Measurement of the Aerosol Phase Function
at the Pierre Auger Observatory
S.Y. BenZvi a, B.M. Connolly a, J.A.J. Matthews b, M. Prouza a,
E.F. Visbal a,c, and S. Westerhoff a
aColumbia University, Department of Physics and Nevis Laboratories, 538 West
120 th Street, New York, NY 10027, USA
bUniversity of New Mexico, Department of Physics and Astronomy, Albuquerque,
NM 87131, USA
cCarnegie Mellon University, Department of Physics, Pittsburgh, PA 15213, USA
Abstract
Air fluorescence detectors measure the energy of ultra-high energy cosmic rays by
collecting fluorescence light emitted from nitrogen molecules along the extensive air
shower cascade. To ensure a reliable energy determination, the light signal needs
to be corrected for atmospheric effects, which not only attenuate the signal, but
also produce a non-negligible background component due to scattered Cherenkov
light and multiple-scattered light. The correction requires regular measurements
of the aerosol attenuation length and the aerosol phase function, defined as the
probability of light scattered in a given direction. At the Pierre Auger Observatory
in Malargüe, Argentina, the phase function is measured on an hourly basis using
two Aerosol Phase Function (APF) light sources. These sources direct a UV light
beam across the field of view of the fluorescence detectors; the phase function can
be extracted from the image of the shots in the fluorescence detector cameras.
This paper describes the design, current status, standard operation procedure, and
performance of the APF system at the Pierre Auger Observatory.
Key words: Ultra-high energy cosmic rays; air fluorescence detectors; atmospheric
monitoring; aerosol phase function
PACS: 42.68.-w, 42.68.Jg, 92.60.Mt, 92.60.Sz, 96.50.sd
1 Introduction
The Pierre Auger Observatory in Malargüe, Argentina, is designed to study
the origin of ultra-high energy cosmic rays with energies above 1018 eV. While
Preprint submitted to Astroparticle Physics 30 October 2018
http://arxiv.org/abs/0704.0303v2
still under construction, scientific data taking began in 2004, and first results
have been published [1,2,3].
The Pierre Auger Observatory is a hybrid detector that combines two tech-
niques traditionally used to measure cosmic ray air showers: surface particle
detection and air fluorescence detection. Both detector types measure the cos-
mic ray primary indirectly, using the Earth’s atmosphere as part of the de-
tector medium. When the primary particle enters the atmosphere, it interacts
with air molecules, initiating a cascade of secondary particles, the so-called ex-
tensive air shower. Surface detectors in the form of ground arrays sample the
shower front as it impacts the ground, whereas air fluorescence detectors make
use of the fact that the particles in the air shower excite nitrogen molecules
in the air, causing UV fluorescence. Using photomultiplier cameras to record
air shower UV emission, we can observe showers as they develop through the
atmosphere and obtain a nearly calorimetric estimate of the shower energy.
Upon completion, the surface detector (SD) array of the Pierre Auger Ob-
servatory will comprise 1600 water Cherenkov detector tanks, deployed in a
hexagonal grid over an area of 3000 km2, and four fluorescence detector (FD)
stations overlooking the SD from the periphery. An advantage of combining
both detector types at the same site is the possibility to cross-calibrate. Based
on the subset of events seen with both detectors, the nearly calorimetric in-
formation of the FD provides the energy calibration of the SD.
For the calibration to be meaningful, the properties of the calorimeter, i.e.
the atmosphere, must be well-known. At the Pierre Auger Observatory, this is
achieved by an extensive program to monitor the atmosphere within the overall
FD aperture and measure atmospheric attenuation and scattering properties
in the 300 to 400 nm wavelength band recorded by the FDs [4,5,6].
Two primary forms of atmospheric light scattering need to be considered:
molecular, or Rayleigh, scattering, mainly due to nitrogen and oxygen molecules;
and aerosol scattering due to airborne particulates. The angular distribution
of scattered light in both types of scattering may be described by a phase
function P (θ), defined as the probability per unit solid angle of scattering
through an angle θ.
Rayleigh scattering allows for an analytical treatment, and assuming isotropic
scattering, the Rayleigh phase function has the well known 1 + cos2 θ angular
dependence. Matters are more complicated for aerosols, because the scatter-
ing cross section depends on the size distribution and shape of the scatter-
ers. Forward scattering typically dominates in this case, but the fraction of
forward-scattered light varies strongly with aerosol type. Moreover, a rigorous
analytical treatment is not possible, though the literature gives various ap-
proximations. For example, if one assumes spherical particles with a known or
estimated size distribution, then aerosol scattering can be described analyti-
cally using Mie theory [7]. In practice, however, aerosols vary a great deal in
size and shape, and the aerosol content of the atmosphere changes on short
time scales as wind lifts up dust, weather fronts pass through, or rain removes
dust from the atmosphere.
The FD reconstruction of the primary cosmic ray particle energy must account
not only for light that is “lost” between the shower and the camera due to
scattering, but also for direct and indirect Cherenkov light contributing to
the FD signal. The amount of Cherenkov light seen by the FDs depends on
the viewing angle, i.e. the angle between the shower axis and the FD line of
sight, and can be calculated once the geometry of the air shower is determined.
At small viewing angles, direct Cherenkov light dominates, while at viewing
angles greater than ∼ 20◦, the FDs detect mainly “indirect” Cherenkov light
scattered into the FD field of view. To calculate this scattered component, the
aerosol phase function needs to be known. Finally, a small multiple scattering
component also adds to the contamination of the fluorescence light and must
be removed [8].
The Aerosol Phase Function (APF) light sources [9,10], in conjunction with
the fluorescence detectors at the Pierre Auger Observatory, are designed to
measure the aerosol phase function on an hourly basis during FD data tak-
ing. The APF light sources direct a near-horizontal pulsed light beam across
the field of view of a nearby FD. The aerosol phase function can then be re-
constructed from the intensity of the light observed by the FD cameras as a
function of scattering angle. Since the FD telescopes cover about 180◦ in az-
imuth, the aerosol phase function is measured over a wide range of scattering
angles.
Currently, APF light sources are installed and operating at two of the FDs.
With their ability to measure the angular distribution of the scattered light,
the APF light sources are meant to complement other atmospheric monitoring
tools at the Auger site which measure the optical depth, and therefore the
amount of attenuation due to aerosols.
This paper describes the design and performance of the APF light sources.
It is structured as follows. Section 2 gives a description of the APF facilities.
Section 3 describes how the aerosol phase function is determined from the
APF data. In Section 4, we show first results for data taken between June and
December 2006. Section 5 summarizes the paper.
Fig. 1. Schematic layout of the Pierre Auger Observatory. The shaded area indicates
the shape and size of the surface detector area. The fluorescence detectors are placed
at the periphery of the surface detector array. The field of view of the 6 bays of each
fluorescence detector (FD) is indicated by the lines. From the Central Laser Facility
(CLF) [6] in the center of the surface detector array, a pulsed UV laser beam is
directed into the sky, providing another test beam which can be observed by the FDs.
2 APF Light Sources
2.1 Detector Buildings, Optics, and Electronics
The Auger FD comprises four detector stations (see Fig. 1). At present, the
sites at Los Leones, Coihueco, and Los Morados are completed and fully opera-
tional, while the fourth site at Loma Amarilla is under construction. APF light
sources are operating at the Coihueco and Los Morados FD sites. Both were
built by the University of New Mexico group [10]. Fig. 2 shows a photograph
of the APF container building at Los Morados.
