The use of aerosol data in Auger Fluorescence Detector analysis

The Pierre Auger Observatory’s Fluorescence Detector (FD) consists of 27 telescopes arranged in four sites around the perimeter of the 3000 square kilometre Surface Detector (SD). Cosmic ray extensive air showers are viewed via the nitrogen fluorescence light they induce in the atmosphere. Careful treatment of light attenuation processes must be made, especially given that some showers are viewed at distances in excess of 30 km. Of particular importance is the attenuation due to scattering by aerosol particles, a challenging topic given that aerosol concentrations can vary on time-scales of hours. At the Auger Observatory, the vertical distribution of aerosols is measured hourly with a series of bi-static lidar systems (consisting of central laser facilities and each of the FD sites), and three times per night with a Raman lidar system. In this contribution we describe the use of aerosol profiles in the analysis of air shower data, in particular in the estimation of the cosmic ray primary energy, and the depth of shower maximum, Xmax. We also demonstrate how statistical and systematic uncertainties in the aerosol concentrations propagate through to a contribution to energy and Xmax uncertainties.


The Central Laser Facility
The Central Laser Facility, described in detail elsewhere Briefly, the CLF uses a frequency tripled Nd:YAG lase calibrated pulsed UV beam into the sky. Its wavelength part of the nitrogen fluorescence spectrum [12]. The s sky is better than 99%. Light scattered from this beam CLF is located near the middle of the array, nearly eq sites, at an altitude of 1416 m above sea level. The dista above sea level), Los Morados (1416.4 m), Loma Ama FD sites are 26.0 km, 29.6 km, 40 km, and 30.3 km, res CLF is shown. The CLF is solar-powered and operated e CLF fires 50 vertical shots at 0.5 Hz repetition rate every 15 minutes during the FD quisition. Specific GPS timing is used to distinguish laser from air shower events. The on, time, and relative energy of each laser pulse is recorded at the CLF and later matched to responding laser event in the FD data. n upgrade [13] to the CLF is planned for the near future. This upgrade will add a backscatter LIDAR receiver, a robotic calibration system, and replace the current flash lamp pumped y a diode pumped laser.

