Techniques for Measuring Aerosol Attenuation using the Central Laser Facility at the Pierre Auger Observatory

The Pierre Auger Observatory in Malarg\"ue, Argentina, is designed to study the properties of ultra-high energy cosmic rays with energies above 1018 eV. It is a hybrid facility that employs a Fluorescence Detector to perform nearly calorimetric measurements of Extensive Air Shower energies. To obtain reliable calorimetric information from the FD, the atmospheric conditions at the observatory need to be continuously monitored during data acquisition. In particular, light attenuation due to aerosols is an important atmospheric correction. The aerosol concentration is highly variable, so that the aerosol attenuation needs to be evaluated hourly. We use light from the Central Laser Facility, located near the center of the observatory site, having an optical signature comparable to that of the highest energy showers detected by the FD. This paper presents two procedures developed to retrieve the aerosol attenuation of fluorescence light from CLF laser shots. Cross checks between the two methods demonstrate that results from both analyses are compatible, and that the uncertainties are well understood. The measurements of the aerosol attenuation provided by the two procedures are currently used at the Pierre Auger Observatory to reconstruct air shower data.

Direct measurements of primary cosmic rays at ultra-high energies (above 10 18 eV) above the at-2 mosphere are not feasible because of their extremely low flux. The properties of primary particles 3 -energy, mass composition, arrival direction -are deduced from the study of cascades of sec-4 ondary particles of Extensive Air Showers (EAS), originating from the interaction of cosmic rays 5 with air molecules. The Pierre Auger Observatory [1] in Argentina (mean altitude about 1400 m 6 a.s.l.) combines two well-established techniques: the Surface Detector, used to measure photons 7 and charged particles produced in the shower at ground level; the Fluorescence Detector, used to 8 measure fluorescence light emitted by air molecules excited by secondary particles during shower 9 development. The Fluorescence Detector (FD) [2] consists of 24 telescopes located at four sites 10 around the perimeter of the Surface Detector (SD) array. It is only operated during clear nights 11 with a low illuminated moon fraction. The field of view of a single telescope is 30 • in azimuth, 12 and 1.5 • to 30 • in elevation. Each FD site covers 180 • in azimuth. The hybrid feature and the large 13 area of 3000 km 2 of the observatory enable the study of ultra-high energy cosmic rays with much 14 better precision and much greater statistics than any previous experiment. 15 The fluorescence technique to detect EAS makes use of the atmosphere as a giant calorimeter 16 whose properties must be continuously monitored to ensure a reliable energy estimate. Atmo-17 spheric parameters influence both the production of fluorescence light and its attenuation towards 18 the FD telescopes. The molecular and aerosol scattering processes that contribute to the overall 19 attenuation of light in the atmosphere can be treated separately. In particular, aerosol attenuation of 20 light is the largest time dependent correction applied during air shower reconstruction, as aerosols 21 are subject to significant variations on time scales as little as one hour. If the aerosol attenuation is 22 not taken into account, the shower energy reconstruction is biased by 8 to 25% in the energy range 23 measured by the Pierre Auger Observatory [3]. On average, 20% of all showers have an energy 24 correction larger than 20%, 7% of showers are corrected by more than 30% and 3% of showers are 25 corrected by more than 40%. Dedicated instruments are used to monitor and measure the aerosol 26 parameters of interest: the aerosol extinction coefficient α aer (h), the normalized differential cross 27 section -or phase function -P(θ ), and the wavelength dependence of the aerosol scattering, pa-28 rameterized by the Ångstrom coefficient γ. 29 At the Pierre Auger Observatory, molecular and aerosol scattering in the near UV are measured 30 using a collection of dedicated atmospheric monitors [3]. One of these is the Central Laser Facility 31 (CLF) [4] positioned close to the center of the array, as shown in Fig. 1. A newly built second 32 laser station, the eXtreme Laser Facility (XLF), positioned north of the CLF, has been providing an 33 additional test beam since 2009. The two systems produce calibrated 355 nm vertical and inclined 34 laser shots during FD data acquisition. These laser facilities are used as test beams for various 35 applications: to calibrate the pointing direction of telescopes, for the determination of the FD/SD 36 time offset, and for measuring the vertical aerosol optical depth τ aer (h) and its differential α aer (h). 37 An hourly aerosol characterization is provided in the FD field of view with two independent ap-38 proaches using the same CLF vertical laser events. In the near future, those approaches will be 39 applied to XLF vertical events. The FRAM robotic telescope is used for a passive measurement of  In addition to the CLF and XLF, four monostatic LIDARs [5] and four Infrared Cloud Cam-  To measure the Aerosol Phase Function (APF), a Xenon flash lamp at two of the FD sites 49 fires a set of five shots with a repetition rate of 0.5 Hz once every hour [7]. The shots are fired 50 horizontally across the field of view of five out of the six telescopes in each building. The resulting 51 angular distribution of the signal gives the total scattering phase function P(θ ) as a function of the 52 scattering angle θ .