Each APF building contains sources which operate at different wavelengths in
the region of interest between 300 nm and 400 nm. During the initial studies
described in this paper, only one light source with a Johnson U-band filter
of central wavelength 350 nm was used. However, in the near future, we plan
to operate the light sources at several wavelengths to study the wavelength
dependence of the phase function over the full range of the FD sensitivity.
The light beam is provided by a broad-band Xenon flash lamp source from
Fig. 2. Photos of the enclosure (left) and the light source (right) at the Los Morados
APF facility. In the photograph on the left, the Los Morados FD can be seen on the
horizon (to the left of the container).
Perkin Elmer Optoelectronics (model LS-1130-4 FlashPac with FX-1160 flash
lamp). The Xenon flash lamps were chosen because of their excellent stability
in intensity and pulse shape. A Johnson/Cousins (Bessel) U-band filter from
Omega Optical Inc. (part number XBSSL/U/50R) selects a central wavelength
of ∼ 350 nm, FWHM 60 nm) from the broad flash lamp spectrum. The beam
is focused using a 20.3 cm diameter UV enhanced aluminum spherical mirror
(speed f/3) from Edmund Scientific Co. (part number R43-589). All optical
components are assembled on a commercial optical plate. We use Thor optical
table parts, assembled from Nomex Epoxy/Fiberglass 1.91 cm panels from
TEKLAM (part number N507EC).
The Xenon lamps rest inside refurbished 6.1 m shipping containers, and the
light is sent through a 0.749 cm thick acrylite UV transmitting window (Cyro
Industries acrylite OP-4 UVT acrylic). Each light source provides a nearly
horizontal beam of divergence ≤ 10 mrad pulsed across the field of view of the
nearby fluorescence detector. Computer control occurs from the correspond-
ing FD building. A serial radio link (YDI Wireless, model 651-900001-001
(TranzPoint ESC-II Kit)) connects the computer to a commercial ADC/relay
system (model ADC-16F 16 channel 8 bit ADC and RH-8L 8-relay card from
Electronic Energy Control Inc.) at the light source.
Once during each hour of FD data taking, the ADC/relay system enables a
1 Hz GPS pulser (CNS Systems Inc., model CNSC01 with TAC32 software)
and a 12 V to 24 V inverter to power the Xenon flash lamps. Each lamp fires
a set of 5 shots, pulsed at 2 second intervals. The APF events are flagged by
the FD data acquisition system and the corresponding FD data are stored on
disk in especially designated APF data files.
When the light sources are not operating, only the radio link and the ADC
board are powered. The total current draw is therefore only ∼ 0.2 A at 12 V,
and the whole system can be powered by batteries recharged during the day
with 12 V solar panels (two Siemens SP75 75 W solar modules with Trace
C35 controller).
2.2 APF Signals in the Fluorescence Detectors
The light beam produced by the APF sources is observed by the cameras of
the corresponding FD site. The FD detectors of the Pierre Auger Observatory
are described in detail elsewhere [11]. Here, we only give a short summary of
the main characteristics relevant for the analysis of APF shots.
Each Auger FD site contains six bays, and each bay encloses a UV telescope
composed of a spherical light-collecting mirror, a photomultiplier camera at
the focal surface, and a UV transmitting filter in the aperture. The mirrors
have a radius of curvature of 3.4 m and an area of about 3.5 × 3.5 m2. The
camera consists of 440 photomultipliers with a hexagonal bialkaline photo-
cathode, arranged in a 20× 22 array. Each camera has a field of view of 30.0◦
in azimuth and 28.6◦ in elevation, covering an elevation angle range from 1.6◦
to 30.2◦ above horizon. To reduce optical aberrations, including coma, the FD
telescopes use Schmidt optics with a circular diaphragm of diameter 2.2 m
placed at the center of curvature of the mirror, and a refractive corrector ring
at the telescope aperture.
Fig. 3 shows an APF shot as seen by the Coihueco FD. Five out of the 6 bays
of the Coihueco FD site observe light from the Coihueco APF facility. In this
figure, the light travels from right to left. Fig. 4 shows the relative positions
of the APF source and the FD at the Coihueco site. The geometry is in part
dictated by the local topography, and consequently is slightly different for the
Los Morados site.
Fig. 3. The APF pulse as seen by the Coihueco FD. The light travels from right
to left, and each PMT Cluster observes 30◦ in azimuth. Note that the projection of
the approximately horizontal APF beam onto the spherical FD surface results in a
curved track.
Fig. 4. Scheme of the location of the Coihueco APF light source relative to the
Coihueco FD. Located at the center is the Coihueco FD with its field of view in-
dicated. The value of α is 26◦ and β is 38◦, measured from the North. The shot
direction γ is about 24◦.
3 Determination of the Aerosol Phase Function
The signal from the APF light source observed by the ith pixel of a fluorescence
detector can be expressed as
Si = I0 · Ti ·
·∆zi ·∆Ωi · ǫi . (1)
In this equation, I0 is the light source intensity; Ti is the transmission factor
e−ri/Λtot which accounts for light attenuation from the beam to the pixel; ri
is the distance from the beam to the detector; Λtot, Λm, and Λa are the total,
molecular, and aerosol extinction length, respectively; and σ−1m dσm/dΩ and
σ−1a dσa/dΩ are the normalized differential molecular and aerosol scattering
cross sections, respectively, which are identical to the phase functions Pm(θ)
and Pa(θ). The integral of Pm(θ) and Pa(θ) over all solid angles is equal to 1.
Finally, ∆zi, ∆Ωi, and ǫi are the track length, detector solid angle, and the
efficiency for the ith pixel of the detector.
The data come in the form of total PMT signal per pixel from a particular shot.
Those data are binned as a function of azimuth and averaged between the five
shots taken within 10 seconds. In this analysis, 5◦ bins are used, although the
fit is relatively insensitive to the number of bins. Each FD pixel is hexagonally
shaped, so for those lying at the boundary of two azimuth bins, the fractional
area of the hexagon in each bin is used to properly distribute the signal. The
signal in each pixel is divided by ∆zi, 1/r
i and ǫi to correct for the geometry of
the beam and pixel calibration. Note that in the roughly cylindrical geometry
of the FD-APF beam, the ∆zi and 1/r
i corrections almost completely cancel
Typical values for the aerosol extinction length in dry atmospheres are be-
tween 10 km and 20 km, reaching 40 km for very clear conditions. Since the
perpendicular distance from the beam to the FD is only on the order of a
few hundred meters, it is reasonable to assume full atmospheric transmission
(Ti = 1) over the length of the beam. In reality, this assumption does not
hold well for the most distant beam points, so these points are not used in
the present study. In the near future, measurements of the extinction length
from the Auger lidar stations [5] will be used to improve the APF analysis.
In another approximation, we assume that the extinction lengths are identi-
cal for each pixel for single measurements and do not require an index i. In
principle, the extinction length depends on the number density of scatterers
and is therefore a function of the density (temperature, pressure) of the air.
Given corrections for geometry, attenuation, and pixel efficiency, Eq. 1 reduces
Si = C ·
, (2)
where C is a constant whose value is unimportant because arbitrary units are
sufficient in determining the phase function.
From the theory of Rayleigh scattering it is known that the Rayleigh phase
function is
Pm(θ) =
16 π(1 + 2 γ)
(1 + 3 γ) + (1− γ) cos2 θ
where γ accounts for the effect of molecular anisotropy on Rayleigh scattering.