Aerosol Characterisation
Molecular, or Rayleigh, scattering is a more significant attenuation process than aerosol scattering. The molecular vertical optical depth between ground level and an altitude of 5 km is about 0.23 at 350 nm. This compares with an average value for the aerosol vertical optical depth of about 0.05 to the same height. However, the molecular atmosphere is much more stable than the aerosol one, and to the detector. By comparing the profile in a given hour to one from the reference night (where we assume that the only attenuation process is Rayleigh scattering) we can obtain (using an analytic expression [3], and taking care with possible cloud contamination) the vertical aerosol optical depth (VAOD) as a function of height, VAOD(h). An example is shown in the right-hand plot of figure 5.
This process is repeated for all four FD stations viewing either the CLF or the XLF (typically the XLF for the northerly Loma Amarilla detector), and the VAOD(h) data is loaded into a MySQL database for use during shower reconstruction. The VAODs derived within the same hour using di↵erent combinations of laser and detector site are consistent within uncertainties [3], implying near-uniform aerosol conditions across the Observatory at a given time. With the aid of the database of VAOD(h), and the horizontally-uniform aerosol assumption, the shower analysis can calculate the aerosol attenuation between any two points in space.
The DN method fills the majority of hours in the aerosol database. For hours where the DN fails for some reason, holes are filled with the alternate Laser Simulation (LS) analysis. As the name implies, we simulate the received signals from the CLF or XLF under a variety of aerosol conditions, and use this library of simulations to  aerosol atmosphere is horizontally uniform, and that m not contribute to the light flux measured at the FD, is flux profile of a single CLF vertical shot seen from the Los Leones FD own in figure 5 is used. Right: 50 shots average profile.
of various hourly profiles affected by different atmospheric conditions are the profile is due to the FD camera structure, in which adjacent pixels are llectors. A profile measured on a night in which the aerosol attenuation anel (a). Profiles measured on nights in which the aerosol attenuation are respectively shown in panels (b), (c) and (d). As conditions become count decreases. The two bottom profiles (e) and (f) represent cloudy r in CLF light profiles as peaks or holes depending on their position. A the CLF and the FD can block the transmission of light in its travel from s the fluorescence telescopes, appearing as a hole in the profile (e). The anywhere between the CLF and the FD site, therefore its altitude cannot usly. A cloud directly above the CLF appears as a peak in the profile, n the cloud enhances the amount of light scattered towards the FD (f). to directly derive the altitude of the cloud from the peak in the photon reference clear night R as defined in section 4.1 returns the normalization constant that fixes the relative energy scale between measured and simulated laser profiles. Using this normalization procedure, the dependence on FD or CLF absolute calibrations is avoided and only the relative Measuring Aerosols Laser Simulation (LS) method files is simulated for each FD site, a reference energy, to normalize the ach measured profile is compared to ulated profile closest to the measured nd its associated parameters are used ( figure 4). During the procedure, and the aerosol attenuation profile is loud lower layer height. d systematic error estimates s were indentified in the methods for f τ aer (h) profiles. The uncertainties -estimated and are now separated into tical contributions. These assignments er the effect of the uncertainty would the EAS data sample, or would be from one EAS to the next (see table 1). see [6]. Since each method is based was estimated as due to the choice of the reference clear night. Finally the uncorrelated error due to the atmospheric fluctuations within the hour is estimated on a event-byevent basis and is about 3%. These errors are estimated for each of the two methods described. In the Laser Simulation Analysis a 2% uncorrelated uncertainty is added to take into account how well the parametric model used describes the real aerosol attenuation conditions. A study was performed on hybrid events to estimate the effect on reconstructed EAS energy and Xmax when moving τ aer (h) up or down by its systematic uncertainty. It was found that the energy varies from +2.4% to -2.5%, and Xmax from 0.8 to -1.2 g · cm 2 .

2004-2012 Aerosol Attenuation Profiles
The hourly aerosol attenuation profiles over 9 years (from January 2004 to December 2012) have been measured using the two analyses described.

The aerosol phase function
Calculation of DVAOD via Equation 6.4 requires a priori knowledge of the aerosol volume scattering coefficient, and the aerosol scattering phase function, as a function of height. The first of these issues is addressed later in Section 6.4. Here we will discuss the dependence of the correction on the aerosol phase function.
The form of the aerosol phase function used for calculations at the Pierre Auger Observatory is the modified Henyey-Greenstein phase function It describes the fraction of light per unit solid angle that is scattered in a particular direction by aerosols.

The aerosol phase function
Calculation of DVAOD via Equation 6.4 requires a priori knowledge of the aeros volume scattering coefficient, and the aerosol scattering phase function, as a functi of height. The first of these issues is addressed later in Section 6.4. Here we w discuss the dependence of the correction on the aerosol phase function.
The form of the aerosol phase function used for calculations at the Pierre Aug Observatory is the modified Henyey-Greenstein phase function It describes the fraction of light per unit solid angle that is scattered in a particu direction by aerosols.     shower at a distance of 10 km which has a depth of maximum of 750 g cm 2 . X max is shifted deeper into the atmosphere by the aerosol scattering correction to the VAOD. The magnitude of the correction is based on the DVAOD expected for a laser at 26 km and an atmosphere with a typical VAOD of 0.04.

