Recent advancements in gamma-ray astronomy have led to the identification of young Supernova Remnants (SNR) as the primary sources of cosmic rays, a discovery made a century after cosmic rays were first detected The challenge in pinpointing these sources stems from the bending of cosmic rays within the Milky Way's magnetic field, complicating their association with known celestial objects However, the detection of gamma rays exceeding one TeV has revealed these emissions originate from the shells of young SNRs, facilitated by neutral pions formed during cosmic ray interactions with the interstellar medium High-resolution X-ray images of several SNRs have been analyzed alongside gamma-ray data, reinforcing the connection and confirming that young SNRs are likely the main source of galactic cosmic rays Furthermore, the finding that cosmic rays emanate from the shells rather than the centers of SNRs supports the theory of Diffusive Shock Acceleration (DSA) as the predominant acceleration mechanism.
Recent findings have not yet clarified the extragalactic component of Ultra High Energy Cosmic Rays (UHECR), hindering the identification of their sources and acceleration mechanisms Current gamma ray observatories are insufficient for detecting UHECR-induced gamma rays due to their extremely low flux, estimated at about one particle per square kilometer per century above 20 EeV If Diffusive Shock Acceleration (DSA) is indeed the acceleration mechanism for UHECR, it necessitates shock and confinement volumes—size multiplied by magnetic field—much larger than those found in Supernova Remnants (SNRs) This points to Active Galactic Nuclei (AGN) and potentially Gamma Ray Bursts (GRB) as the most promising candidates for UHECR sources.
The recent construction of the Pierre Auger Observatory (PAO) has significantly advanced our understanding of ultra-high-energy cosmic rays (UHECR) Associated with our laboratory, the PAO features an extensive network of 1,600 Cherenkov counters, enabling groundbreaking research in this field.
The PAO has gathered an unprecedented sample of ultra-high-energy cosmic rays (UHECRs) exceeding 50 EeV from a 3000 km² area in the Argentinean pampas, enabling significant advancements in UHECR physics Two key findings have emerged: the detection of a cut-off in the energy distribution around 100 EeV, linked to pion photoproduction during interactions with the Cosmic Microwave Background (CMB), and evidence suggesting a correlation between UHECRs with energies over 60 EeV and nearby extragalactic matter within 75 Mpc.
Recent comparisons with existing galaxy catalogs reveal that approximately 38±7% of selected Ultra High Energy Cosmic Rays (UHECRs) are associated with active galactic nuclei (AGN) within a 3.1-degree radius, significantly higher than the 21% expected from an isotropic distribution This correlation was nearly double in 2007, at 69±12%, suggesting a large statistical fluctuation Notably, there is strong evidence of a significant correlation with the Centaurus A (Cen A) region.
The Pierre Auger Observatory (PAO) has observed a trend indicating that primary cosmic rays become heavier as energy increases, particularly below 50 EeV This conclusion is based on measurements of the atmospheric depth at which shower development reaches its maximum, known as the elongation rate, which is expected to be higher for massive nuclei compared to protons However, the analysis of muon density at ground level remains inconclusive due to discrepancies between actual observations and predictions from conventional hadronic shower models Additionally, there are compelling arguments suggesting that in the ultra-high-energy cosmic ray (UHECR) region, the presence of nuclei other than iron and hydrogen is likely to be minimal.
The mystery surrounding ultra-high-energy cosmic rays (UHECRs) remains unresolved, with a potential explanation suggesting that those directed towards nearby galaxies, particularly Centaurus A, may be protons, while others could be iron nuclei However, fully ionized iron nuclei are likely to experience significant deflection in the Milky Way's magnetic field, complicating their source association Ultimately, further data and research are essential to address the existing questions in this field.
This article presents a significant contribution to the research program, emphasizing methods that utilize ground muon density for identifying primary masses Specifically, it highlights the "jump method," which was developed at LAL-Orsay and serves as a key inspiration for this work The article is structured into six chapters, including this introduction.