For isotropic scattering, γ = 0, this reduces to the familiar
Pm(θ) =
(1 + cos2 θ) . (4)
The effect of the anisotropy is small and wavelength-dependent. Bucholtz [12]
Fig. 5. Schematic of track seen by ith pixel.
estimates γ ≃ 0.015 at 360 nm and concludes that the correction leads to
a ∼ 3% systematic increase in the Rayleigh scattering cross section, and a
fractional change ≤ 1.5% from the approximate (1 + cos2 θ). In our analysis,
only the shape of the function is relevant, and we use Eq. 4 as an approximation
of Eq. 3.
The aerosol phase function is often parameterized by the Henyey-Greenstein
function [13]:
Pa(θ) =
1− g2
(1 + g2 − 2gµ)3/2
, (5)
where µ = cos θ and g is an asymmetry parameter equal to the mean cosine of
the scattering angle: g = 〈cos θ〉. The parameter g is a measure of how much
light is scattered in the forward direction; a greater g means more light is
forward-scattered. Values for g range from g = 1 (total forward scattering) to
g = −1 (total backward scattering), with g = 0 indicating isotropic scattering.
The Henyey-Greenstein function works well for pure forward scattering, but
it cannot describe realistic aerosol conditions, which typically give rise to non-
negligible backscattering. Following [14,15], we modify Eq. 5 so that
Pa(θ) =
1− g2
(1 + g2 − 2gµ)3/2
3µ2 − 1
2(1 + g2)3/2
. (6)
The new term in this expression is proportional to the second Legendre poly-
nomial, and it is introduced to describe the extra backscattering component.
The value f is a fit parameter used to tune the relative strength of forward to
backward scattering.
The binned APF signal observed in the FD is therefore subjected to a 4-
parameter fit:
Si = A · (1 + µ
i ) +B · (1− g
(1 + g2 − 2gµi)3/2
3µ2i − 1
2(1 + g2)3/2
, (7)
where A, B, g and f are the fit parameters.
In principle, the parameters A and B, which describe the relative amount of
Rayleigh and Mie scattering, can be determined from measurements of the
extinction lengths Λm and Λa and assumptions about the particle albedo,
i.e. the ratio of light scattered by the aerosol particle in all directions to the
amount of incoming light. The albedo is close to one if the particle is mostly
reflective. Since local information on the extinction lengths was not available
for this analysis, we use A and B as additional fit parameters. We find that
the distinct shapes of the two phase functions does allow a determination of
A and B from the data themselves.
At Coihueco, the APF signal is seen in 5 out of the 6 mirrors, so the track is
visible over ∼ 150◦ in azimuth. At the boundary between each mirror there
is some overlap in the fields of view of pixels. This overlap produces a double
counting of signal resulting in the value of bins at boundaries being too large.
These bins are simply ignored in the fit. The values of the other bins and their
errors are obtained from the mean and standard deviation of the five APF
shots in each shot sequence.
On clear nights with few or no aerosols, the fit to Eq. 7 returns unphysical val-
ues for the parameters B, f , and g. In those cases, we re-fit the data to a pure
Rayleigh function by setting B, f , and g equal to zero. Two examples of fits,
one for a night with aerosol content, and one for a night with pure Rayleigh
scattering, are shown in Fig. 6. The aerosol, molecular, and total phase func-
tions are shown. The aerosol phase function is obtained by subtracting the
molecular component determined by the fit.
We fit the data only over a subrange of the available scattering angles, from
θmin ≃ 32.5
◦ to θmax ≃ 147.3
◦. As Fig. 6 indicates, the data deviates from
the theoretical prediction for scattering angles below θmin and above θmax.
At smaller and larger angles, several effects corrupt the signal and make it
unusable for the fit to the phase function. Due to the local geometry at the
Coihueco site (see Fig. 4), the APF shot is not visible for θ < 24◦, and below
30◦, the signal is incomplete because the beam is still partially beneath the
detector field of view. At large scattering angles, the beam is at a rapidly in-
creasing distance to the corresponding FD bay, and attenuation of light from
the beam to the detector becomes important. As mentioned earlier, because
local measurements of the optical depth are not yet available, we simply as-
sume T = 1. As measurements of T become available, the attenuation of light
scattered at large angles can be used to correct the data.
]° [θscattering angle 
0 20 40 60 80 100 120 140 160 180
A         46.2±  8602 
B         1814± 2.696e+05 
g         0.0036± 0.6804 
f         0.0147± 0.4977 
Aerosol Phase Function
Total phase function
Rayleigh phase function
Mie phase function
]° [θscattering angle 
0 20 40 60 80 100 120 140 160 180
10000
15000
20000
25000
30000
35000
40000
45000
50000
A         19± 1.011e+04 Aerosol Phase Function
Total phase function
Rayleigh phase function
Mie phase function
Fig. 6. Two examples for APF data fits on different days. In the upper plot (June
28, 2006, 5:12 am local time) aerosols are visible. Data are fit to the function given
in Eq. 7. The phase function in the lower plot (July 2, 2006, 3:12 am local time) is
consistent with pure Rayleigh scattering. Data are fit to Eq. 7, with B = 0, f = 0,
and g = 0. Error bars for both plots are the standard deviation of the 5 APF events.
In order to apply geometrical corrections when binning the data, the angle at
which the APF light source shoots (γ in Fig. 4) with respect to the FD and the
elevation angle of the shot direction needs to be known. We determined these
values from the data themselves. The elevation angle was determined from a
reconstruction of APF shots with the FD offline reconstruction [16], and γ was
determined from the analysis of APF shots on nights where aerosol scattering
was negligible. The data from these nights were fit to the Rayleigh component
of the phase function, with the position of the minimum (nominally at 90◦
scattering angle) as a free parameter. The fit value of this angle was then used
to deduce the direction which the APF light source shoots relative to the FD
(∼ 24◦ at Coihueco).
4 First Results
We have applied the analysis described in Section 3 to data recorded between
June and December 2006 at the Coihueco site. Since the APF light sources
operate during all nights of FD operation, this data set includes all moonless
nights, with the exception of nights with rain or strong winds when the FDs
remain closed. Fig. 7 shows the distribution of the asymmetry parameter g
(left) and the backscatter parameters f (right). For most nights with aerosol
contamination, the value of g at the experiment site in Malargüe is ∼ 0.6,
with an average of 0.59 and a standard deviation of 0.07 for the data period
analyzed here. Values of g = 0 indicate hours where the measured phase
function can be described by pure Rayleigh scattering, so the aerosol phase
function is effectively negligible. Fig. 7 also shows the asymmetry parameter
as a function of time for the analyzed period. With the limited amount of data
taken so far, no conclusions concerning seasonal variations can be drawn. The
asymmetry parameter appears to be stable during the observed time period.
With more data becoming available over the next few years, we plan to monitor
the month-to-month variation in g and analyze possible correlations with other
weather measurements.
One of the main tasks of the APF, in addition to providing the in situ aerosol
phase function for every hour of FD data taking, is the identification of “clear”
nights with small aerosol contamination. These nights play an important role
in the calibration of other atmospheric monitoring devices such as the Central
Laser Facility (CLF) [6]. On clear nights, the measured phase function can be
described by pure Rayleigh scattering (measurements where this is the case
appear as g = 0 in Fig. 7).
