Ultra high energy cosmic rays and the Pierre Auger Observatory
Generalities on cosmic rays
At the end of the 19th century, scientists were intrigued by the spontaneous discharge of electroscopes, indicating the presence of ionizing radiation on Earth In 1909, Wulf conducted an experiment atop the Eiffel Tower, suspecting Earth radioactivity as the cause, but found that the discharge rate did not decrease with altitude as expected, hinting at a downward radiation component Between 1911 and 1913, Austrian physicist Viktor Hess conducted balloon experiments reaching five kilometers high, discovering "unknown penetrating radiation coming from above, likely of extraterrestrial origin." His groundbreaking work earned him the Nobel Prize in Physics in 1936, shared with Carl Anderson.
In the following years cosmic rays became the subject of intense research, in particular with Millikan (who coined the name in 1925) and Anderson at Pikes Peak In
1927 the measurement of the east-west asymmetry and of the dependence of the rate on latitude established unambiguously that cosmic rays were charged particles, not photons
In 1938, Pierre Auger discovered extensive air showers (EAS) by utilizing coincidence counters, revealing that these phenomena are generated by extremely high-energy primary particles, with energies reaching at least 10^15 eV, interacting with the Earth's atmosphere.
In the 1930s and 1940s, cosmic rays served as a key laboratory for particle physics research before the rise of accelerators Notable discoveries during this period included Anderson's identification of the positron in 1932 and the muon in 1936, followed by Powell and Occhialini's discovery of the pion in 1947 This era also saw the emergence of strange particles such as kaons and hyperons However, by the 1950s, the focus shifted as accelerators became the primary tool for particle studies, leading to a decline in the exploration of cosmic rays for their intrinsic properties.
For many years following, major effort was devoted to the study of cosmic rays, telescopes, reached very high energies (John Linsley at Volcano Ranch saw the first
Space astronomy has significantly advanced the understanding of low-energy cosmic rays, especially solar energetic particles A notable example of this progress is NASA's Advanced Composition Explorer, launched in 1997 to the Lagrange point between the Earth and the Sun, which has provided valuable measurements in solar astronomy.
Over the past two decades, significant advancements in astrophysics and the development of high-energy accelerators have sparked a renewed interest in cosmic ray physics, now known as astroparticle physics Notably, the construction and operation of TeV gamma-ray detectors have been pivotal, as they offer the unique advantage of accurately identifying sources without interference from magnetic field deflections.
Figure 1.1 The pioneers: Viktor Hess and his balloon (upper panels), Pierre Auger at the
Jungfraujoch (lower left), and Anderson with his cloud chamber (lower right)
A new generation of ground detectors has emerged to study cosmic rays, with innovative plans to utilize the entire Earth's atmosphere as a radiator observable from space Additionally, pioneering efforts in neutrino astronomy are underway, advancing our understanding of these elusive particles.
Cosmic rays are highly energetic, ionized nuclei that travel through space, reaching energies around 10^20 eV Although they are relatively sparse, their contribution to the universe's energy density is comparable to that of the Cosmic Microwave Background (CMB), visible light, and magnetic fields, estimated at approximately 1 eV/cm³ Their energy spectrum follows a power law distribution, spanning 32 decades, with an approximate form of E^(-2.7).
Cosmic rays exhibit abundances akin to the elemental compositions found in their surrounding environments, indicating their acceleration from interstellar matter In galactic settings, hydrogen and helium are predominant, with even-even nuclei being favored and an enhancement observed in the iron region due to strong nuclear binding A key distinction lies in the valleys being filled by spallation reactions that occur as cosmic rays traverse the interstellar medium, averaging around 7 g/cm².
Figure 1.2 The cosmic ray energy spectrum displaying its main features
The low-energy portion of cosmic rays primarily originates from the Sun, but most of these rays do not reach Earth due to its protective magnetic field The energy density of cosmic rays on Earth is approximately 10^-12 erg/cm^3, with the majority believed to have a galactic origin This is attributed to the magnetic trapping within the Milky Way, which results in a galactic escape time of about 3 million years Consequently, the power of cosmic rays is significant.
Cosmic rays account for approximately 10% of the energy released by supernova (SN) explosions, which deliver around 10^51 erg per event, totaling roughly 10^-25 erg/cm³ With an estimated three supernovae occurring per century in the disk, the energy output from these explosions can be compared to the cosmic ray power of about 10^-26 erg/cm³ per second.
In the higher energy segment of the spectrum, an extragalactic component is detectable, with an estimated energy density of approximately 2 x 10^-19 erg/cm^3, indicating a significant power output.