Chapter 2 introduces cosmic ray physics, focusing on ultra-high-energy cosmic rays (UHECRs) as analyzed by the Pierre Auger Observatory (PAO) It begins with an overview of cosmic rays, followed by a concise description of the PAO's key features and a review of the current status of primary cosmic ray identification.
Chapter 3 focuses on the jump method, providing an in-depth analysis of its effectiveness in distinguishing between iron and proton primary particles The chapter examines how jump analyses vary with energy and includes an energy-independent analysis that rules out the possibility that discrepancies between measured and predicted muon densities on the ground are due to a shift in the energy scale.
Chapters 4 and 5 present simulations aimed at simplifying the study of shower development mechanisms to address the discrepancies between observed muon density on the ground and predictions from advanced models Chapter 4 focuses on electromagnetic shower development, utilizing only two processes—pair creation and bremsstrahlung—and two particle types: electrons and photons This streamlined approach facilitates straightforward parameterization of the mean longitudinal shower profile and its fluctuations Additionally, the model examines the Landau-Pomeranchuk-Migdal effect and the Perkins effect, both of which have minimal influence in the ultra-high-energy cosmic ray (UHECR) region.
Chapter 5 delves into the complex challenge of developing hadronic showers, presenting and discussing the intricacies of the simulation model This model faces numerous uncertainties due to the unexplored nature of the ultra-high-energy cosmic ray (UHECR) domain, which lies one to two orders of magnitude beyond the reach of current accelerator experiments Most interactions in this domain involve pion-proton collisions, with a scarcity of high-energy pion-proton data available Additionally, UHECR physics is dominated by forward production, in contrast to the central production prevalent in collider physics The interactions also involve nuclei, primarily nitrogen from the atmosphere and possibly iron as primaries, for which there is a lack of accelerator data in the relevant energy range While the task of fully utilizing the developed simulation model remains ahead, preliminary results are shared to highlight its key features.
Finally a summary and some concluding remarks are presented in Chapter 6 tel-00630205, version 1 - 7 Oct 2011
G ENERALITIES ON COSMIC RAYS
At the end of the 19th century, scientists observed spontaneous discharges in electroscopes, indicating the presence of ionizing radiation on Earth In 1909, Wulf discovered that discharge rates decreased with altitude while conducting experiments on the Eiffel Tower Between 1911 and 1913, Austrian physicist Viktor Hess conducted balloon measurements up to five kilometers high, identifying an "unknown penetrating radiation" believed to originate from above, likely of extraterrestrial origin His groundbreaking work earned him the Nobel Prize in Physics in 1936, shared with Carl Anderson.
In the years following their discovery, cosmic rays became a focal point of extensive research, particularly by notable scientists such as Millikan, who coined the term in 1925, and Anderson at Pikes Peak By 1927, studies measuring east-west asymmetry and the dependence of cosmic ray rates on latitude conclusively demonstrated that cosmic rays are charged particles rather than photons In 1938, Pierre Auger utilized coincidence counters to identify extensive air showers (EAS), 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 Significant discoveries during this period included the positron identified by Anderson in 1932 and the muon in 1938, 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 physics, leading to a decline in the study of cosmic rays.
For many years, significant efforts have been dedicated to understanding the origin of cosmic rays, utilizing ground detectors and large arrays, as well as fluorescence telescopes that achieved remarkably high energies, with John Linsley observing the first 10^20 eV shower in 1962 Space astronomy has significantly advanced the study of low-energy cosmic rays, particularly solar energetic particles A notable example of space measurements in solar astronomy is NASA's Advanced Composition Explorer, launched in 1997 to the Lagrange point between the Sun and Earth.
Over the past two decades, significant advancements in astrophysics and the development of high-energy accelerators have revitalized interest in cosmic ray physics, now referred to as astroparticle physics Notably, the construction and operation of TeV gamma ray detectors have emerged, offering a key advantage: their ability to accurately identify sources without interference from magnetic field deflections.
