How were the cosmic-ray Open Data selected?
The Open Data includes 10% of the data set used in the Auger physics analyses presented at the International Cosmic Ray Conference in 2019. They correspond to the events for which the identification number ("sdid") ends with a zero.
The Open Data recorded with the water-Cherenkov detector arrays are the result of a set of selection criteria applied to detected events. The first requires that the WCD with the highest signal, or closest to the core, is surrounded by a hexagon of six stations that are operational. This requirement ensures adequate sampling of the shower and allows for the evaluation of the aperture of the surface detector in a purely geometrical manner in the energy regime where the array is fully efficient [Nucl.Instrum.Meth.A 613 (2010) 29-39 (arXiv), JCAP 08(2014) 019 (arXiv)], [ Eur. Phys. J. C 81, 966 (2021) (arXiv)]. The detection-efficiency of the SD1500 array is greater than 97% for events with energy above 2.5 x 1018eV arriving from a zenith angle (θ) less than 60°, and 4 x 1018 eV for showers arriving between 60° and 80°. For the SD750 array, the detection efficiency becomes greater than 98% at around 1017eV.
The Open Data of the surface detector arrays have also been subjected to criteria that guarantee good performance of operation: for example, time intervals during which the data acquisition was unstable are excluded; photomultipliers with unstable baseline, loss of calibration data, unstable ratio between high- and low-gain channels, etc., are also excluded.
The Open Data for the hybrid events are selected by requiring the fulfillment of several criteria, including hardware status (at the level of the telescope and pixels) and requiring the quality of the reconstruction of shower geometry and profile (including uncertainties associated with the energy and depth of maximum). Additionally, the atmospheric characterization (including information on the presence of aerosols and clouds, and the vertical optical transparency) is taken into account. Specific fiducial volume cuts are applied for different analyses in order to achieve uniform acceptance and minimize the uncertainties on the corresponding observables. Events passing the selection for the energy spectrum, the calibration, and/or the depth of maximum analyses, are flagged accordingly ("hdSpectrum","hdCalib","hdXmax").
How were the cosmic-ray Open Data reconstructed?
To illustrate the reconstruction procedures used for events recorded with WCD arrays and with the air-fluorescence telescopes (and the related variables) two exemplary events are used. One (event 81847956000) triggered simultaneously the SD1500 array and two FD sites, the other (event 141476578900) triggered the SD750 array and the HEAT-Coihueco telescopes. The figures are extracted from the event-display, where these events are available: event 81847956000, event 141476578900.
Footprint of an extensive air shower hitting WCD stations in the SD750 array (see text)
Footprint of an extensive air shower hitting WCD stations in the SD1500 array (see text)
In the adjacent figures the ground view of each event is shown. The colored squares indicate the FD sites that observed the shower. The colored dots correspond to SD1500 (SD750) stations which were hit by the shower particles and that have been selected for the reconstruction process ("recstations"). The areas of the dots are proportional to the logarithm of the magnitude of the signal sizes, while the colors represent the time of arrival ("t") at the different stations (green: early stations; red: late stations). The grey dots indicate detectors which have recorded no signal, while the black dots represent those which, even if a signal was recorded, were not part of the shower event ("isSelected=0"), but due to an unassociated cosmic ray (usually a muon). The position of the core ("x", "y", "z"), where the highest signal would be observed, is marked by the head of the blue arrow, which indicates the azimuth angle ("phi") of the shower direction of arrival.
The signal timing and signal sizes measured in each selected station, as well as the positions of the stations (the stations coordinates can be found in sdMap.csv), are the inputs for the reconstruction of the events [JINST 15 (2020) P10021 (arXiv)].
The signal features are computed from the output of the flash analogue-to-digital converters (FADCs) associated with each photomultiplier (PMT). Examples of such signals in two stations in the event are displayed in the figure below.
FADC traces of the PMTs signals in two different WCD stations hit by the shower
The FADC trace, shown for each of the 3 PMTs with different colors, are for a station 565 m away from the core (top figure) and one 2602 m away (bottom figure). They are expressed in terms of VEMs (Vertical Equivalent Muons) where one VEM is the signal due to a single muon traversing a detector. The FADCs are digitised so as to give a measurement every 25 ns. The traces from the closer detector are relatively smooth and are compressed into ~1000 ns while at the greater distance the signal arrives over a period of ~4000 ns. Most of the large spikes seen in the more distant FADC signals are probably due to muons which cross the detector, though high-energy electrons that would penetrate the full depth of the water may be present close to the shower axis and are expected to arrive early in the time window. More typically, however, the mean energy of an electron or photon in a shower at several 100 metres from the shower axis is ~10 MeV in contrast to typical muon energies of > 500 MeV. The energy loss of a relativistic particle that traverses a tank in a vertical direction is ~250 MeV.