To confirm the reliability of the fit where both the normalization of the Mie
and the Rayleigh contribution are fit parameters, Fig. 8 shows the Rayleigh
normalization factor A for the same data set. One might expect the molecular
asymmetry parameter g
0 0.2 0.4 0.6 0.8 1
backscatter parameter f
-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Jun 2006 Jul 2006 Aug 2006 Sep 2006 Oct 2006 Nov 2006 Dec 2006
Fig. 7. Top: Distribution of the asymmetry parameter g (top left) and the backscatter
parameter f (top right) for all measurements performed between June and December
2006. Values of g = 0 (and f = 0) indicate that the phase function can be described
with pure Rayleigh scattering. Bottom: Asymmetry parameter g as a function of
time.
contribution to be rather stable, and in fact this parameter does not change
much with time.
It is instructive to compare the average asymmetry parameter obtained from
the APF with model expectations and measurements at comparable locations.
Typically, measurements are performed at optical wavelengths and cannot be
directly compared to measurements at UV wavelengths. However, a compi-
lation at different wavelengths from 450 nm to 700 nm [17] shows that the
wavelength dependence of g is small; values at 450 nm are a few percent
larger than at 550 nm.
Rayleigh normalization
4000 6000 8000 10000 12000 14000 16000
Fig. 8. Distribution of the Rayleigh normalization parameter A for all measurements
performed between June and December 2006.
To first order, g = 0.7 is often used as a generic value for g in radiative transfer
models. A smaller value for g is expected at dry locations. A parameterization
of aerosol optical properties by d’Almeida et al. [18] suggests values for g
between 0.64 and 0.83 at 550 nm depending on aerosol type and season, with
higher averages for high relative humidity.
The Pierre Auger Observatory is located east of the Andes in the Pampa
Amarilla, an arid high plateau at 1420 m a.s.l., so values around 0.6 are within
expectations. For comparison, recent measurements carried out in the South-
ern Great Planes of the US [19] yield values for g at 550 nm of 0.60± 0.03 for
dry conditions and 0.65± 0.05 for ambient conditions.
The aerosol phase function most commonly used in fluorescence detector data
analysis, both for the High Resolution Fly’s Eye (HiRes) Experiment [20],
which operated in Utah between 1997 and 2006, and the Pierre Auger FD de-
tectors, is the function obtained from a desert aerosol simulation by Longtin [21].
Longtin’s desert model is based on Mie scattering theory and assumes that the
desert atmosphere has three major components: carbonaceous particles, water-
soluble particles, and sand. For each aerosol component, the model assumes a
characteristic log normal size distribution and refractive index. Longtin per-
formed his calculations for several wavelengths and wind speeds; those made
at 550 nm with a wind speed of 10 m/s most closely match the 300 nm to
400 nm nitrogen fluorescence band observed by the FDs and have therefore
been traditionally used in air fluorescence data analysis.
]° [θscattering angle 
0 20 40 60 80 100 120 140 160 180
Aerosol Phase Function
 = 550 nm, wind = 10 m/s)λLongtin (
This work: f = 0.5, g = 0.7
This work: f = 0.4, g = 0.6
Fig. 9. Comparison of the Longtin aerosol phase function (desert atmosphere simu-
lated with a wind speed of 10 m/s) with the default phase function used in the Auger
atmospheric database (f = 0.5, g = 0.7) and the typical phase function measured by
the APF (f = 0.4, g = 0.6).
Fig. 9 compares the Longtin aerosol phase function at 550 nm to the modi-
fied Henyey-Greenstein function of Eq. 6 with two sets of f and g: f = 0.5
and g = 0.7, the default values used by the Auger atmospheric database; and
f = 0.4 and g = 0.6, the values determined in this study to be more typical
of the detector location. The comparison shows that, on average, the differ-
ence between the Longtin function and the measured phase function is small
for those scattering angles relevant in fluorescence measurements — ∼ 30◦
to 150◦. Only at the largest scattering angles above 160◦ do the phase func-
tions differ notably. This region is outside the current range of validity of our
measurement.
Our primary interest in aerosol scattering is its effect on the air shower recon-
struction, most notably the determination of the shower energy. However, it is
not straightforward to estimate the extent to which the use of measured rather
than averaged values of f and g changes the energy reconstruction, as this
depends strongly on other atmospheric parameters, for example the aerosol
optical depth. Rather than singling out the phase function measurement, we
need to study the effect of the combined measurement of all atmospheric pa-
rameters, a task which is beyond the scope of this paper.
We can, however, get an estimate of the relevance of the phase function mea-
surement by studying its effect on the energies of events that are of particu-
lar importance for the energy calibration of the detector, the “golden hybrid
hist1
Mean   0.6996
RMS    0.7913
) / Eapf - Estd(E
-10 -8 -6 -4 -2 0 2 4 6 8 10
210 hist1
Mean   0.6996
RMS    0.7913
f > 0, g > 0
Mean   0.71
RMS    0.79
f = 0, g = 0
Mean   1.87
RMS    2.34
Weather Conditions
f > 0, g > 0
f = 0, g = 0
Fig. 10. Differences in the energies of golden hybrid events reconstructed with de-
fault phase function values (Estd) and those reconstructed using phase function fit
parameters determined from APF measurements (Eapf). The red (bold) histogram
represents data taken during nights with measurable aerosols; the blue (light) his-
togram depicts events observed on purely molecular nights.
events.” These are events observed by one or more fluorescence detectors and
three or more surface array tanks. For “golden hybrid events” observed by the
Coihueco FD site between June and December 2006, we performed the recon-
struction twice: first, using the default parameters f = 0.5 and g = 0.7 to
estimate aerosol scattering; and second, using the fit parameters determined
from APF measurements. In both cases atmospheric extinction was simu-
lated using an average aerosol profile model representative of the Malargüe
site [22,23].
Fig. 10 depicts the relative differences in energies caused by reconstructing
showers with the default phase function and the measured phase function.
The red (bold) histogram represents data taken during nights with aerosol
contamination (f > 0, g > 0) while the blue (light) histogram represents
data taken during nights where according to the APF analysis scattering is
purely molecular. The correction is typically of order one percent. However,
on those nights when aerosol loading is extremely low, so that atmospheric
scattering may be characterized as purely molecular, the use of the default
scattering parameters causes larger errors in the shower reconstruction. Under
such conditions, the total phase function lacks the strong forward-scattering
component typical of aerosols. During these periods, incorrectly accounting
for aerosol scattering starts to impact the energy calibration of the detector.
A correct determination of the phase function on a regular basis is therefore
an important part of the atmospheric monitoring efforts at the site.
5 Conclusions and Outlook
As part of the atmospheric monitoring program at the Pierre Auger Obser-
vatory, the aerosol phase function at 350 nm is routinely measured at two of
the four FD sites. A first analysis of data taken from June to December 2006
shows that values of g = 〈cos θ〉 ≃ 0.6 for the mean cosine of the scattering
angle θ are typical for aerosols at the site of the experiment. Over the next
several years, the APF light sources will produce a data set of unprecedented
size of the scattering properties of aerosols. This data set will enable us to
carefully study any seasonal change in the aerosol content. The APF light
sources and the other atmospheric monitoring instruments at the Auger site
will accumulate one of the largest sets of continuous measurements in the
300 nm to 400 nm range ever recorded for a single location.
The APF light sources are currently operating at a wavelength of 350 nm only.
In the near future, we will add regular measurements at 330 nm and 390 nm to
study the dependence of the phase function on the wavelength of the scattered
light.
Acknowledgements
We are grateful to the following agencies and organizations for financial sup-
port: The APF light sources were built by a grant from the Department of
Energy (DOE) Office of Science (USA) (DE-FG03-92ER40732). Parts of the
APF analysis were performed during the 2006 REU (Research Experience for
Undergraduates) program at Columbia University’s Nevis Laboratories which
is supported by the National Science Foundation (USA) under contract num-
ber NSF-PHY-0452277.