~10 37 erg/Mpc 3 /s [8] Both active galactic nuclei (AGN) and gamma ray bursts (GRB) stand, from the point of view of energy, as possible sources
Particles emitted by the Sun can reach energies of several MeV and are primarily linked to solar activity and flares Coronal mass ejections and the subsequent interplanetary shocks also show a strong correlation with this solar activity In contrast, galactic cosmic rays are negatively correlated, as increased solar activity strengthens the Earth's magnetic field, which serves as a protective shield.
Gamma rays, unlike cosmic rays, travel directly through the universe, allowing them to point back to their sources They effectively detect high-energy decay photons resulting from neutral pions generated by the interaction of high-energy cosmic rays with interstellar matter Gamma ray astronomy has revealed that many sources have X-ray counterparts identified as supernova remnants (SNRs), indicating that a significant portion of galactic cosmic rays likely originates from these SNRs.
There are two primary types of Supernova Remnants (SNRs): Type Ia and Type II Type Ia arises when a white dwarf in a binary system accumulates matter from its companion star, reaching the Chandrasekhar mass limit of 1.4 solar masses, resulting in a fully burned core and a nearly empty SNR shell In contrast, Type II occurs when a massive star collapses into a neutron star, which may be identified as a pulsar, and its wind provides energy to the remnant, known as a plerion.
The High Energy Stereoscopic System (HESS) in Namibia features four telescopes arranged at the corners of a 120×120 m² square, designed to operate above 100 GeV With a field of view of 5 degrees and a resolution of just a few arc minutes, HESS can capture an image of the Crab Nebula in only 30 seconds.
Figure 1.4 Very high resolution X ray images of SNRs (Chandra) [12]
From left to right: Cassopieia A, the Crab, Kepler (SN 1604), Tycho (SN 1572) and N49
The Pierre Auger Observatory
The Pierre Auger Observatory (PAO) is a hybrid detector spanning 3000 km² that detects ultra-high energy cosmic rays (UHECR) through the fluorescence they emit in the atmosphere and their interactions with a ground detector array Its primary objective is to analyze the characteristics of UHECR, specifically those with energies exceeding 1 EeV (10^18 eV), focusing on the angular and energy dependence of their flux, mass composition, and the underlying mechanisms of their origin and acceleration.
Figure 1.10 Plan view of the PAO
The baseline design was finalized in June 2008, coinciding with the collection of the world's largest cosmic ray observation data set, which began in January 2004 during the Observatory's construction phase.
When a primary cosmic ray penetrates the Earth's atmosphere, it triggers a series of interactions that generate numerous mesons, leading to a cascade of events until the primary energy is depleted through ionization losses This process results in the formation of an extensive air shower (EAS), characterized by a longitudinal profile that gradually evolves with energy, proportional to its logarithm, while its energy content is also impacted.
A significant portion of mesons produced are pions, both neutral and charged Neutral pions quickly decay into two photons, which do not contribute to the hadronic cascade but instead create electromagnetic showers primarily composed of electrons, positrons, and photons, developing over a radiation length that is half the interaction length of the hadronic cascade Charged pions may decay into a muon-neutrino pair if their decay length of 56 m/GeV is sufficiently short relative to the interaction length.
As a result, the muon to electron/photon ratio increases with depth
Figure 1.11 Longitudinal development of an extensive air shower [23]
Around 30 EeV, the UHECR flux is about 0.2 km −2 century −1 sr −1 EeV −1 and drops rapidly at higher energies, implying a very large coverage, but the showers contain billions of particles when reaching ground and cover several square kilometers, allowing for a thin sampling [24] The PAO covers 3000 km 2 in the Argentinean pampas, of which only 5 ppm are covered by detectors These include 1600 Cherenkov detectors making up the surface detector (SD), and 24 fluorescence telescopes making up the fluorescence detector (FD) Data are transferred by radio to an acquisition centre which filters them and sends them out for subsequent dispatching to the laboratories associated with this research, including VATLY in Ha Noi
The SD is described in detail in the next section
The FD consists of four stations, each equipped with six telescopes that monitor the PAO area, capturing fluorescence light generated by the interaction of shower charged particles with atmospheric nitrogen molecules These telescopes operate only on clear, moonless nights, leading to a duty cycle of just 13% Each telescope has a 30° azimuth and 28.6° elevation field of view, reflecting filtered light onto an array of 440 hexagonal PMT pixels via a concave mirror While a single telescope can theoretically determine the shower axis direction, accurate measurements typically require binocular detection or simultaneous data from ground Cherenkov detectors Energy measurement relies on the longitudinal profile, which, when fully captured, allows for calorimetric evaluation of shower energy, with neutrinos and muons contributing about 10% of the total energy However, practical challenges arise due to the need for precise knowledge of air transparency, atmospheric Cherenkov light contamination, and the partial containment of the shower within the field of view.