The signal timing, in terms of start- and stop-times (located at "signalStartBin", "signalStopBin" in the trace, respectively), is determined from a separate analysis of the structures of the FADC traces, after the subtraction of the baselines, in the high-gain channel of each working PMTs in a station. By merging the extracted information from the PMTs, the start-time ("t") that is determined represents the best estimate of the beginning of the passing shower front. The procedure applied to determine the stop-time ensures that all particles belonging to the shower are included while excluding as many accidental signals as possible. The signal size ("signal") is obtained by integrating the final trace (converted in VEMs), which consists of the bin-by-bin average of the traces of the PMTs in the high-gain channel ("sat=0"), or low-gain channel if the high-gain is saturated ("sat=1", "sat=2"), between the determined start and stop times.
To initiate the reconstruction of the zenith and azimuth angles of the shower arrival direction ("theta", "phi"), an estimation of the location of the core on the ground is obtained as the signal-weighted center-of-mass of the selected stations in an event. Then the start-times of the signals in each station are fitted to a model that describes the shower particles as moving with the speed of light in a curved shower front. Thus the two directional cosines and the time at which the core strikes the ground are determined. The radius of curvature ("R") is also set as a free parameter when five or more stations are selected for the event reconstruction. The arrival direction is determined to a precision of about 1°, a figure that falls as the energy (and hence the multiplicity of stations triggered) rises.
Fall-off of the signals size as a function of the distance to the shower core (blue dots) fitted with the lateral distribution function (yellow line)
The reconstruction of the arrival direction of the shower is followed by the calculation of the energy estimator and of the position of the impact point at the ground ("x", "y", "z"). For vertical events, a fit to a lateral distribution function (ldf) is performed. In the adjacent figure the fall-off of the signal sizes (blue dots) with distance ("spDistance"), in a plane perpendicular to the direction of the shower, is shown together with a yellow line that defines the ldf used to fit the event. The signal at an “optimal distance”, which depends predominantly on the spacing between detectors and can be found accurately independent of knowledge of the exact shape of the ldf, represents the shower size and acts as a surrogate for the energy of the primary particle which has initiated the shower. For a spacing of 1500 m the optimal distance is 1000 m, thus the reference signal is S(1000), ("s1000"), while for a spacing of 750 m the optimal distance is 450 m and the reference signal is is S(450), ("s450"). The uncertainty in the measurement of S(1000) decreases from 15% at a shower size of 10 VEM (roughly corresponding to E ~ 2.5 x 1018 eV) to 5% at the highest shower sizes. The uncertainty on the impact point is of order 50 m. The reference signal is influenced by changes in atmospheric conditions that affect shower development [JINST 12 (2017) P02006 (arXiv)] and by the geomagnetic field that impacts on the shower particle-density [JCAP11 (2011) 022 (arXiv)]. Corrections of order 2% and 1% for the atmospheric and geomagnetic effects ("wcorr", "gcorr"), respectively, are made to the reference signal.
Parameterized densities of muons for a 10 EeV proton shower at zenith angles of 60°, 70° and 80°arriving from azimuth, φ = 0°. Radial units are in kilometers. The coordinate system is defined in the plane perpendicular to the shower direction with the y-axis parallel to the projection of the Earth’s magnetic field on that plane. The magnitude of the muon densities are indicated along the solid line.
For inclined events, the method used for reconstruction of the energy estimator and core position is modified. Due to their long path in the atmosphere, muons, the particles that contribute most of the signal for inclined showers, are deflected in the Earth’s magnetic field. As a result, the near-cylindrical symmetry of the showers is lost and the distribution of the signals at the ground is described with a 2D ldf (so-called muon map). By scaling the muon map of a reference proton shower at 1019 eV an energy estimator, N19 ("n19"), is obtained. The uncertainty in N19 decreases from 13% at E ~ 4 x 1018 eV to 4% at the highest energy. The uncertainty on the impact point is of order 100 m [ JCAP 08(2014) 019 (arXiv)].