A new generation of ground detectors has been developed to study cosmic rays, while innovative plans are underway to utilize the entire Earth's atmosphere as a radiator observable from space Additionally, pioneering efforts in neutrino astronomy are currently being advanced.
Figure 2.1: The pioneers: Viktor Hess and his balloon (upper panels), Pierre Auger at the Jungfraujoch (lower right), and Anderson with his cloud chamber (lower left)
Cosmic rays are highly energetic, ionized nuclei that travel through space, reaching energies around 10^20 eV, equivalent to 16 Joules 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 that closely resemble the elemental compositions found in their surroundings, indicating they are accelerated from interstellar matter In galactic environments, hydrogen and helium are the most abundant elements, with even-even nuclei being favored and an enhancement observed in the iron region due to strong nuclear binding A key distinction is that the valleys in elemental abundance are filled by spallation reactions occurring as cosmic rays interact with matter during their journey through the interstellar medium.
Figure 2.2: The cosmic ray energy spectrum displaying its main features
Cosmic rays primarily originate from galactic sources, as the Earth's magnetic field shields it from most low-energy solar cosmic rays The energy density of cosmic rays on Earth is approximately 10^-12 erg/cm^3, with a power output around 10^-26 erg/cm^3 s This power level is comparable to that produced by supernova (SN) explosions, which is about 10^-25 erg/cm^3, considering there are roughly three SN explosions per century in the Milky Way Consequently, cosmic rays account for about 10% of the energy output generated by supernovae.
In the higher energy spectrum, an extra galactic component is present, with an estimated energy density of approximately 2 x 10^-19 erg/cm^3, corresponding to a power of around 10^37 erg/Mpc^3/s Potential sources of this energy include active galactic nuclei (AGN) and gamma-ray bursts (GRB).
Particles emitted by the Sun can reach energies of several MeV and are primarily linked to solar activity and flares, with coronal mass ejections and associated interplanetary shocks showing a similar correlation In contrast, galactic cosmic rays are negatively correlated with solar activity, as increased solar activity enhances the Earth's magnetic field, which serves as a protective shield.
Gamma rays travel directly through the universe and indicate their sources, making them effective for detecting high-energy decay photons from neutral pions generated by interactions between high-energy cosmic rays and interstellar matter Gamma ray astronomy has revealed several sources with identified X-ray counterparts, particularly supernova remnants (SNRs), supporting the conclusion that most galactic cosmic rays likely originate from these SNRs.
The High Energy Stereoscopic System (HESS) in Namibia features four telescopes arranged at the corners of a 120×120 m² square, designed to operate at energies exceeding 100 GeV With a field of view of 5 degrees and a resolution of just a few arc minutes, HESS can capture images of the Crab Nebula in only 30 seconds.
Figure 2.4: Very high resolution X ray images of SNRs (Chandra) From left to right:
Cassopieia A, the Crab, Kepler (SN 1604), Tycho (SN 1572) and N49
There are two primary types of supernova remnants (SNRs): Type Ia and Type II Type Ia supernovae occur in binary systems where a white dwarf accumulates matter from its companion star until it reaches the Chandrasekhar limit of 1.4 solar masses, resulting in a fully burned core and an almost empty SNR shell In contrast, Type II supernovae arise from the collapse of massive stars into neutron stars, which may be detected as pulsars; the pulsar's wind energizes the surrounding remnant, known as a plerion.
Figure 2.5 illustrates the correlation between high-energy X-rays and those emitted by a supernova remnant (SNR) source, confirming their origin from the shell The SNR shell structures are characterized by the explosion blast wave that compresses interstellar matter (ISM) in the forward shock, causing it to decelerate as it accumulates mass Subsequently, the reverse shock heats the ejected material, leading to nuclear reactions that generate new heavy elements As the SNR gathers enough mass, it transitions into the Sedov phase, gradually dispersing into the ISM While thermal particles and magnetic fields are concentrated within the shell, relativistic particles extend over greater distances, with synchrotron emissions localized in magnetic field regions The structure of the shock is influenced by the age of the SNR.