The aerosol phase function
Calculation of DVAOD via Equation 6.4 requires a priori knowledge of the aerosol volume scattering coefficient, and the aerosol scattering phase function, as a function of height. The first of these issues is addressed later in Section 6.4. Here we will discuss the dependence of the correction on the aerosol phase function.
The form of the aerosol phase function used for calculations at the Pierre Auger Observatory is the modified Henyey-Greenstein phase function It describes the fraction of light per unit solid angle that is scattered in a particular direction by aerosols. Traditionally the Longtin phase function [208] has been used in fluorescence detector data analysis, such as at the High Resolution Fly's Eye (HiRes) Experiment, and in the early days of Auger. The Longtin phase function was developed through simulations based on Mie scattering theory of 3 different Improvements to aerosol attenuation measurements at the Pierre Auger Observatory Max Malacari constructed shower profiles in both shape and normalization. Reconstructed shower energies are increased on average by 1.5% at 10 17.5 eV, up to 3% at an energy of 10 19.5 eV. Showers of higher energy tend to be detected at larger distances, meaning the aerosol transmission is lower, and hence the relative decrease in the aerosol transmission under these aerosol analysis improvements is larger. Changes in the average depth of shower maximum are driven by the elongation of the decaying tail of shower profiles and range from 2 g/cm 2 at 10 17.5 eV, up to 5 g/cm 2 at an energy of 10 19.5 eV. The larger VAOD increases close to the ground (shown in Fig. 2) lead to a modest elongation of the trailing edge of reconstructed energy deposit profiles, shifting their depth of maximum development slightly deeper in the atmosphere. Both the energy and X max increases are small on average, and are within current aerosol transmission related systematic uncertainties in the energy and X max scales published in [8,9]. Los Morados X max σ X max ≤ 20 g/cm 2 ∆ sys ≤ 10 g/cm 2 S 1000  The slow control system (SCS) assures a secure remote operation of the FD system. The SCS works autonomously and continuously monitors detector and weather conditions. Commands from the remote operator are accepted only if they do not violate safety rules that depend on the actual experimental conditions: high voltage, wind speed, rain, light levels inside/outside the buildings, etc. In case of external problems, such as power failures or communication breakdowns, the SCS performs an orderly shutdown, and also a subsequent start up of the fluorescence detector system if the conditions have changed. If parts of the SCS itself fail, the system automatically reverts to a secure mode so that all critical system states (open shutters, high voltage on, etc.) are actively maintained.
The observation of air showers via fluorescence light is possible only at night. Moreover, night sky brightness should be low and thus nights without a significant amount of direct or scattered moonlight are required. We also require that the sun be lower than 181 below the horizon, the moon remain below the horizon for longer than 3 h, and that the illuminated fraction of the moon be less than dark obse The on varies slig pointing remaining operated wind spee ness (caus