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In this paper, we will describe the analysis techniques used to estimate aerosol attenuation from 54 CLF laser shots. In Sec. 2 we will review atmospheric attenuation due to aerosols and molecules.

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In Sec. 3, we will discuss the setup, operation and calibration of the CLF. Sec. 4 contains the 56 description of the two analysis methods used to estimate the aerosol attenuation. Comparisons 57 between the two methods and conclusions follow in Sec. 5 and 6.

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Molecules in the atmosphere predominantly scatter, rather than absorb, fluorescence photons in the UV range 1 . Molecular and aerosol scattering processes can be treated separately. In the following, the term "attenuation" is used to indicate photons that are scattered in such a way that they do not 62 contribute to the light signal recorded by the FD. The molecular and aerosol attenuation processes 63 can be described in terms of atmospheric transmission coefficients T mol (λ , s) and T aer (λ , s), indi-64 cating the fraction of transmitted light intensity as a function of the wavelength λ and the path length s. The amount of fluorescence light recorded at the FD aperture I(λ , s) can be expressed in 66 terms of the light intensity at the source I 0 (λ , s) as The molecular transmission factor T mol (λ , s) is a function of the total wavelength-dependent 77 Rayleigh scattering cross section σ mol (λ ) and of the density profile along the line of sight s in 78 atmosphere n mol (s), The Rayleigh scattering cross section σ mol (λ ) is where N s is the atmospheric molecular density, measured in molecules per m −3 , n air is the refrac-81 tive index of the air, and F air is the King factor that accounts for the anisotropy in the scattering 82 introduced by the non-spherical N 2 , O 2 molecules [8].

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The atmospheric density profile along the line of sight n mol (s) is calculated using altitude-84 dependent temperature and pressure profiles, 4) where N A is Avogadro's number and R is the universal gas constant. The most absorbing atmospheric gases in the atmosphere are ozone and NO 2 . In the 300 to 400 nm range, the contribution of their absorption to the transmission function is negligible [3]. during the ascent. The balloons were able to reach altitudes of 25 km a.s.l. on average. Vertical profiles are complemented by temperature, pressure and humidity data from five ground-based 91 weather stations. The measured profiles from these launches have been averaged to form monthly 92 mean profiles (Malargüe Monthly Models) which can be used in the simulation and reconstruction 93 of showers [9,3]. Currently, the Global Data Assimilation System (GDAS) is used as a source 94 for atmospheric profiles. GDAS combines measurements and forecasts from numerical weather 95 prediction to provide data for the whole globe every three hours. For the location of the Pierre 96 Auger Observatory, reasonable data have been available since June 2005. Comparisons with on-97 site measurements demonstrate the applicability of the data for air shower analyses [10]. 98 Aerosol scattering can be described by Mie scattering theory. However, it relies on the assump-99 tion of spherical scatterers, a condition that is not always fulfilled. Moreover, scattering depends 100 on the nature of the particles. A program to measure the dimensions and nature of aerosols at 101 the Pierre Auger Observatory is in progress and already produced first results, but more study is 102 needed [11]. Therefore, the knowledge of the aerosol transmission factor T aer (λ , s) depends on 103 frequent field measurements of the vertical aerosol optical depth τ aer (h), the integral of the aerosol 104 extinction α aer (z) from the ground to a point at altitude h observed at an elevation angle ϕ 2 , assum-105 ing a horizontally uniform aerosol distribution (cf. Fig. 4), (2.5) Hourly measurements of τ aer (h) are performed at each FD site using the data collected from the 107 CLF.

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The Central Laser Facility, described in detail elsewhere [4], generates an atmospheric "test beam".