Figure 2.5: Comparison of radial intensity profiles measured in X-rays (ASCA) and & rays (HESS) in separate octants of SNR RX J1713 The overall correlation coefficient between the two radial distributions is 80%
T HE P IERRE A UGER O BSERVATORY
The Pierre Auger Observatory (PAO) is a hybrid detector spanning 3000 km² that detects ultra-high energy cosmic rays (UHECR) by capturing the fluorescence they emit in the atmosphere and their impacts on a ground detector array Its primary goal is to analyze the properties of UHECR, specifically those with energies exceeding 1 EeV (10¹⁸ eV), focusing on the angular and energy dependence of their flux, mass composition, and ultimately, to explore their origins and acceleration mechanisms.
The baseline design was finalized in November 2008, coinciding with the commencement of stable data collection in January 2004 During the construction phase of the Observatory, the largest global dataset of cosmic ray observations was already amassed.
When a primary cosmic ray penetrates the Earth's atmosphere, it generates numerous mesons through interactions, leading to a cascade of further interactions until the primary energy is depleted by ionization losses This process results in an extensive air shower (EAS), characterized by a longitudinal profile that evolves gradually with energy in logarithmic proportion, while the energy content manifested as ionization losses is directly proportional to the energy.
Figure 2.9: Plan view of the PAO
Figure 2.10: Longitudinal development of an extensive air shower [7] tel-00630205, version 1 - 7 Oct 2011
A significant portion of the mesons produced are pions, which can be either neutral or charged Neutral pions quickly decay into two photons, leading to the formation of electromagnetic showers primarily composed of electrons, positrons, and photons These showers develop longitudinally over a scale of radiation length, which is half the interaction length that dictates the progression of hadronic cascades In contrast, charged pions have the potential to decay into a muon-neutrino pair, depending on their decay length.
56 m/GeV, is short enough in comparison with the interaction length As a result, the muon to electron/photon ratio increases with depth
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 [8] The PAO covers 3000 km 2 in the Argentinean pampas, of which only 5 ppm are covered by detectors These include
The surface detector (SD) consists of 1,600 Cherenkov detectors, while the fluorescence detector (FD) is composed of 24 fluorescence telescopes Data collected from these detectors is transmitted via radio to an acquisition center, where it is filtered before being sent to various laboratories involved in the research, including VATLY.
The SD is described in detail in the next section
Figure 2.11: Left: A fluorescence station: schematic view (on top) and its photograph
Right: Photograph of an eye
The FD consists of four stations, each equipped with six telescopes, strategically positioned to monitor the PAO area These telescopes detect fluorescence light in the near UV spectrum, generated by interactions between charged particles from cosmic showers and atmospheric nitrogen molecules Their operation is limited to clear, moonless nights, resulting in a duty cycle of only 13% Each telescope provides a field of view of 30 degrees in azimuth and 28.6 degrees in elevation, allowing for effective observation of cosmic events.
The 11 m² concave mirror (tel-00630205, version 1) is designed to focus light onto an array of 440 hexagonal PMT pixels for shower axis direction measurement While a single telescope can theoretically determine this direction by analyzing the timing of pixel hits, accurate measurement often necessitates binocular detection or simultaneous data from ground Cherenkov detectors Energy measurement relies on the longitudinal profile, which, when fully captured, offers a direct calorimetric evaluation of shower energy, with neutrinos and muons accounting for about 10% of energy loss However, practical challenges arise due to the need for precise knowledge of air transparency and atmospheric Cherenkov light interference, along with the issue of the shower often being only partially within the field of view.