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	Introduction
	APF Light Sources
	Detector Buildings, Optics, and Electronics
	APF Signals in the Fluorescence Detectors
	Determination of the Aerosol Phase Function
	First Results
	Conclusions and Outlook
	Acknowledgements
	References

  Air fluorescence detectors measure the energy of ultra-high energy cosmic
rays by collecting fluorescence light emitted from nitrogen molecules along the
extensive air shower cascade. To ensure a reliable energy determination, the
light signal needs to be corrected for atmospheric effects, which not only
attenuate the signal, but also produce a non-negligible background component
due to scattered Cherenkov light and multiple-scattered light. The correction
requires regular measurements of the aerosol attenuation length and the aerosol
phase function, defined as the probability of light scattered in a given
direction. At the Pierre Auger Observatory in Malargue, Argentina, the phase
function is measured on an hourly basis using two Aerosol Phase Function (APF)
light sources. These sources direct a UV light beam across the field of view of
the fluorescence detectors; the phase function can be extracted from the image
of the shots in the fluorescence detector cameras. This paper describes the
design, current status, standard operation procedure, and performance of the
APF system at the Pierre Auger Observatory.

Introduction
The Pierre Auger Observatory in Malargüe, Argentina, is designed to study
the origin of ultra-high energy cosmic rays with energies above 1018 eV. While
Preprint submitted to Astroparticle Physics 30 October 2018
http://arxiv.org/abs/0704.0303v2
still under construction, scientific data taking began in 2004, and first results
have been published [1,2,3].
The Pierre Auger Observatory is a hybrid detector that combines two tech-
niques traditionally used to measure cosmic ray air showers: surface particle
detection and air fluorescence detection. Both detector types measure the cos-
mic ray primary indirectly, using the Earth’s atmosphere as part of the de-
tector medium. When the primary particle enters the atmosphere, it interacts
with air molecules, initiating a cascade of secondary particles, the so-called ex-
tensive air shower. Surface detectors in the form of ground arrays sample the
shower front as it impacts the ground, whereas air fluorescence detectors make
use of the fact that the particles in the air shower excite nitrogen molecules
in the air, causing UV fluorescence. Using photomultiplier cameras to record
air shower UV emission, we can observe showers as they develop through the
atmosphere and obtain a nearly calorimetric estimate of the shower energy.
Upon completion, the surface detector (SD) array of the Pierre Auger Ob-
servatory will comprise 1600 water Cherenkov detector tanks, deployed in a
hexagonal grid over an area of 3000 km2, and four fluorescence detector (FD)
stations overlooking the SD from the periphery. An advantage of combining
both detector types at the same site is the possibility to cross-calibrate. Based
on the subset of events seen with both detectors, the nearly calorimetric in-
formation of the FD provides the energy calibration of the SD.
For the calibration to be meaningful, the properties of the calorimeter, i.e.
the atmosphere, must be well-known. At the Pierre Auger Observatory, this is
achieved by an extensive program to monitor the atmosphere within the overall
FD aperture and measure atmospheric attenuation and scattering properties
in the 300 to 400 nm wavelength band recorded by the FDs [4,5,6].
Two primary forms of atmospheric light scattering need to be considered:
molecular, or Rayleigh, scattering, mainly due to nitrogen and oxygen molecules;
and aerosol scattering due to airborne particulates. The angular distribution
of scattered light in both types of scattering may be described by a phase
function P (θ), defined as the probability per unit solid angle of scattering
through an angle θ.
Rayleigh scattering allows for an analytical treatment, and assuming isotropic
scattering, the Rayleigh phase function has the well known 1 + cos2 θ angular
dependence. Matters are more complicated for aerosols, because the scatter-
ing cross section depends on the size distribution and shape of the scatter-
ers. Forward scattering typically dominates in this case, but the fraction of
forward-scattered light varies strongly with aerosol type. Moreover, a rigorous
analytical treatment is not possible, though the literature gives various ap-
proximations. For example, if one assumes spherical particles with a known or
estimated size distribution, then aerosol scattering can be described analyti-
cally using Mie theory [7]. In practice, however, aerosols vary a great deal in
size and shape, and the aerosol content of the atmosphere changes on short
time scales as wind lifts up dust, weather fronts pass through, or rain removes
dust from the atmosphere.
The FD reconstruction of the primary cosmic ray particle energy must account
not only for light that is “lost” between the shower and the camera due to
scattering, but also for direct and indirect Cherenkov light contributing to
the FD signal. The amount of Cherenkov light seen by the FDs depends on
the viewing angle, i.e. the angle between the shower axis and the FD line of
sight, and can be calculated once the geometry of the air shower is determined.
At small viewing angles, direct Cherenkov light dominates, while at viewing
angles greater than ∼ 20◦, the FDs detect mainly “indirect” Cherenkov light
scattered into the FD field of view. To calculate this scattered component, the
aerosol phase function needs to be known. Finally, a small multiple scattering
component also adds to the contamination of the fluorescence light and must
be removed [8].
The Aerosol Phase Function (APF) light sources [9,10], in conjunction with
the fluorescence detectors at the Pierre Auger Observatory, are designed to
measure the aerosol phase function on an hourly basis during FD data tak-
ing. The APF light sources direct a near-horizontal pulsed light beam across
the field of view of a nearby FD. The aerosol phase function can then be re-
constructed from the intensity of the light observed by the FD cameras as a
function of scattering angle. Since the FD telescopes cover about 180◦ in az-
imuth, the aerosol phase function is measured over a wide range of scattering
angles.
Currently, APF light sources are installed and operating at two of the FDs.
With their ability to measure the angular distribution of the scattered light,
the APF light sources are meant to complement other atmospheric monitoring
tools at the Auger site which measure the optical depth, and therefore the
amount of attenuation due to aerosols.
This paper describes the design and performance of the APF light sources.
It is structured as follows. Section 2 gives a description of the APF facilities.
Section 3 describes how the aerosol phase function is determined from the
APF data. In Section 4, we show first results for data taken between June and
December 2006. Section 5 summarizes the paper.
Fig. 1. Schematic layout of the Pierre Auger Observatory. The shaded area indicates
the shape and size of the surface detector area. The fluorescence detectors are placed
at the periphery of the surface detector array. The field of view of the 6 bays of each
fluorescence detector (FD) is indicated by the lines. From the Central Laser Facility
(CLF) [6] in the center of the surface detector array, a pulsed UV laser beam is
directed into the sky, providing another test beam which can be observed by the FDs.
2 APF Light Sources
2.1 Detector Buildings, Optics, and Electronics
The Auger FD comprises four detector stations (see Fig. 1). At present, the
sites at Los Leones, Coihueco, and Los Morados are completed and fully opera-
tional, while the fourth site at Loma Amarilla is under construction. APF light
sources are operating at the Coihueco and Los Morados FD sites. Both were
built by the University of New Mexico group [10]. Fig. 2 shows a photograph
of the APF container building at Los Morados.
Each APF building contains sources which operate at different wavelengths in
the region of interest between 300 nm and 400 nm. During the initial studies
described in this paper, only one light source with a Johnson U-band filter
of central wavelength 350 nm was used. However, in the near future, we plan
to operate the light sources at several wavelengths to study the wavelength
dependence of the phase function over the full range of the FD sensitivity.