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Briefly, the CLF uses a frequency tripled Nd:YAG laser, control hardware and optics to direct a 126 calibrated pulsed UV beam into the sky. Its wavelength of 355 nm is near the center of the main 127 part of the nitrogen fluorescence spectrum [12]. The spectral purity of the beam delivered to the 128 sky is better than 99%. Light scattered from this beam produces tracks in the FD telescopes. The  The laser is mounted on an optical table that also houses most of the other optical components.

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The arrangement is shown in Fig

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The light scattered out of the CLF laser beam is recorded by the FD (see Fig. 4 for the laser-FD 162 geometry layout). The angles from the beam to the FD for vertical shots are in the range of 90 • 163 to 120 • . As the differential scattering cross section of aerosol scattering is much smaller than the 164 Rayleigh scattering cross section in this range, the scattering of light is dominated by well-known 165 molecular processes. Laser tracks are recorded by the telescopes in the same format used for air 166 shower measurements. In Fig. 5, a single 7 mJ CLF vertical shot as recorded from the Los Leones 167 FD site is shown. In the left panel of Fig. 6, the corresponding light flux profile for the same event 168 is shown. In Fig. 6, right panel, an average profile of 50 shots is shown.  Laser light is attenuated in the same way as fluorescence light as it propagates towards the 170 FD. Therefore, the analysis of the amount of CLF light that reaches the FD can be used to infer 171 the attenuation due to aerosols. The amount of light scattered out of a 6.5 mJ laser beam by the 172 atmosphere is roughly equivalent to the amount of UV fluorescence light produced by an EAS of 5 × 10 19 eV at a distance to the telescope of about 16 km, as shown in Fig. 7. Also shown is the more attenuated light profile of an almost identical shower at a larger distance.

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Besides determining the optical properties of the atmosphere, the identification of clouds is  In this case, it is possible to directly derive the altitude of the cloud from the peak in the photon 191 profile since the laser-detector geometry is known.  real and simulated CLF profiles changes by less than 3%.

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As a final check to verify that the chosen nights are reference clear nights we analyze the 237 measurement of the aerosol phase function (APF) [7] for that night, measured by the APF monitor 238 (see Sec. 1). The molecular part of the phase function P mol (θ ) can be calculated analytically from temperature, pressure and humidity at ground provided by weather stations. After subtraction of the 240 2 the Kolmogorov-Smirnov test calculates probabilities for histograms containing counts, therefore here the returned value is defined as a pseudo-probability. molecular phase function, the aerosol phase function remains. In a reference clear night, the total 241 phase function is dominated by the molecular part with almost no contribution from aerosols. Since 242 the APF light source only fires approximately horizontally, this method to find the reference nights 243 is insensitive to clouds, so it can only be used as a verification of reference nights that were found 244 using the procedure described in this section. After verification, the reference night is assumed to 245 be valid for the complete CLF epoch. In Fig. 8, panel (a), an averaged light profile of a reference 246 night is shown.  After h cloud is determined, a preliminary full hour profile is made by averaging all the available 266 quarter hour profiles. One or more quarter hour profiles can be missing due to the start or stop of FD 267 data taking, heavy fog, or problems at the CLF. Only one quarter hour profile is required to make 268 a full hour profile. Outlying pixels that triggered randomly during the laser event are rejected and  The maximum valid height h valid of the profile is then determined. If there is a hole in the 274 profile of two bins or more due to the rejection of outliers or clouds, h valid is marked at that point.

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As with h cloud , if no such holes exist, then h valid is set to the height corresponding to the top of the 276 FD camera field of view. If h valid is lower than h cloud , the minimum cloud height is set to be the 277 maximum valid height. Points above h valid are not usable for data analysis.  279 Using the laser-FD viewing geometry shown in Fig. 4, and assuming that the atmosphere is hori-zontally uniform, it can be shown [14] that the vertical aerosol optical depth is τ aer (h) = − sin ϕ 1 sin ϕ 2 sin ϕ 1 + sin ϕ 2 ln

Aerosol optical depth calculation
Two separate profiles are then generated corresponding to the values of τ meas aer ± σ syst , as shown on 332 the right panels of Fig. 9.