The SD samples the footprint of showers on the ground using a triangular array of water Cherenkov counters with a mesh size of 1.5 km, positioned at an altitude of 1400 meters to capture the maximum development of ultra-high-energy cosmic rays (UHECRs) Upon reaching the ground, these showers primarily consist of low-energy electrons, positrons, photons, and muons with kinetic energies around a few GeV The muon signal in both water Cherenkov counters and scintillator plates correlates with track length, making the signal proportional to the detector volume, regardless of the angle of incidence In contrast, electrons and photons generate small showers that are fully contained in water Cherenkov counters but only partially in scintillator plates, resulting in a sky coverage that is twice as effective as that of 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, taking into account the minor curvature of the shower front.
Energy measurement in this context is indirect yet simpler than in the FD case, relying on a standard function known as the lateral distribution function (LDF) This function represents the average signal detected in a Cherenkov tank, based on variables such as shower energy, distance from the shower axis, and zenith angle The dependence on zenith angle is assessed under the assumption of an isotropic cosmic ray flux Ultimately, energy is determined by normalizing the measured signals to the standard LDF at a distance of 1000 meters from the shower axis.
The selection of a reference point is influenced primarily by two 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 The final energy scale is calibrated using data from hybrid events, as demonstrated in the referenced figures Figure 2.12 illustrates this calibration process, while Figure 2.13 provides a summary of the information collected by the Surface Detector (SD), highlighting both the shower footprint and the fit to the Lateral Distribution Function (LDF) Additionally, Figure 2.14 showcases the first four-fold hybrid event recorded in May 2007, with all Fluorescence Detector (FD) stations operational.
Figure 2.12: Left: Correlation between the decimal logarithms of the energy measured in the FD (abscissa) and of the normalization (ordinate) of the measured
The study analyzes the value of S(1000) at a zenith angle of 38 degrees for 795 hybrid events, highlighting the best fit line Additionally, it examines the fractional difference between the calorimetric energy (E FD) and the energy estimate from the surface detector (E), as derived from the calibration curve for these selected events.
Event 211377 is a typical example of a cosmic event with an energy of approximately 5x10^18 eV The top left image displays the top view of the triggered tanks, while the lower left shows the fit to the lateral distribution function (LDF) On the right, the FADC traces from four detectors are presented, with signal sizes measured in units of VEM, as detailed in Section 2.2.3.
Figure 2.14: 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 contained within a highly diffusive plastic bag that fits snugly inside the tank, allowing the Cherenkov light produced to be detected by three 9" spherical photocathode photomultiplier tubes (PMTs) through high transparency windows Although the PMTs are not shielded from the Earth's magnetic field, they are strategically oriented to enhance their response Each PMT features a two-part amplification chain, consisting of a central foil dynode and a standard linear focus chain of seven dynodes, which amplifies the charge collected from the last dynode to exceed the anode charge by a factor of 32 The signals are processed using 50 Z in 10 bits 40 MHz flash analog to digital converters (FADC), but the steep slope of the lateral distribution function (LDF) near the shower core can occasionally cause saturation of the dynode signal.
I DENTIFICATION OF THE PRIMARIES
Low energy cosmic rays exhibit a composition similar to interstellar matter, primarily consisting of protons However, at ultra-high energy cosmic ray (UHECR) levels, the mass composition of primary particles remains uncertain Some theories even propose the presence of particles beyond atomic nuclei in this higher energy range Excluding these exotic possibilities, it is crucial to measure the mass distribution of primary cosmic rays, which spans from protons to iron nuclei, with higher mass nuclei being 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 to form after traveling one interaction length, with their starting depth showing a variance equal to one interaction length In contrast, an iron shower can be conceptualized as the combination of 56 proton showers, each contributing 1/56 of the nucleus's energy, leading to an earlier onset and less fluctuation in its starting point Although this explanation offers a simplified view of the processes involved, the actual dynamics are much more intricate and not fully understood, as not all nucleons within the colliding nuclei interact uniformly; some are referred to as "wounded nucleons."