Figure 1.12 Left: A fluorescence station: schematic view (on top) and its photograph
Right: Photograph of an eye
The SD samples the footprint of the showers on ground It is made of a triangular
At an altitude of 1400 meters, an 11 m² mirror captures high-energy ultra-high-energy cosmic rays (UHECRs) during their maximum shower development Upon reaching the ground, these showers primarily consist of low-energy electrons, positrons, photons, and muons with kinetic energies around a few GeV In water Cherenkov counters and scintillator plates, the muon signal correlates with track length, resulting in a signal proportional to the detector volume, regardless of incidence angle In contrast, electrons and photons generate smaller showers at radiation length scales, which are fully contained in water Cherenkov counters but only partially in scintillator plates Consequently, water Cherenkov counters offer twice the sky coverage compared to an array of scintillator plates.
The detection of shower particles in a minimum of three counters enables accurate measurement of the azimuth and zenith angles of the shower axis, while considering the slight curvature of the shower front.
Energy measurement in this context is indirect yet simpler than in the FD case It involves creating a standard function known as the lateral distribution function (LDF), which reflects the average signal recorded in a Cherenkov tank based on shower energy, distance from the shower axis, and zenith angle The evaluation of zenith angle dependence assumes an isotropic cosmic ray flux Ultimately, energy is determined by normalizing the measured signals to the standard LDF at a specified distance.
The reference point of 1000 meters from the shower axis, known as S(1000), is determined by two key factors: the tank spacing of 1.5 km and the logarithmic increase of the detectable shower footprint on the ground with energy In practice, the tank spacing has a more significant impact on this measurement The final energy scale is calibrated using fluorescence detector data from hybrid events, as shown in Figure 1.13.
Figure 1.13 Left: Correlation between the decimal logarithms of the energy measured in the FD
The analysis focuses on the normalization of measured SD signals to the reference value of S(1000) at a zenith angle of 38 degrees, utilizing 795 hybrid events for the fit The best fit line is illustrated, alongside the fractional difference between the calorimetric energy (E FD) and the energy estimate from the surface detector (E), derived from the calibration curve for the selected events.
Figure 1.14 illustrates the data collected by the SD, highlighting the shower's ground footprint and its alignment with the LDF Additionally, Figure 1.15 presents the inaugural four-fold hybrid event documented in May 2007, featuring all FD stations in operation.
Event 211377, showcasing a typical energy level of approximately 5x10^18 eV, is illustrated in Figure 1.14 The top left section displays a top view of the activated tanks, while the lower left presents the fit to the lateral distribution function (LDF) On the right, the FADC traces from four detectors highlight the varying signal sizes captured during the event.
Figure 1.15 The first four-fold hybrid event
Each Cherenkov counter consists of a resin tank designed to hold a cylindrical volume of ultra-pure water, measuring 1.2 m in height and 3.6 m in diameter The water is enclosed in a highly diffusive plastic bag that fits snugly within the resin tank, allowing Cherenkov light generated in the water to be detected by three 9" spherical photomultiplier tubes (PMTs) through high-transparency windows Although the PMTs are not shielded from the Earth's magnetic field, they are oriented in a manner that optimizes their response Each PMT features a two-part amplification chain, comprising a central foil dynode and a linear focus chain with seven dynodes, amplifying the charge collected from the last dynode to exceed the anode charge by a factor of 32 The signals are read using 50 Ω in 10-bit, 40 MHz fast analog-to-digital converters (FADCs) The high dynamic range resulting from the steep slope of the lateral distribution function (LDF) near the shower core can occasionally lead to saturation of the dynode signal.
Energy calibration is continuously monitored by recording low-energy atmospheric muons between triggers These relativistic muons pass through the tank, and their charge spectrum mirrors the distribution of track lengths in water, aligned with the typical cosine squared zenith angle distribution Notably, muons with small zenith angles constitute a significant portion of the total, creating a peak in the charge distribution that serves as a reference for monitoring the energy scale.
Figure 1.16 A photograph (left) and an exploded view of an Auger water tank
Identification of the primaries
Low energy cosmic rays exhibit abundances akin to interstellar matter, predominantly consisting of protons However, at ultra-high energy cosmic ray (UHECR) levels, the mass composition of primary particles remains uncertain While some theories propose the existence of particles beyond atomic nuclei in this energy range, the primary focus is on measuring the mass distribution of particles from protons to iron nuclei, as heavier nuclei are significantly less probable.
