijman, ANTARES-PHYS-2007-002.
8- M. Spurio and A. Margiotta, ANTARES-SOFT-2007-005.
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