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The to 34 Mbps point, dis are distributed over a sphere with surface 4pr 2 i , where r i denotes the distance of the detector. Due to atmospheric attenuation only a fraction T i of them reach the detector aperture with area A. Given a light detection efficiency of e, the measured fluorescence light flux y f i can be written as where the abbreviation d i ¼ eT i ðA=ð4pr 2 i ÞÞ is used. For the sake of clarity the wavelength dependence of Y, T and e will be disregarded in the following, but discussed later.
The number of Cherenkov photons emitted at the shower is proportional to the number of charged particles above the Cherenkov threshold energy. Since the electromagnetic  [4,5,16,17] at this point of the atmosphere, the number of photons produced at the shower in a slant depth interval DX i is Here w i denotes the energy deposited per unit depth at slant depth X i (cf. Fig. 1) and is defined as where dE dep =dV is the energy deposit per unit volume and (j; R; z) are cylinder coordinates with the shower axis at R ¼ 0. The distance interval Dz i along the shower axis is given by the slant depth interval DX i . The fluorescence yield Y f i is the number of photons expected per unit deposited energy for the atmospheric pressure and temperature at slant depth X i . The photons from Eq. (1) are distributed over a sphere with surface 4pr 2 i , where r i denotes the distance of the detector. Due to atmospheric attenuation only a fraction T i of them reach the detector aperture with area A. Given a light detection efficiency of e, the measured fluorescence light flux y f i can be written as f f component dominates the shower development, the emitted Cherenkov light, N C g , can be calculated from where N e i denotes the number of electrons and positrons above a certain energy cutoff, which is constant over the full shower track and not to be confused with the Cherenkov emission energy threshold. Details of the Cherenkov light production like these thresholds are included in the Cherenkov yield factor Y C i [15,18-20]. Although Cherenkov photons are emitted in a narrow cone along the particle direction, they cover a considerable angular range with respect to the shower axis, because the charged particles are deflected from the primary particle direction due to multiple scattering. Given the fraction f C ðb i Þ of Cherenkov photons per solid angle emitted at an angle b i with respect to the shower axis [18,20], the light flux at the detector aperture originating from direct Cherenkov light is where f e ðE; X i Þ denotes the norma distribution and w e ðEÞ is the energy l single electron with energy E. A [15,19,20], the electron energy s universal in shower age s i ¼ 3=ð1 þ not depend on the primary mass or e relative distance to the shower maxim thus be simplified to Production at the shower Light at the FD angular range with respect to the shower axis, because the charged particles are deflected from the primary particle direction due to multiple scattering. Given the fraction f C ðb i Þ of Cherenkov photons per solid angle emitted at an angle b i with respect to the shower axis [18,20], the light flux at the detector aperture originating from direct Cherenkov light is Due to the forward peaked nature of Cherenkov light production, an intense Cherenkov light beam builds up along the shower as it traverses the atmosphere (cf. Fig. 1).
If a fraction f s ðb i Þ of the beam is scattered toward the observer it can contribute significantly to the total light received at the detector. In a simple one-dimensional model the number of photons in the beam at depth X i is just the sum of Cherenkov light produced at all previous depths X j attenuated on the way from X j to X i by T ji : Similar to the direct contributions, the scattered Cherenkov light received at the detector is then X i the number of photons in the beam at depth X i is just the sum of Cherenkov light produced at all previous depths X j attenuated on the way from X j to X i by T ji : Similar to the direct contributions, the scattered Cherenkov light received at the detector is then Finally, the total light received at the detector at the time t i is obtained by adding the scattered and direct light contributions:

Analytic shower profile reconstruction
The aim of the profile reconstruction is to estimate the energy deposit and/or electron profile from the light flux observed at the detector. At first glance this seems to be hopeless, since at each depth there are the two unknown variables w i and N e i , and only one measured quantity, Similar to the direct contributions, the scattered Cherenkov light received at the detector is then (7 Finally, the total light received at the detector at the time t is obtained by adding the scattered and direct ligh contributions:

Analytic shower profile reconstruction
The aim of the profile reconstruction is to estimate the energy deposit and/or electron profile from the light flux observed at the detector. At first glance this seems to be hopeless, since at each depth there are the two unknown variables w i and N e i , and only one measured quantity namely y i . Since the total energy deposit is just the sum o the energy loss of electrons, w i and N e i are related via e Z 1 i i i i

Analytic shower profile reconstruction
The aim of the profile reconstruction is to estimate the energy deposit and/or electron profile from the light flux observed at the detector. At first glance this seems to be hopeless, since at each depth there are the two unknown variables w i and N e i , and only one measured quantity, namely y i . Since the total energy deposit is just the sum of the energy loss of electrons, w i and N e i are related via cence matrix the inverse can be calculated quic matrices with large dimension. As the matrix Eq. (12) are always X0, C is never singular. The statistical uncertainties of b w are obtain propagation: It is interesting to note that even if the measure uncorrelated, i.e. their covariance matrix V y the calculated energy loss values b w i are not. Thi the light observed during time interval i does originate from w i , but also receives a contrib earlier shower parts w j , joi, via the ''Cher beam''.
inally, the total light received at the detector at the time t i obtained by adding the scattered and direct light ntributions:

Analytic shower profile reconstruction
The aim of the profile reconstruction is to estimate the ergy deposit and/or electron profile from the light flux served at the detector. At first glance this seems to be peless, since at each depth there are the two unknown riables w i and N e i , and only one measured quantity, mely y i . Since the total energy deposit is just the sum of e energy loss of electrons, w i and N e i are related via Due to the triangular cence matrix the inver matrices with large di Eq. (12) are always X The statistical unce propagation: It is interesting to note uncorrelated, i.e. their the calculated energy l the light observed du originate from w i , bu earlier shower parts beam''.