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The statistical uncertainty σ stat is due to fluctuations in the quarter hour profiles and is consid-   The atmospheric aerosol model adopted in this analysis is based on the assumption that the aerosol 341 distribution in the atmosphere is horizontally uniform. The aerosol attenuation is described by 342 two parameters, the aerosol horizontal attenuation length L aer and the aerosol scale height H aer .

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The former describes the light attenuation due to aerosols at ground level, the latter accounts for 344 its dependence on the height. With this parameterization, the expression of the aerosol extinction 345 α aer (h) and the vertical aerosol optical depth τ aer (h) are given by Using Eq. 2.5, the aerosol transmission factor along the path s can be written as where h 1 and h 2 are the altitudes above sea level of the first and second observation levels and ϕ 2 349 is the elevation angle of the light path s (cf. Fig. 4).

Optical depth determination and cloud identification
For each quarter hour average profile, the aerosol attenuation is determined obtaining the pair 386 L best aer , H best aer corresponding to the profile in the simulated grid closest to the analyzed event. The 387 quantification of the difference between measured and simulated profiles and the method to iden-388 tify the closest simulation are the crucial points of this analysis. After validation tests on sim-389 ulations of different methods, finally the pair L best aer and H best aer chosen is the one that minimizes 390 the square difference D 2 between measured and simulated profiles computed for each bin, where and Φ i are reconstructed photon numbers at the FD aperture in each 392 time bin. In Fig. 11, an average measured profile as seen from Los Leones compared to the sim-393 ulated chosen profile is shown. The small discrepancy between measured and simulated profiles, 394 corresponding to boundaries between pixels, has no effect on the measurements.  If the average profile under study shows any anomaly or if a cloud is detected between the laser 405 track and the FD, it is rejected. If a cloud is detected above the laser track, the profile is truncated 406 at the cloud base height and this lower part of the profile is reanalyzed, since the first search for clouds only identifies the optically thicker cloud layer. If a lower layer of clouds is detected in the truncated profile, or the cloud height is lower than 5500 m a.s.l., the profile is rejected.
If no clouds are detected (either in the whole average profile or in the lower part), the pair L best aer , 410 H best aer , together with the maximum height of the profile are stored and the procedure is completed.

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The quarter hour τ aer (h) profile is calculated according to Eq. 4.5 together with the associated 412 statistical and systematic uncertainties. The information is stored, and the quarter hour τ aer (h) 413 profiles are averaged to obtain the hourly vertical aerosol optical depth profile and the aerosol 414 extinction profile α aer (h). is not using a parametric model for the aerosol attenuation. This comparison for each height shows 437 that aerosol profiles are compatible within 2% at each altitude.

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The uncertainty related to the method defined to choose the best matching simulated profile 439 as a function of the altitude is also estimated. As described in Sec. 4.3.3, the parameters L best aer and 440 H best aer minimize the quantity profile; then the four measured aerosol profiles are averaged to obtain the hourly information 447 needed for the air shower reconstruction. The same procedure is adopted to obtain the uncer-tainties related to the hourly aerosol attenuation profile. As a final step, the hourly uncertainty on 449 τ aer (h) is propagated to the aerosol extinction α aer (h). The Loma Amarilla FD site is too far from the CLF to obtain fully reliable results. The XLF is 474 closer and will produce aerosol attenuation measurements for Loma Amarilla in the near future.

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Values of τ aer (5 km) measured during austral winter are systematically lower than in summer.

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In the right column of Fig. 13, the τ aer (5 km) distribution over six years is shown for aerosol 477 attenuation measurements using the FD sites at Los Leones, Los Morados and Coihueco. More   The dashed line is a diagonal indicating perfect agreement, the solid line is a fit to the data. Also shown is the vertical aerosol optical depth profile τ aer (h) above ground from Laser Simulation (blue) and Data Normalized (red) analyses in atmospheric conditions with a low (b), average (c), and high (d) aerosol concentration together with the corresponding uncertainties. The laser data was recorded with the FD at Los Leones on July 8th, 2008 between 8 and 9 a.m., April 4th, 2008 between 4 and 5 a.m., and January 5th, 2008 between 3 and 4 a.m. local time, respectively.
showers by 8 to 25% in the energy range measured by the Pierre Auger Observatory. This includes 487 a tail of 7% of all showers with an energy correction larger than 30%.

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To determine the vertical aerosol optical depth profiles for the Pierre Auger Observatory, verti-