The primary distinction between showers caused by protons and iron nuclei lies in their initial interactions within the upper atmosphere Proton showers typically begin developing after traversing one interaction length, with their starting depth varying by the same measure In contrast, an iron shower can be viewed as the combined effect of 56 proton showers, each contributing 1/56 of the total nucleus energy, resulting in an earlier onset and less fluctuation in its starting point compared to proton showers Although this simplified model provides a basic understanding, the actual processes are much more intricate and not fully comprehended Notably, nucleons within the colliding nuclei do not all interact uniformly; some, known as wounded nucleons, behave as independent entities, while others, referred to as spectator nucleons, do not engage in the same manner.
− are unaffected This, again, is an oversimplified view of reality Glauber model [46] provides a recipe to evaluate the number of wounded nucleons
Nevertheless, as a general rule, in order to distinguish between light and heavy incident nuclei one will aim at measuring quantities that are sensitive to the early shower development
The significance of these measurements is clear, particularly in light of previous findings that suggest a substantial iron population may account for the lack of identifiable counterparts for some of the highest energy Ultra High Energy Cosmic Rays (UHECR).
The fluorescence detector (FD) at the Pierre Auger Observatory accurately measures the longitudinal profile of cosmic ray showers and determines the depth of maximum shower development (X max) At specific energy levels, both the average and the variability of the X max distribution are linked to the mass composition of cosmic rays Proton-induced showers penetrate further into the atmosphere, resulting in larger X max values and broader distributions compared to those produced by heavier nuclei.
Measuring shower particles presents challenges, necessitating a stringent selection of relevant events A favorable angular resolution of 0.6° is achieved by detecting shower particles in at least one Cherenkov tank of the Surface Detector (SD) and filtering out showers directed toward the telescope, requiring a pixel hit recording time of over 5 microseconds Additionally, the reconstructed X max must be clearly defined and within the field of view, necessitating an observed profile that spans at least 320 g cm−2 The reduced χ² of a fit to a reference profile must not exceed 2.5 and should be at least 4 units lower than that of a straight line fit Furthermore, uncertainties in the shower maximum and total energy must remain below 40 g cm−2 and 20%, respectively, with the uncertainty on the X max measurement determined from stereo events at 21±1.5 g cm−2 Recent results from the Pierre Auger Observatory (PAO) are illustrated alongside predictions from prominent hadronic models for protons and iron nuclei.
Figure 1.22 ⟨X max ⟩ and RMS(X max ) compared with air shower simulations [51] using different hadronic interaction models [34,35]
The time profile of particles reaching the ground is influenced by shower development, with muons arriving earlier than electrons and photons Each tank's FADC trace has a defined risetime (t 1/2), measuring the time it takes to go from 10% to 50% of the total integrated signal Both risetime and X max are expected to correlate with primary mass composition, which is evidenced by analyzing the risetime's dependence on zenith angle and distance to the shower axis A standard function is defined using a reference energy of 10^19 eV, similar to the approach for S(1000) at a distance of 1000 meters The derived quantity, Δ i, increases with energy, indicating deeper atmospheric shower development, and shows a clear correlation with X max While this correlation provides insights into mass composition, it primarily highlights the relative energy dependencies of X max and Δ i.
Figure 1.23 SD events: Dependence of the mean value of Δ i on energy
Figure 1.24 illustrates the relationship between the mean value of Δ i and X max in hybrid events, revealing a correlation that can be described by a linear fit The shaded regions represent the estimated uncertainty, calculated by randomly varying each data point within its measured error bar and reapplying the fitting method.
The risetime of particle showers exhibits a dependence on the tank azimuth ζ, particularly in inclined showers where upstream tanks are hit first, probing the shower's early development Due to geometric effects, upstream tanks detect a larger signal as particles reach them more quickly compared to downstream tanks While muon responses are generally independent of the angle of incidence, the responses of electrons and photons vary with it, leading to an azimuthal asymmetry in tank responses that increases with distance from the shower axis This asymmetry, particularly evident in the risetime's azimuthal dependence, peaks at a zenith angle θ max that correlates with the depth of shower density decline A fitting model reveals that the asymmetry ratio b/a is maximal around θP o, regardless of energy, contrasting with predictions from hadronic models that suggest an energy-dependent increase in the zenith angle for maximum asymmetry This finding implies a rise in mean primary masses with energy, aligning with FD measurements that indicate a shift from proton dominance to iron dominance as energy increases from 1 to 30 EeV.
Figure 1.25 Measured dependence of the position of maximum asymmetry on primary energy Lines correspond to fitted distributions of MC samples for proton (blue) and iron (red) primaries
The relative abundance of muons serves as an indicator of shower age, with older showers exhibiting higher muon levels Consequently, at the same depth, iron showers are anticipated to have a greater muon richness compared to proton showers Although direct measurements of muon abundance have not yet been conducted, various related quantities, such as risetime, have been extensively studied.