= dE/dX(X i )
Cherenkov light is also signal -reconstruct w = dE/dX profile by matrix method a four-parameter fit depending on the observed track length and number of detected photons of the respective event (cf. [111]).
Finally, the calorimetric energy of the shower is obtained by integrating Eq. (8) and the total energy is estimated by correcting for the "invisible energy" carried away by neutrinos and high energy muons [115]. An example of the measured light at aperture and the reconstructed light contributions, and energy deposit profile is shown in Fig. 34(a) and (b).

SD event reconstruction
The reconstruction of the energy and the arrival direction of the cosmic rays producing air showers that have triggered the surface detector array is based on the sizes and times of signals registered from individual SD stations. At the highest energies, above 10 EeV, the footprint of the air shower on the ground extends over more than 25 km 2 . By sampling both the arrival times and the deposited  The CLF fires 50 vertical shots at 0.5 Hz repetition rate every 15 minutes during the FD data acquisition. Specific GPS timing is used to distinguish laser from air shower events. The direction, time, and relative energy of each laser pulse is recorded at the CLF and later matched to the corresponding laser event in the FD data.
An upgrade [13] to the CLF is planned for the near future. This upgrade will add a backscatter Raman LIDAR receiver, a robotic calibration system, and replace the current flash lamp pumped laser by a diode pumped laser.

CLF data analysis
The light scattered out of the CLF laser beam is recorded by the FD (see figure 4 for the laser-FD geometry layout). The angles from the beam to the FD for vertical shots are in the range of 90 to 120 . As the differential scattering cross section of aerosol scattering is much smaller than the Rayleigh scattering cross section in this range, the scattering of light is dominated by well-known molecular processes. Laser tracks are recorded by the telescopes in the same format used for air shower measurements. In figure 5, a single 7 mJ CLF vertical shot as recorded from the Los Leones FD site is shown. In the left panel of figure 6, the corresponding light flux profile for the same event is shown. In figure 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 FD. Therefore, the analysis of the amount of CLF light that reaches the FD can be used to infer

Aerosol Characterisation
Molecular, or Rayleigh, scattering is a more significant attenuation process than aerosol scattering. The molecular vertical optical depth between ground level and an altitude of 5 km is about 0.23 at 350 nm. This compares with an average value for the aerosol vertical optical depth of about 0.05 to the same height. However, the molecular atmosphere is much more stable than the aerosol one, and we have shown that the GDAS description of the molecular atmosphere is perfectly adequate. The challenge is to monitor the aerosol concentrations locally at the Observatory, and on time scales of an hour or less.
Our primary techniques use the Central Laser Facility (CLF) and the eXtreme Laser Facility (XLF) as part of a "bistatic" lidar for which the receiving optics are the FD stations ( figure 4). In the past, cross-checks of the aerosol content have been provided by the standard elastic lidar stations at the FD sites. More recently, the FRAM telescope is contributing with aerosol estimates along the axes of interesting shower events [1,7]. Finally, the "industry to the detector. By comparing the profile in a given hour to one from the reference night (where we assume that the only attenuation process is Rayleigh scattering) we can obtain (using an analytic expression [3], and taking care with possible cloud contamination) the vertical aerosol optical depth (VAOD) as a function of height, VAOD(h). An example is shown in the right-hand plot of figure 5.
This process is repeated for all four FD stations viewing either the CLF or the XLF (typically the XLF for the northerly Loma Amarilla detector), and the VAOD(h) data is loaded into a MySQL database for use during shower reconstruction. The VAODs derived within the same hour using di↵erent combinations of laser and detector site are consistent within uncertainties [3], implying near-uniform aerosol conditions across the Observatory at a given time. With the aid of the database of VAOD(h), and the horizontally-uniform aerosol assumption, the shower analysis can calculate the aerosol attenuation between any two points in space.
The DN method fills the majority of hours in the aerosol database. For hours where the DN fails for some reason, holes are filled with the alternate Laser Simulation (LS) analysis. As the name implies, we simulate the received signals from the CLF or XLF under a variety of aerosol conditions, and use this library of simulations to find the best match with a real hourly profile. For technical reasons (accounting for systematics in the laser simulation) a clean reference night is also used in this method. The DN and LS results for many hours have been compared and found to be consistent [3]. which propagate through to systematic and statistical errors in the VAOD, and to quantities such as shower energy and X max . Correlated errors are correlated across a sample of EAS, while uncorrelated errors could vary in magnitude and sign from one EAS to the next.