In the Glauber model, nucleons are treated as independent entities that interact with each other, while other nucleons, known as spectator nucleons, remain unaffected This approach simplifies the complex interactions in nuclear physics and offers a method for calculating the number of wounded nucleons involved in these interactions.
To effectively differentiate between light and heavy incident nuclei, it is essential to measure quantities that are sensitive to early shower development This approach is crucial, especially in light of previous findings suggesting a significant iron population, which may help clarify why certain ultra-high-energy cosmic rays (UHECR) do not correlate with any known counterparts.
The fluorescence detector (FD) at the Pierre Auger Observatory effectively measures the longitudinal profile of cosmic ray showers, particularly identifying the depth at which the shower reaches its maximum (X max) At specific energy levels, both the average and the variance of the X max distribution are linked to the mass composition of cosmic rays Notably, proton showers penetrate deeper into the atmosphere, exhibiting larger X max values and broader distributions compared to heavier nuclei.
In practice, however, such a measurement is difficult and a strict selection of useful events is mandatory A good geometry (average angular resolution of 0.6 o )
To obtain accurate measurements of cosmic shower particles, simultaneous detection in at least one Cherenkov tank of the surface detector (SD) is required, while rejecting showers directed toward the telescope, necessitating a recording time of over 5 years The reconstructed X max must be clearly identified and fall within the field of view, achieved by ensuring the observed profile spans at least 320 g/cm² Additionally, the reduced chi-squared value from a fit to a reference profile should not exceed 2.5 and must be at least 4 units smaller than that of a straight line fit The estimated uncertainties for the shower maximum and total energy should be less than 40 g/cm² and 20%, respectively, with the uncertainty on the X max measurement derived from stereo events being 21±1.5 g/cm².
Recent PAO results indicate a clear trend towards higher masses, as illustrated in Figure 2.21, alongside predictions from popular hadronic models for protons and iron nuclei However, interpreting these results is complex; for a pure proton-iron mixture, one would expect the root mean square (rms) value to rise when transitioning from pure proton to pure iron, which contradicts the observed data The rms value is anticipated to peak approximately 12% above the iron line for a mixture of about one-third protons and two-thirds iron.
Figure 2.21: < X max > and RMS(X max ) energy distributions compared with air shower simulations [35] using different hadronic interaction models [19, 20]
The timing of particles reaching the ground is influenced by the development of the shower, with the initial signal primarily consisting of muons These muons arrive earlier and within a shorter timeframe compared to electrons and photons.
[36] A risetime (t 1/2 ) is defined for each tank FADC trace as the time to go from tel-00630205, version 1 - 7 Oct 2011
The integrated signal, ranging from 10% to 50%, reveals a significant correlation between risetime and X max, influenced by the primary mass composition This relationship is analyzed by examining the risetime's dependence on zenith angle and distance to the shower axis, employing a standard function similar to the lateral distribution function (LDF) with a reference energy of 10^19 eV The derived quantity, ∆ i, shows an expected increase with energy, indicating that showers penetrate deeper into the atmosphere, and it exhibits a clear correlation with X max.
Figure 2.22 illustrates the relationship between the mean value of ∆∆∆∆ i and energy for SD events on the left, and the mean value of ∆∆∆∆ i and X max for hybrid events on the right A correlation is identified and is described using a linear fit The shaded regions represent the estimated uncertainties, calculated by randomly fluctuating each data point within its measured error bar and reapplying the fitting process.
This correlation can be utilized to calibrate the risetime scale based on mass composition; however, it does not provide significant additional insights, except for some understanding of the relative energy dependencies of X max and ∆ i.