The light beam is provided by a broad-band Xenon flash lamp source from
Fig. 2. Photos of the enclosure (left) and the light source (right) at the Los Morados
APF facility. In the photograph on the left, the Los Morados FD can be seen on the
horizon (to the left of the container).
Perkin Elmer Optoelectronics (model LS-1130-4 FlashPac with FX-1160 flash
lamp). The Xenon flash lamps were chosen because of their excellent stability
in intensity and pulse shape. A Johnson/Cousins (Bessel) U-band filter from
Omega Optical Inc. (part number XBSSL/U/50R) selects a central wavelength
of ∼ 350 nm, FWHM 60 nm) from the broad flash lamp spectrum. The beam
is focused using a 20.3 cm diameter UV enhanced aluminum spherical mirror
(speed f/3) from Edmund Scientific Co. (part number R43-589). All optical
components are assembled on a commercial optical plate. We use Thor optical
table parts, assembled from Nomex Epoxy/Fiberglass 1.91 cm panels from
TEKLAM (part number N507EC).
The Xenon lamps rest inside refurbished 6.1 m shipping containers, and the
light is sent through a 0.749 cm thick acrylite UV transmitting window (Cyro
Industries acrylite OP-4 UVT acrylic). Each light source provides a nearly
horizontal beam of divergence ≤ 10 mrad pulsed across the field of view of the
nearby fluorescence detector. Computer control occurs from the correspond-
ing FD building. A serial radio link (YDI Wireless, model 651-900001-001
(TranzPoint ESC-II Kit)) connects the computer to a commercial ADC/relay
system (model ADC-16F 16 channel 8 bit ADC and RH-8L 8-relay card from
Electronic Energy Control Inc.) at the light source.
Once during each hour of FD data taking, the ADC/relay system enables a
1 Hz GPS pulser (CNS Systems Inc., model CNSC01 with TAC32 software)
and a 12 V to 24 V inverter to power the Xenon flash lamps. Each lamp fires
a set of 5 shots, pulsed at 2 second intervals. The APF events are flagged by
the FD data acquisition system and the corresponding FD data are stored on
disk in especially designated APF data files.
When the light sources are not operating, only the radio link and the ADC
board are powered. The total current draw is therefore only ∼ 0.2 A at 12 V,
and the whole system can be powered by batteries recharged during the day
with 12 V solar panels (two Siemens SP75 75 W solar modules with Trace
C35 controller).
2.2 APF Signals in the Fluorescence Detectors
The light beam produced by the APF sources is observed by the cameras of
the corresponding FD site. The FD detectors of the Pierre Auger Observatory
are described in detail elsewhere [11]. Here, we only give a short summary of
the main characteristics relevant for the analysis of APF shots.
Each Auger FD site contains six bays, and each bay encloses a UV telescope
composed of a spherical light-collecting mirror, a photomultiplier camera at
the focal surface, and a UV transmitting filter in the aperture. The mirrors
have a radius of curvature of 3.4 m and an area of about 3.5 × 3.5 m2. The
camera consists of 440 photomultipliers with a hexagonal bialkaline photo-
cathode, arranged in a 20× 22 array. Each camera has a field of view of 30.0◦
in azimuth and 28.6◦ in elevation, covering an elevation angle range from 1.6◦
to 30.2◦ above horizon. To reduce optical aberrations, including coma, the FD
telescopes use Schmidt optics with a circular diaphragm of diameter 2.2 m
placed at the center of curvature of the mirror, and a refractive corrector ring
at the telescope aperture.
Fig. 3 shows an APF shot as seen by the Coihueco FD. Five out of the 6 bays
of the Coihueco FD site observe light from the Coihueco APF facility. In this
figure, the light travels from right to left. Fig. 4 shows the relative positions
of the APF source and the FD at the Coihueco site. The geometry is in part
dictated by the local topography, and consequently is slightly different for the
Los Morados site.
Fig. 3. The APF pulse as seen by the Coihueco FD. The light travels from right
to left, and each PMT Cluster observes 30◦ in azimuth. Note that the projection of
the approximately horizontal APF beam onto the spherical FD surface results in a
curved track.
Fig. 4. Scheme of the location of the Coihueco APF light source relative to the
Coihueco FD. Located at the center is the Coihueco FD with its field of view in-
dicated. The value of α is 26◦ and β is 38◦, measured from the North. The shot
direction γ is about 24◦.
3 Determination of the Aerosol Phase Function
The signal from the APF light source observed by the ith pixel of a fluorescence
detector can be expressed as
Si = I0 · Ti ·
·∆zi ·∆Ωi · ǫi . (1)
In this equation, I0 is the light source intensity; Ti is the transmission factor
e−ri/Λtot which accounts for light attenuation from the beam to the pixel; ri
is the distance from the beam to the detector; Λtot, Λm, and Λa are the total,
molecular, and aerosol extinction length, respectively; and σ−1m dσm/dΩ and
σ−1a dσa/dΩ are the normalized differential molecular and aerosol scattering
cross sections, respectively, which are identical to the phase functions Pm(θ)
and Pa(θ). The integral of Pm(θ) and Pa(θ) over all solid angles is equal to 1.
Finally, ∆zi, ∆Ωi, and ǫi are the track length, detector solid angle, and the
efficiency for the ith pixel of the detector.
The data come in the form of total PMT signal per pixel from a particular shot.
Those data are binned as a function of azimuth and averaged between the five
shots taken within 10 seconds. In this analysis, 5◦ bins are used, although the
fit is relatively insensitive to the number of bins. Each FD pixel is hexagonally
shaped, so for those lying at the boundary of two azimuth bins, the fractional
area of the hexagon in each bin is used to properly distribute the signal. The
signal in each pixel is divided by ∆zi, 1/r
i and ǫi to correct for the geometry of
the beam and pixel calibration. Note that in the roughly cylindrical geometry
of the FD-APF beam, the ∆zi and 1/r
i corrections almost completely cancel
Typical values for the aerosol extinction length in dry atmospheres are be-
tween 10 km and 20 km, reaching 40 km for very clear conditions. Since the
perpendicular distance from the beam to the FD is only on the order of a
few hundred meters, it is reasonable to assume full atmospheric transmission
(Ti = 1) over the length of the beam. In reality, this assumption does not
hold well for the most distant beam points, so these points are not used in
the present study. In the near future, measurements of the extinction length
from the Auger lidar stations [5] will be used to improve the APF analysis.
In another approximation, we assume that the extinction lengths are identi-
cal for each pixel for single measurements and do not require an index i. In
principle, the extinction length depends on the number density of scatterers
and is therefore a function of the density (temperature, pressure) of the air.
Given corrections for geometry, attenuation, and pixel efficiency, Eq. 1 reduces
Si = C ·
, (2)
where C is a constant whose value is unimportant because arbitrary units are
sufficient in determining the phase function.
From the theory of Rayleigh scattering it is known that the Rayleigh phase
function is
Pm(θ) =
16 π(1 + 2 γ)
(1 + 3 γ) + (1− γ) cos2 θ
where γ accounts for the effect of molecular anisotropy on Rayleigh scattering.
For isotropic scattering, γ = 0, this reduces to the familiar
Pm(θ) =
(1 + cos2 θ) . (4)
The effect of the anisotropy is small and wavelength-dependent. Bucholtz [12]
Fig. 5. Schematic of track seen by ith pixel.
estimates γ ≃ 0.015 at 360 nm and concludes that the correction leads to
a ∼ 3% systematic increase in the Rayleigh scattering cross section, and a
fractional change ≤ 1.5% from the approximate (1 + cos2 θ). In our analysis,
only the shape of the function is relevant, and we use Eq. 4 as an approximation
of Eq. 3.