Alternative methods for identifying muons involve detecting sudden jumps in the FADC traces, known as the "jump method," as well as directly assessing the muon signal by subtracting the electron-photon contributions from the FADC trace.
The electron-photon signal in FADC traces is influenced by energy, zenith angle, and depth relative to X max, based on the assumption of isotropic shower detection and energy dependence from hadron models Under these conditions, the muon abundance remains the only variable, measured to be 1.53+0.08 (stat.)+0.21 (syst.) when compared to proton primaries, while a pure iron composition would suggest a lower value around 1.3.
The analysis of hybrid events provides crucial evidence by utilizing the longitudinal profile to differentiate between proton and iron hypotheses, ultimately allowing for accurate predictions of the ground signal amplitude.
Figure 1.26 illustrates the measured longitudinal and lateral profiles for a hybrid event, highlighting that the best-matching simulation is represented by squares and a dashed line in the lateral distribution Notably, the measured SD signal, depicted as circles and solid lines, exceeds the simulation by more than double.
Analyses of the FADC traces, particularly using the jump method, indicate that the muon abundance is significantly higher than what is predicted for iron by established hadronic models This discrepancy is illustrated in Figure 1.27, which suggests a potential 30% underestimate of the FD energy scale However, even accounting for this, the measured muon abundance remains above expectations for iron Furthermore, a recent energy-independent analysis indicates that the hadronic models may predict an excessively steep muon lateral distribution function, which could account for the increased muon component observed in the SD's D range This finding also aligns with the azimuthal asymmetry of the risetime, which correlates with the FD X max measurement, as both assessments independently evaluate the longitudinal profile, separate from the lateral distribution function.
Figure 1.27 illustrates the number of muons detected at a distance of 1000 meters relative to QGSJET-II/proton across different SD analyses, focusing on events with energy levels of log 10 (E/eV) = 19.0 ± 0.02 and angles θ ≤ 50° The results indicate that iron primaries produce 1.32 times more muons compared to protons, as represented by the horizontal lines in the figure.
FADC traces
General features
This section focuses on comparing the three FADC traces from the same tank to identify and explain any inconsistencies The analysis reveals that the inconsistencies are primarily related to two well-known issues: after pulses and early time PMT asymmetries Importantly, this analysis is performed without any preconceived assumptions about the expected outcomes.
The study is limited to dynode spectra, focusing on channels that do not saturate and excluding tanks with malfunctioning PMTs Data is processed by subtracting the baseline and scaling to VEM units using standard procedures, with the baseline averaging 51±7 ADC counts and the ADC to VEM conversion factor at 184±23, equating to 0.0054±0.0007 VEM per channel.
Figure 2.1 shows the distributions of the channel contents for the whole spectrum and for its lower part In each case the individual PMT spectra (full line) are shown
1 Using data from sdt4_v0r4_2006_05_01[2345]_12h00.root
The baseline subtraction is performed using an algorithm that combines the root mean square (RMS) of the signals with a mean spectrum, which is scaled by a factor of three for convenience This process clearly reveals the noise component, demonstrating its Gaussian nature, as illustrated in Figure 2.2 The individual PMT spectra exhibit a standard deviation of σ=0.0032 VEM, while the mean spectrum shows a reduced standard deviation of σ=0.0024 VEM.
The ADC counts were narrower than expected, with a ratio of 1/√3 suggesting a mean spectrum σ of 0.0018 VEM However, one ADC count was wider than σ at 0.0054 VEM versus 0.0032 VEM, necessitating consideration of this discrepancy A toy Monte Carlo simulation was employed, generating Gaussian noise with σ=0.0028 VEM, resulting in individual spectra in bins of 0.0054 VEM having σ=0.0032 VEM The mean spectrum's σ was found to be 0.0018 VEM, contrasting with the observed 0.0024 VEM, indicating a correlation among the three PMT noises To address this, the Monte Carlo simulation was adjusted to include two Gaussian noise contributions for each PMT: one specific and one common across all three With equal contributions of 0.0020 VEM, the PMT distributions maintained an rms of 0.0032 VEM, while the mean adjusted to 0.0024 VEM, aligning with the data The mean rms calculated to zero, representing the square root of one third of the sum of the squares of the three PMT signals, was 0.0027 VEM, closely matching the 0.0028 VEM observed in the data.
Figure 2.1 illustrates the distributions of channel contents across the entire spectrum on the left and specifically highlights the lower part of the spectrum on the right The individual PMT spectra are represented by full lines, accompanied by the mean spectra, which have been scaled up by a factor of three for clarity.