Cross-checks
Since both methods for measuring the VAOD (DN and LS) use a reference night, we are not sensitive to systematic errors in the absolute laser or FD calibration, but we must take care of possible drifts in the relative calibrations between the reference night and the night in question. This is the origin of the "correlated" errors in the first three rows of Contribution to total uncertainties -energy

Correlated errors on shower energy
The Energy Scale of the Pierre Auger Observatory 33RD INTERNATIONAL COSMIC RAY CONFERENCE, RIO DE JANEIRO 2013 December 2012. The number of showers above 3 ⇥ 10 18 eV is 1475. The fit takes into account the resolutions of both E FD and S 38 (see table 2). The resolution of E FD is determined using all uncorrelated uncertainties described above. The fit yields: A = (0.190 ± 0.005) ⇥ 10 18 eV and B = 1.025 ± 0.007 and with a correlation coefficient of -0.98. The root-mean-square deviation of the distribution of AS B 38 /E FD is about 18.5%. It is dominated by low-energy showers and is compatible with the expected resolution obtained from the quadratic sum of all the uncertainties listed in table 2 (18% at 3 ⇥ 10 18 eV).

Uncertainties entering into the SD calibration fit
Aerosol optical depth 3%÷6% Horizontal uniformity 1% Atmosphere variability 1% Nightly relative calibration 3% Statistical error of the profile fit 5%÷3% Uncertainty in shower geometry 1.5% Invis. energy (shower-to-shower fluc.) 1.5% Sub total FD energy resolution 7% ÷ 8% Statistical error of the S(1000) fit [3] 12% ÷ 3% Uncert. in lateral distrib. function [3] 5% shower-to-shower fluctuations [3] 10% Sub total SD energy resolution 17% ÷ 12% Table 2: Uncertainties uncorrelated between different show-have found that E SD is stable within 5%, significantly above the statistical uncertainties. Even though these variations of E SD are consistent with the quoted systematic uncertainties, we use them conservatively to introduce another uncertainty of 5%. The FD uncertainties correlated between different showers should be propagated to the SD energy scale by shifting all FD energies coherently by their uncertainties. This means that the correlated uncertainties propagate entirely to the SD energies. Table 3 lists all uncertainties on the Auger energy scale. Most of them have a mild dependence on energy. When this dependence is non-negligible, we report the variation of the uncertainty in the energy range between 3 ⇥ 10 18 eV and 10 20 eV. The total uncertainty is about 14% and approximately independent of energy. We stress that we have made a significant improvement by comparison with the total 22% uncertainty reported previously [3].
Contribution to total uncertainties -X max understanding o and Cherenkov For this purpose the collection an of light expecte optical system a the shower. We larger in data t of observed-to-The correspond reconstruction l 10 17.8 eV which energies. Since observed and e camera is not un sided systematic data we estimate distribution can tainty from the The negative slope indicates that the aerosol content of the atmosphere has been underestimated. (b) Following the improvements made to aerosol extinction measurements. The slope is fully compatible with zero, demonstrating internal consistency within the data.

Conclusion
Two simplifying assumptions used in the calculation of the aerosol transmission properties of the atmosphere above the Pierre Auger Observatory have been removed. These refinements • However we continue fine tuning and cross checks, and we are in the process of tuning the assignment of uncertainties.
• For more detail on Auger's atmospheric measurements and analysis, see talks by my colleagues! Steven Saffi, University of Adelaide