For a cosmic ray of a given energy, the shower size estimators depend on the zenith angle because, once it has passed the depth of shower maximum, a shower is attenuated as it traverses the atmosphere. The intensity of cosmic rays, defined as the number of events per steradian above some S(1000)/S(450)/ N19 threshold, is thus dependent on zenith angle. Given the highly isotropic flux, the intensity is expected to be independent from the zenith angle after correction for the attenuation. Based on this principle, an empirical procedure, the so-called Constant Intensity method, is used to determine the attenuation curve as a function of the zenith angle and therefore an energy estimator, independent of the zenith angle. This can be thought as being the signal at 1000 (450) meters, or N19, that a shower would have produced had it arrived at 38° (35°) or 68°, the median angles of the zenith distribution for the SD1500 (SD750) array in the respective angular ranges (vertical or inclined). The energy ("energy") associated with the SD event is derived from a calibration between the energy estimator S38 (S35) or N68, "s38" ("s35") or "n68", and the energy measured by the FD ("totalEnergy") in golden-hybrid events. The SD1500 energy resolution is about 20% at 2x1018 eV and about 7% above 2x1019 eV. The systematic uncertainty on the energy scale is 14% [Physical Review D 102, 062005 (2020) (arXiv)]. The SD750 energy resolution is about 22% at 1017 eV and about 12% above 1018 eV [ Eur. Phys. J. C 81, 966 (2021) (arXiv)].Camera view for Coihueco
Camera view for HEAT-Coihueco
In the adjacent figure the shower images observed with the Los Leones, Coihueco, and HEAT-Coihueco fluorescence telescopes are displayed. The colors show the time at which the light reaches each pixel ("pixelTime"). The trigger conditions require some pixels to be aligned, but background light can also be recorded (the variable "pixelStatus" will also tell up to which level they are used to reconstruct the shower).
Together with the telescope position, the direction that the pixels point to in the sky (shown in Elevation and Azimuth angles -- from fdPixelMap.csv) determine a plane containing the shower development in the atmosphere ("SDP") . The shower axis within this plane is obtained from the time of arrival of the light at the camera ("TimeFit"), summing the contributions of two distances traveled at the speed of light: the distance crossed by the shower front to a point where light is emitted and the distance this light crosses to the telescope. The time at which the shower front reaches the ground, given by the timing information from the WCD station with the highest signal ("hottestStationId"), sets a strong constraint on the hybrid geometrical reconstruction, (providing "theta", "phi", "x", "y", "z"). For this event, the hottest WCD station is found at ("distSdpStation") around 500 m from the shower detector plane defined with Los Leones and around 250 m for the plane defined with Coihueco (at slightly larger distances from the reconstructed shower axis, "distAxisStation").
The next figure shows the energy deposited ("energyDepositProf") in the atmosphere as a function of the slant depth crossed by the cosmic ray ("atmDepthProf"), as seen independently in the two FD sites. LL is shown in blue and CO in green: the density of points and the uncertainty changes with the position from which the shower is seen.
The integral of this curve gives a direct measurement of the calorimetric energy ("calEnergy") of the primary particle, while the depth at which the maximum of the energy deposition occurs ("xmax") is used to infer the primary particle properties. The reconstruction of each point in the profile from the light seen on the camera ("pixelCharge") depends on the distance to the telescope and on the height in the atmosphere at which the energy is deposited ("distXmax" and "heightXmax").
The detected fluorescence light is proportional to the energy deposition and is emitted isotropically. Cherenkov light is emitted in the forward direction and enters the telescope directly when the shower axis is viewed from the telescope at a small angle ("minViewAngle"). It can also be scattered and reach the telescope at later times, which usually accounts for a fraction of the total detected photons ("cherenkovFraction"). For this example, the minimum viewing angles are 18° and 52°, at LL and CO, respectively; with corresponding Cherenkov fractions of 17% and 7%. Both Fluorescence and Cherenkov light are used in the reconstruction [Nucl.Instrum.Meth.A 798 (2015) 172-213 (arXiv)]. The light is attenuated and scattered when crossing the atmosphere, so both the distance traveled and the atmospheric parameters must be taken into account when estimating the expected number of detected photons that correspond to the emission at each position in the shower development, which is proportional to the deposited energy. The energy deposited per unit depth (dE/dX) in the atmosphere increases, at first, with the multiplication of particles in the shower, and then decreases as the energy loss by ionisation starts to exceed that by Bremsstrahlung. This behavior gives rise to a reasonably universal profile shape, where the position of the maximum Xmax depends on the primary particle type (and its energy). The shape of the profile is described by xmax and the corresponding dEdXmax and two other variables (upsL and uspR) [JCAP 03 (2019) 018 (arXiv)]. The integration of the profile provides a direct calorimetric measurement of the total energy of the primary cosmic ray (calEnergy), pending the correction from the energy taken away by muons (that can be partially detected in the SD) and neutrinos (which will go undetected) [Phys. Rev. D 100, 082003 (2019) (arXiv)] to finally obtain the totalEnergy.