Figure 2.2 Distribution of the noise component for both the individual PMT spectra (left) and for their mean (right)
In summary, evidence indicates the presence of Gaussian noise with an rms of 0.0028 VEM, which aligns with two similar Gaussian components of 0.0020 VEM each—one linked to each PMT and the other shared among all three PMTs The ADC count's significant width results in a wider noise spectrum, measured at an rms of 0.0032 VEM Implementing a cut at 0.015 VEM on individual PMT spectra effectively enhances noise rejection.
Scanning event displays has uncovered instances where traces become negative over extended periods Preliminary investigations indicate that in the later sections of the FADC trace, the baseline occasionally dips into negative territory, particularly as the charge measured in the early part of the trace increases This phenomenon is observed in both anode and dynode traces.
The study utilizes raw dynode data prior to baseline subtraction and ADC count to VEM conversion, with an enhanced algorithm defining the baseline Initially, the maximum and minimum FADC bin contents are identified within each of the sixteen 48-bin intervals from the traces of three PMTs, revealing a distribution of differences as illustrated in Figure 2.3 In intervals lacking complete signal occupancy, noise remains within 4 counts, where the maximum equals the minimum Subsequently, the mean and RMS values of the FADC content, measured in ADC counts, are calculated for bins where the content exceeds minimum+3 Figure 2.4 presents a comparison of this baseline evaluation against the standard method used in the official Auger software for selected intervals.
Figure 2.3 Distributions of the difference between maximum and minimum ADC counts in some
Figure 2.4 Distribution of the difference between the baseline in intervals 1, 6, 7, 8 (upper left), 9,
10, 11, 12 (upper right) and 13, 14, 15, 16 (lower) and the Auger official baseline (corresponding essentially to interval 1) The red curves show the effect of the present correction (see text)
In the initial intervals, the current and official baseline evaluations align perfectly, as the official baseline is primarily derived from the first interval However, in intervals 6 and 7, the signal density is such that the current baseline definition often fails From the eighth interval onward, several traces indicate a lower baseline compared to earlier evaluations Notably, when the current baseline aligns with the official baseline in the final interval, this consistency holds throughout; conversely, when there is a disagreement in the last interval, this discrepancy is observed consistently across all intervals.
A base-line correction is therefore defined accordingly with a standard shape displayed in Figure 2.5
Figure 2.5 Shape of the baseline correction (below bin 260 there is no correction)
The baseline correction for a given trace utilizes the last interval, characterized by low signal density, as a reference to appropriately scale the standard shape Consequently, the baseline is accurately adjusted in both the last and initial intervals As depicted in Figure 2.4, this correction results in an average baseline accuracy of better than 0.1 ADC count across all intervals, except for traces with very strong early signals (typically 200 VEM or more), which should be excluded in studies focused on identifying small signals However, in analyses where data near the shower core is significant, such as evaluating the lateral distribution function, these strong signals must be retained.
The previously described effect is attributed to the recovery time of the divider chain capacitors, with dynode amplifier traces showing minimal impact However, the bump observed around bin 500 is not explained by this effect; it is linked to after pulses that increase in density with the amplitude of the main signal These after pulses average 0.12 VEM in amplitude, and their identification as significant signals depends on the threshold set for detection The distinction between the bump in Figure 2.5 and the underlying undershoot is crucial, as further discussion will occur in Section 4.2.1 regarding stopping muon decays.
A preliminary estimate suggests that the uncertainty in photoelectron statistics is about 50 photoelectrons per VEM, while other sources indicate this figure is closer to 100 This discrepancy prompts the need for a direct evaluation from existing data However, conducting such an evaluation is challenging due to the suboptimal operation mode of the SD PMTs, which makes it nearly impossible to distinguish a single photoelectron peak from multiple photoelectrons.
This analysis employs baseline correction and raw ADC counts prior to conversion to VEM The "strong segment," characterized by a higher charge, significantly influences the disturbance level from after pulses and related effects Traces with a strong signal charge exceeding 20 VEM or a total charge over 40 VEM are excluded from the analysis Isolated two-bin segments are selected to capture low-intensity signals, potentially originating from photoelectrons due to the photoelectric effect or thermal noise A single photoelectron is expected to fit within a few nanoseconds, making segments wider than 2 bins unnecessary Isolation criteria require fewer than 3 ADC counts in the two bins before and after the segment for each PMT, totaling 12 counts Additionally, the signal condition mandates that the content of the other two PMT segments exceeds a threshold, S_thr, which is set to prevent bias The segment content, S_i, is considered valid only if S_m and S_n exceed S_thr, where i, m, and n represent a permutation of the PMTs Early segments (below bin 200) are identified as noise, while late segments (above bin 260) may contain signals.