The risetime of a shower is influenced by the tank azimuth ζ, particularly in inclined showers When an inclined shower hits the ground, upstream tanks are activated first, capturing the shower's earlier development stages, while downstream tanks are triggered later This timing difference is compounded by a geometric effect: particles have a shorter path to reach upstream tanks, allowing them to detect signals under a larger solid angle compared to downstream tanks Consequently, upstream tanks register a stronger signal Additionally, most muons possess sufficient energy to penetrate the tanks effectively.
The response of the tank to incoming particles is generally independent of the angle of incidence, while the behavior of electrons and photons, which create small showers in water, is angle-dependent, leading to an azimuthal asymmetry around the shower axis This asymmetry increases with the distance from the axis and is particularly evident in the azimuthal dependence of the risetime, peaking at a zenith angle sensitive to the depth where shower density begins to decline A fitting model indicates that the asymmetry's dependence on zenith angle is maximal around a specific point, regardless of energy levels Popular hadronic models, however, suggest that this maximum zenith angle increases with energy, implying that mean primary masses rise with energy This observation aligns with fluorescence detector measurements, which indicate a transition from proton dominance to iron dominance in the mass composition as energy escalates from 1 to 30 EeV.
Figure 2.23: 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 muon abundance serves as a key indicator of shower age, with older showers exhibiting higher muon levels At equivalent depths, iron showers are anticipated to contain more muons compared to proton showers Although direct measurements of muon abundance are currently lacking, various methods to assess related quantities, such as risetime, have been investigated.
Other approaches include attempts at identifying muons from sudden jumps
The analysis of muon signals in FADC traces utilizes two methods: the "jump method" and a direct evaluation through the subtraction of electron-photon contributions The electron-photon signal is influenced by energy, zenith angle, and depth relative to X max, with its zenith angle dependence based on the assumption of isotropic detected showers and energy dependence derived from hadron models Under these conditions, the muon abundance remains the only variable, which, when compared to predictions for proton primaries, is measured at 1.53+0.08 (stat.)+0.21 (syst.), whereas a pure iron composition would suggest a lower value around 1.3.
I NTRODUCTION
This section aims to utilize the PAO surface detector to gather independent insights into the nature of Ultra-High-Energy Cosmic Rays (UHECR) primaries Correlation data indicates that UHECRs are primarily protons at the highest energies, while elongation rate data suggests a mix of protons and iron at slightly lower energies The objective is to provide additional information through the surface detector, as the quantity of muons detected on the ground could effectively differentiate between light and heavy primary particles.
Various methods are employed to assess the number of muons per FADC trace in each Cherenkov tank of the Auger SD, aiming to gather independent insights into the nature of primary particles A notable technique in this context is the jump method, which has been developed at LAL-Orsay.
An important difference between the different methods is the amount of reliance that they imply on the shower models used to predict the muon abundance
An extreme perspective involves complete trust in simulated data, leading to the challenge of identifying the optimal discriminator between simulated proton and iron data, which is fundamentally a mathematical problem This viewpoint is exemplified by the Catania team, who are utilizing neural networks to tackle this issue.
An alternative method minimizes reliance on complex detector response simulations This involves measuring the muon fraction by directly analyzing muon signals from FADC traces Nevertheless, this technique still requires some simulation, as a shower development model is essential for distinguishing between various primary particles.
Both perspectives are valuable and should not be compared in terms of superiority, as mastering both is essential for drawing reliable conclusions; they complement each other A robust conclusion regarding the nature of the primaries necessitates presenting compelling arguments supporting the validity of the simulation The diverse approaches currently being explored, particularly as they begin to converge, represent a significant advancement in this area.
Many methods depend on the validity of the simulation, varying in their reliance based on application specifics Notably, the jump method presents a compelling case in this regard, which is summarized in the following section.
In the FADC trace, which is averaged over three PMTs for each tank affected by a shower, the total jump (J) is defined as the sum of all differences exceeding 0.5 VEM between a 25 ns time bin and its preceding bin Each trace contains N J occurrences of these differences, while the total charge (Q) represents the sum of all time bin contents Both J and Q are measured in VEM units, whereas N J is dimensionless.