The aerosol phase function is often parameterized by the Henyey-Greenstein
function [13]:
Pa(θ) =
1− g2
(1 + g2 − 2gµ)3/2
, (5)
where µ = cos θ and g is an asymmetry parameter equal to the mean cosine of
the scattering angle: g = 〈cos θ〉. The parameter g is a measure of how much
light is scattered in the forward direction; a greater g means more light is
forward-scattered. Values for g range from g = 1 (total forward scattering) to
g = −1 (total backward scattering), with g = 0 indicating isotropic scattering.
The Henyey-Greenstein function works well for pure forward scattering, but
it cannot describe realistic aerosol conditions, which typically give rise to non-
negligible backscattering. Following [14,15], we modify Eq. 5 so that
Pa(θ) =
1− g2
(1 + g2 − 2gµ)3/2
3µ2 − 1
2(1 + g2)3/2
. (6)
The new term in this expression is proportional to the second Legendre poly-
nomial, and it is introduced to describe the extra backscattering component.
The value f is a fit parameter used to tune the relative strength of forward to
backward scattering.
The binned APF signal observed in the FD is therefore subjected to a 4-
parameter fit:
Si = A · (1 + µ
i ) +B · (1− g
(1 + g2 − 2gµi)3/2
3µ2i − 1
2(1 + g2)3/2
, (7)
where A, B, g and f are the fit parameters.
In principle, the parameters A and B, which describe the relative amount of
Rayleigh and Mie scattering, can be determined from measurements of the
extinction lengths Λm and Λa and assumptions about the particle albedo,
i.e. the ratio of light scattered by the aerosol particle in all directions to the
amount of incoming light. The albedo is close to one if the particle is mostly
reflective. Since local information on the extinction lengths was not available
for this analysis, we use A and B as additional fit parameters. We find that
the distinct shapes of the two phase functions does allow a determination of
A and B from the data themselves.
At Coihueco, the APF signal is seen in 5 out of the 6 mirrors, so the track is
visible over ∼ 150◦ in azimuth. At the boundary between each mirror there
is some overlap in the fields of view of pixels. This overlap produces a double
counting of signal resulting in the value of bins at boundaries being too large.
These bins are simply ignored in the fit. The values of the other bins and their
errors are obtained from the mean and standard deviation of the five APF
shots in each shot sequence.
On clear nights with few or no aerosols, the fit to Eq. 7 returns unphysical val-
ues for the parameters B, f , and g. In those cases, we re-fit the data to a pure
Rayleigh function by setting B, f , and g equal to zero. Two examples of fits,
one for a night with aerosol content, and one for a night with pure Rayleigh
scattering, are shown in Fig. 6. The aerosol, molecular, and total phase func-
tions are shown. The aerosol phase function is obtained by subtracting the
molecular component determined by the fit.
We fit the data only over a subrange of the available scattering angles, from
θmin ≃ 32.5
◦ to θmax ≃ 147.3
◦. As Fig. 6 indicates, the data deviates from
the theoretical prediction for scattering angles below θmin and above θmax.
At smaller and larger angles, several effects corrupt the signal and make it
unusable for the fit to the phase function. Due to the local geometry at the
Coihueco site (see Fig. 4), the APF shot is not visible for θ < 24◦, and below
30◦, the signal is incomplete because the beam is still partially beneath the
detector field of view. At large scattering angles, the beam is at a rapidly in-
creasing distance to the corresponding FD bay, and attenuation of light from
the beam to the detector becomes important. As mentioned earlier, because
local measurements of the optical depth are not yet available, we simply as-
sume T = 1. As measurements of T become available, the attenuation of light
scattered at large angles can be used to correct the data.
]° [θscattering angle 
0 20 40 60 80 100 120 140 160 180
A         46.2±  8602 
B         1814± 2.696e+05 
g         0.0036± 0.6804 
f         0.0147± 0.4977 
Aerosol Phase Function
Total phase function
Rayleigh phase function
Mie phase function
]° [θscattering angle 
0 20 40 60 80 100 120 140 160 180
10000
15000
20000
25000
30000
35000
40000
45000
50000
A         19± 1.011e+04 Aerosol Phase Function
Total phase function
Rayleigh phase function
Mie phase function
Fig. 6. Two examples for APF data fits on different days. In the upper plot (June
28, 2006, 5:12 am local time) aerosols are visible. Data are fit to the function given
in Eq. 7. The phase function in the lower plot (July 2, 2006, 3:12 am local time) is
consistent with pure Rayleigh scattering. Data are fit to Eq. 7, with B = 0, f = 0,
and g = 0. Error bars for both plots are the standard deviation of the 5 APF events.
In order to apply geometrical corrections when binning the data, the angle at
which the APF light source shoots (γ in Fig. 4) with respect to the FD and the
elevation angle of the shot direction needs to be known. We determined these
values from the data themselves. The elevation angle was determined from a
reconstruction of APF shots with the FD offline reconstruction [16], and γ was
determined from the analysis of APF shots on nights where aerosol scattering
was negligible. The data from these nights were fit to the Rayleigh component
of the phase function, with the position of the minimum (nominally at 90◦
scattering angle) as a free parameter. The fit value of this angle was then used
to deduce the direction which the APF light source shoots relative to the FD
(∼ 24◦ at Coihueco).
4 First Results
We have applied the analysis described in Section 3 to data recorded between
June and December 2006 at the Coihueco site. Since the APF light sources
operate during all nights of FD operation, this data set includes all moonless
nights, with the exception of nights with rain or strong winds when the FDs
remain closed. Fig. 7 shows the distribution of the asymmetry parameter g
(left) and the backscatter parameters f (right). For most nights with aerosol
contamination, the value of g at the experiment site in Malargüe is ∼ 0.6,
with an average of 0.59 and a standard deviation of 0.07 for the data period
analyzed here. Values of g = 0 indicate hours where the measured phase
function can be described by pure Rayleigh scattering, so the aerosol phase
function is effectively negligible. Fig. 7 also shows the asymmetry parameter
as a function of time for the analyzed period. With the limited amount of data
taken so far, no conclusions concerning seasonal variations can be drawn. The
asymmetry parameter appears to be stable during the observed time period.
With more data becoming available over the next few years, we plan to monitor
the month-to-month variation in g and analyze possible correlations with other
weather measurements.
One of the main tasks of the APF, in addition to providing the in situ aerosol
phase function for every hour of FD data taking, is the identification of “clear”
nights with small aerosol contamination. These nights play an important role
in the calibration of other atmospheric monitoring devices such as the Central
Laser Facility (CLF) [6]. On clear nights, the measured phase function can be
described by pure Rayleigh scattering (measurements where this is the case
appear as g = 0 in Fig. 7).
To confirm the reliability of the fit where both the normalization of the Mie
and the Rayleigh contribution are fit parameters, Fig. 8 shows the Rayleigh
normalization factor A for the same data set. One might expect the molecular
asymmetry parameter g
0 0.2 0.4 0.6 0.8 1
backscatter parameter f
-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Jun 2006 Jul 2006 Aug 2006 Sep 2006 Oct 2006 Nov 2006 Dec 2006
Fig. 7. Top: Distribution of the asymmetry parameter g (top left) and the backscatter
parameter f (top right) for all measurements performed between June and December
2006. Values of g = 0 (and f = 0) indicate that the phase function can be described
with pure Rayleigh scattering. Bottom: Asymmetry parameter g as a function of
time.
contribution to be rather stable, and in fact this parameter does not change
much with time.