Figure 2.6 S i spectrum for isolated segments above bin 260 having S m,n >4 (upper left), 6 (upper right) and 8 (lower panel) The 0 photoelectron contribution (normalized in the negative region) is superimposed
Figure 2.6 illustrates the distribution of S i for late segments with S thr values of 4, 6, and 8 ADC counts The S i values are adjusted for PMT gains, which vary significantly, by multiplying by the VEM/count for each PMT and dividing by the mean value of 0.0054 There are 21,688 isolated segments in the noise (early) region compared to 53,032 in the signal (late) region, indicating a factor of 2.445 increase This normalization allows for the evaluation of noise contributions in traces without light in the tank, where PMTs m and n fluctuate enough to pass the cut Although this evaluation may overestimate noise segments in the signal region, it represents only a small fraction of the 0-photoelectron peak shown in Figure 2.6 Furthermore, when light reaches PMTs m and n, it is possible that no photoelectrons are emitted from PMT i if light does not reach it or if no photoelectrons are produced, as the quantum efficiency is approximately 20%.
Figure 2.7 Distribution of the (VEM/ADC count) values showing the dispersion of the PMT gains
Figure 2.8 Left: S i spectrum for isolated segments above bin 260 having S m,n >6 The normalized
0 photoelectron contribution is superimposed Right: noise-subtracted (normalized in the negative region) S i spectrum for isolated segments above bin 260 having S m,n >6 Also shown is the
Gaussian fit of the rising edge
The shape of the 0-photoelectron contribution remains consistent, regardless of whether it is influenced by fluctuating noise from PMTs m and n or by light in the tank without photoelectrons reaching the dynode chain of PMT i This contribution is solely attributed to noise causing baseline fluctuations, which is characterized by a known Gaussian shape centered at 0 with a root mean square (rms) of 0.75 ADC counts, indicating a √2 increase compared to a single bin expectation By scaling the noise spectrum in the negative region, one can effectively subtract this contribution, resulting in spectra similar to that illustrated in Figure 2.8.
Pattern recognition
Many SD studies, in particular those concerned with the primary mass composition, imply an evaluation of the muon fraction on ground
Resolving the FADC traces from the PAO surface detector into distinct signals is crucial for differentiating between muon and electron-photon components in a shower, significantly aiding the analysis of PAO data for primary identification Various methods have been explored, including the subtraction of exponential decay tails and standard pattern recognition techniques, as well as identifying upward jumps Additionally, some strategies leverage supplementary data, such as the expectation that muons exhibit greater statistical fluctuations and arrive earlier than electron-photons.
This section focuses exclusively on the challenge of pattern recognition, building upon earlier studies, particularly Reference 67, while enhancing the methodology by incorporating insights from the early time asymmetry of the responses of three photomultiplier tubes (PMTs) within the same tank to a common light source It optimally utilizes the information derived solely from the FADC data The exceptional optical characteristics of the Cherenkov tanks, characterized by a typical decay time of 75 ns and an average of eight successive wall diffusions, combined with the low noise performance of the associated electronics, significantly contribute to the effectiveness of this approach.
The subtraction algorithm discussed in [67] is based on the slow decay of light produced in a Cherenkov tank, which occurs due to absorption in the tank walls, absorption in water, and escape into PMT photocathodes The decay time is a characteristic of the tank and remains relatively consistent across events, as light is quickly randomized Consequently, the light collected in a specific FADC bin (25 ns wide) must be followed in the next bin by light of the same origin, diminished by a constant factor f that is determined solely by the tank's optical properties Any additional light detected must originate from a different source By subtracting the previous bin's content scaled down by f from each bin, the algorithm effectively isolates individual peaks, each corresponding to a distinct source.
The signal's starting point does not align precisely with the beginning of a bin, indicating that the trace should be understood as a representation of fundamental physical properties related to the tank's optics, rather than just a mathematical manipulation.
The emergence of a new light source within a tank is indicated by an upward spike in the FADC trace, leading to a peak after applying the subtraction algorithm outlined in [67] Additionally, a pronounced early time asymmetry in the responses from the three PMTs is a distinctive characteristic of this new light source, as discussed in [66, 75] This asymmetry is closely linked to the azimuth of the particle trajectory that generates the new light, making it a universal feature that can be utilized to identify new signals and potentially enhance the algorithm referenced in [67].
The limitations of non-zero width in FADC bins are intrinsic to the detector and cannot be mitigated When multiple signals occur within the same bin, they remain unresolved Additionally, if two peaks appear in consecutive FADC bins after applying the subtraction algorithm, it is typically impossible to determine whether they correspond to a single signal or multiple signals Consequently, these limitations can only be addressed statistically rather than on an individual event basis.
2.2.2 Preliminary data reduction and selection
The current study utilizes data that adheres to the offline trigger methodology, demonstrating its effectiveness Additionally, a comparison with Reference 67 is conducted using 31 files that were similarly selected, encompassing the entire month of May.
2006 In general, dynode data are used; only when they show saturation are anode data used instead Tanks having one or more PMTs tagged as not working properly are rejected
The baseline correction discussed earlier is utilized to enhance the differentiation between important signals and noise fluctuations Currently, traces with substantial charge collected in the early bins, particularly from tanks near the shower core, are excluded, resulting in the elimination of 13% of the tanks.
Each bin charge \( q_{ij} \) (measured in FADC bin \( i \) of PMT \( j \)) has an associated uncertainty given by \( \Delta q_{ij} = \sqrt{0.66E–5 + 0.0225q_i + 0.00104q_i^2} \) Here, \( q_i \) represents the arithmetic mean (unweighted) of the three PMT charges collected in bin \( i \), expressed in VEM units, noting that one FADC count averages to 0.0054 VEM.
Segments in each tank trace are identified as sets of consecutive bins with charges exceeding 0.025 VEM across three PMTs, averaging 1.7, 0.9, and 2.4 segments per event with widths of 1, 2, or ≥3 bins, respectively Segments less than 3 bins wide, often caused by noise fluctuations or after pulsing, are disregarded in this analysis Therefore, "segment" refers to those that are at least three bins wide, with a mean width of 10.8 bins and a root mean square of 7.6 bins The distributions of zenith angle and energy for the events analyzed are illustrated in Figure 2.19.
The left side of Figure 2.19 illustrates the distribution of zenith angles (in degrees) for the event sample analyzed in this section, while the right side presents the distribution of the decimal logarithm of energy (in EeV) for the same event sample.
The subtraction algorithm outlined in Reference 67 relies on understanding the light decay time, represented by the factor f, which remains consistent across all PMTs within a tank and throughout the FADC trace duration An excessively high value of f leads to significant subtraction, resulting in negative charges in FADC bins, while a value that is too low causes surplus charges in bins with zero charge The optimization process aims to maximize the sum of significance levels associated with the χ² of each bin, testing the hypothesis that it remains empty post-subtraction By ensuring all bins are of equal width, this maximization identifies the optimal f value that maintains the longest time span consistent with zero charge Although it may not be initially clear if the data quality is adequate for this approach, it ultimately proves to be sufficient.
Precisely, for bin i, χ 2 i | empty =(q i – fq i–1 ) 2 /(Δq i 2 +f 2 Δq i–1 2 ) The significance level to be maximized is Σ=∑ i [1−∫exp(−x/2)dx/√(2π x)] where the integral spans from 0 to u = χ 2 i | empty
Then, f =∑{exp(−u/2)/√ (u) s i s i-1 /(Δq i 2 +f 2 Δq i–1 2 )}/ ∑{exp(−u/2)/√ (u) s i 2 /(Δq i 2 +f 2 Δq i–1 2 )}, where s is the bin content after subtraction
The optimization process is completed in four iterations, ensuring convergence is achieved As illustrated in Figure 2.20, the distribution of Σ corresponds to an average value of f = 0.74, with individual values for each tank also displayed.
Following the optimization procedure, the mean value of Σ has seen a modest increase of only 3% As illustrated in Figure 2.21, the values of f obtained post-optimization are tightly clustered within a narrow range of 0.74 ± 0.16, with a root mean square (rms) value of 0.04 With the value of f meticulously adjusted for each tank during each event, it is now possible to analyze the impact of fluctuations on the subtraction algorithm.
The values of f obtained from the inclusive muon signal are larger than those derived from between-event measurements, with the latter showing two distinct peaks at 0.66 and 0.70, the latter being three times smaller The narrower distribution has an rms of 0.02 compared to 0.04 for the former, and there is no correlation between the two methods of evaluating f The mean value of Σ using the inclusive muon signal is 9% smaller than that in Figure 2.21 and 6% smaller than when using f=0.74 for all tanks It's important to note that in 18% of cases, the inclusive value of f is unavailable, leading to the exclusion of those events in comparisons Additionally, smaller f values are observed farther from the shower core, indicating a bias toward larger f values when multiple signals overlap, though this effect is not significant for the current study A cut was applied to events with specific f values when necessary.
Figure 2.20 Distribution of Σ (see text) before (black) and after (red) optimization of the light decay time in each tank
Figure 2.21 Distribution of the decay factors f adjusted in each tank to maximize Σ (see text)