It is instructive to compare the average asymmetry parameter obtained from
the APF with model expectations and measurements at comparable locations.
Typically, measurements are performed at optical wavelengths and cannot be
directly compared to measurements at UV wavelengths. However, a compi-
lation at different wavelengths from 450 nm to 700 nm [17] shows that the
wavelength dependence of g is small; values at 450 nm are a few percent
larger than at 550 nm.
Rayleigh normalization
4000 6000 8000 10000 12000 14000 16000
Fig. 8. Distribution of the Rayleigh normalization parameter A for all measurements
performed between June and December 2006.
To first order, g = 0.7 is often used as a generic value for g in radiative transfer
models. A smaller value for g is expected at dry locations. A parameterization
of aerosol optical properties by d’Almeida et al. [18] suggests values for g
between 0.64 and 0.83 at 550 nm depending on aerosol type and season, with
higher averages for high relative humidity.
The Pierre Auger Observatory is located east of the Andes in the Pampa
Amarilla, an arid high plateau at 1420 m a.s.l., so values around 0.6 are within
expectations. For comparison, recent measurements carried out in the South-
ern Great Planes of the US [19] yield values for g at 550 nm of 0.60± 0.03 for
dry conditions and 0.65± 0.05 for ambient conditions.
The aerosol phase function most commonly used in fluorescence detector data
analysis, both for the High Resolution Fly’s Eye (HiRes) Experiment [20],
which operated in Utah between 1997 and 2006, and the Pierre Auger FD de-
tectors, is the function obtained from a desert aerosol simulation by Longtin [21].
Longtin’s desert model is based on Mie scattering theory and assumes that the
desert atmosphere has three major components: carbonaceous particles, water-
soluble particles, and sand. For each aerosol component, the model assumes a
characteristic log normal size distribution and refractive index. Longtin per-
formed his calculations for several wavelengths and wind speeds; those made
at 550 nm with a wind speed of 10 m/s most closely match the 300 nm to
400 nm nitrogen fluorescence band observed by the FDs and have therefore
been traditionally used in air fluorescence data analysis.
]° [θscattering angle 
0 20 40 60 80 100 120 140 160 180
Aerosol Phase Function
 = 550 nm, wind = 10 m/s)λLongtin (
This work: f = 0.5, g = 0.7
This work: f = 0.4, g = 0.6
Fig. 9. Comparison of the Longtin aerosol phase function (desert atmosphere simu-
lated with a wind speed of 10 m/s) with the default phase function used in the Auger
atmospheric database (f = 0.5, g = 0.7) and the typical phase function measured by
the APF (f = 0.4, g = 0.6).
Fig. 9 compares the Longtin aerosol phase function at 550 nm to the modi-
fied Henyey-Greenstein function of Eq. 6 with two sets of f and g: f = 0.5
and g = 0.7, the default values used by the Auger atmospheric database; and
f = 0.4 and g = 0.6, the values determined in this study to be more typical
of the detector location. The comparison shows that, on average, the differ-
ence between the Longtin function and the measured phase function is small
for those scattering angles relevant in fluorescence measurements — ∼ 30◦
to 150◦. Only at the largest scattering angles above 160◦ do the phase func-
tions differ notably. This region is outside the current range of validity of our
measurement.
Our primary interest in aerosol scattering is its effect on the air shower recon-
struction, most notably the determination of the shower energy. However, it is
not straightforward to estimate the extent to which the use of measured rather
than averaged values of f and g changes the energy reconstruction, as this
depends strongly on other atmospheric parameters, for example the aerosol
optical depth. Rather than singling out the phase function measurement, we
need to study the effect of the combined measurement of all atmospheric pa-
rameters, a task which is beyond the scope of this paper.
We can, however, get an estimate of the relevance of the phase function mea-
surement by studying its effect on the energies of events that are of particu-
lar importance for the energy calibration of the detector, the “golden hybrid
hist1
Mean   0.6996
RMS    0.7913
) / Eapf - Estd(E
-10 -8 -6 -4 -2 0 2 4 6 8 10
210 hist1
Mean   0.6996
RMS    0.7913
f > 0, g > 0
Mean   0.71
RMS    0.79
f = 0, g = 0
Mean   1.87
RMS    2.34
Weather Conditions
f > 0, g > 0
f = 0, g = 0
Fig. 10. Differences in the energies of golden hybrid events reconstructed with de-
fault phase function values (Estd) and those reconstructed using phase function fit
parameters determined from APF measurements (Eapf). The red (bold) histogram
represents data taken during nights with measurable aerosols; the blue (light) his-
togram depicts events observed on purely molecular nights.
events.” These are events observed by one or more fluorescence detectors and
three or more surface array tanks. For “golden hybrid events” observed by the
Coihueco FD site between June and December 2006, we performed the recon-
struction twice: first, using the default parameters f = 0.5 and g = 0.7 to
estimate aerosol scattering; and second, using the fit parameters determined
from APF measurements. In both cases atmospheric extinction was simu-
lated using an average aerosol profile model representative of the Malargüe
site [22,23].
Fig. 10 depicts the relative differences in energies caused by reconstructing
showers with the default phase function and the measured phase function.
The red (bold) histogram represents data taken during nights with aerosol
contamination (f > 0, g > 0) while the blue (light) histogram represents
data taken during nights where according to the APF analysis scattering is
purely molecular. The correction is typically of order one percent. However,
on those nights when aerosol loading is extremely low, so that atmospheric
scattering may be characterized as purely molecular, the use of the default
scattering parameters causes larger errors in the shower reconstruction. Under
such conditions, the total phase function lacks the strong forward-scattering
component typical of aerosols. During these periods, incorrectly accounting
for aerosol scattering starts to impact the energy calibration of the detector.
A correct determination of the phase function on a regular basis is therefore
an important part of the atmospheric monitoring efforts at the site.
5 Conclusions and Outlook
As part of the atmospheric monitoring program at the Pierre Auger Obser-
vatory, the aerosol phase function at 350 nm is routinely measured at two of
the four FD sites. A first analysis of data taken from June to December 2006
shows that values of g = 〈cos θ〉 ≃ 0.6 for the mean cosine of the scattering
angle θ are typical for aerosols at the site of the experiment. Over the next
several years, the APF light sources will produce a data set of unprecedented
size of the scattering properties of aerosols. This data set will enable us to
carefully study any seasonal change in the aerosol content. The APF light
sources and the other atmospheric monitoring instruments at the Auger site
will accumulate one of the largest sets of continuous measurements in the
300 nm to 400 nm range ever recorded for a single location.
The APF light sources are currently operating at a wavelength of 350 nm only.
In the near future, we will add regular measurements at 330 nm and 390 nm to
study the dependence of the phase function on the wavelength of the scattered
light.
Acknowledgements
We are grateful to the following agencies and organizations for financial sup-
port: The APF light sources were built by a grant from the Department of
Energy (DOE) Office of Science (USA) (DE-FG03-92ER40732). Parts of the
APF analysis were performed during the 2006 REU (Research Experience for
Undergraduates) program at Columbia University’s Nevis Laboratories which
is supported by the National Science Foundation (USA) under contract num-
ber NSF-PHY-0452277.
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	Introduction
	APF Light Sources
	Detector Buildings, Optics, and Electronics
	APF Signals in the Fluorescence Detectors
	Determination of the Aerosol Phase Function
	First Results
	Conclusions and Outlook
	Acknowledgements
	References