In principle, J receives contributions from both muons and electrons/photons, with detailed insights provided in Section 3.2 Significant evidence of these contributions from muons is indicated by a distinct shoulder in the distribution of individual jumps, observable in both real and simulated data A thorough analysis of the underlying physics can be found in Reference 47, which establishes a relationship between J and the number of muons, denoted as N !.
J=AJ low +B N ! (3.1) with A= C em (v 1 )/C em (v 2 ) and B= ε ! (v 1 ){1−[C em (v 1 )ε ! (v 2 )]/[ C em (v 2 )ε ! (v 1 )]}
In this context, constants A and B are utilized, with the quantity J low defined as J, differing only by a lower threshold of v 2 = 0.1 VEM compared to v 1 = 0.5 VEM The terms C em and ( à represent average electromagnetic contamination and muon selection efficiency, respectively, derived from simulated data Additionally, Relation (3.1) can be expressed equivalently.
=B=ε ! (v 1 ){1−[C em (v 1 )ε ! (v 2 )]/[ C em (v 2 )ε ! (v 1 )]} and A 2 = −AA 1 = –A 1 C em (v 1 )/C em (v 2 )
Here, again, A 1 and A 2 are constants In Reference 47, Relation (3.1’) is replaced by a proportionality relation
N ! ="J (3.1”) where " is parameterized as a function of energy E, zenith angle ' and distance to the shower core D
Relation (3.1”) facilitates the evaluation of muon counts impacting a specific Cherenkov tank based on measurements of J The accuracy of this evaluation is determined by the width of the N! distribution for a given J value While simulations can guide parameterization of " in relation to E, ' and D, it is crucial to consider potential discrepancies between predicted muon numbers and actual data Relation (3.1) is advantageous as it distinguishes between electron/photon and muon contributions, allowing for a more precise parameterization This approach incorporates both simulated data and variations thereof, including scenarios with no muons or double the expected muon count, enhancing the robustness of the analysis.
Section 3.2 examined muon counting, but a more challenging question remains: how effectively does muon counting differentiate between iron and proton primaries? The answer depends entirely on the accuracy of the shower development model employed in the simulation, especially regarding its treatment of nucleus-nucleus interactions.
In Section 3.3, it is observed that iron and proton primaries of the same energy produce showers with notably different particle densities on the ground, with iron showers exhibiting a higher ground density than proton showers This difference provides several reliable discriminators for identifying the primary particle if the energy is known, including the total jump (J), total charge (Q), and the number of jumps (N J).
The primary energy remains unknown; however, the particle density on the ground, represented by a lateral distribution function, allows for an estimation of the primary energy under the assumption of a proton Different particle densities may indicate either proton showers of varying energies or a proton and an iron shower with the same energy Consequently, distinguishing between these scenarios using only surface detector (SD) information is challenging Section 3.4 explores this issue and examines the circular reasoning involved in identifying primaries through muon counting.
Section 3.5 provides an energy-independent analysis of PAO data, aiming to overcome previous challenges It utilizes energy-independent discriminators, specifically the ratio of total jump to total charge (J/Q), at varying distances from the shower core based on ground density Additionally, Section 3.6 explores ultra-high-energy cosmic ray (UHECR) showers in correlation with Centaurus A (Cen A).
Section 3.7 summarizes the study in the context of recent results of the Pierre Auger Collaboration which give evidence for an apparent inconsistency between the interpretation of FD and SD data, precluding a reliable evaluation of the mass composition from the SD data alone In a nutshell, using the FD energy scale, the amplitude of the muon component estimated from SD data is about twice that predicted for protons, while that predicted for iron is only 4/3 of that predicted for protons A possible interpretation, explored in References 51 and 52, is that the FD underestimates energies by some 30% The energy-independent analysis presented in Section 3.5 shows that such an interpretation may only account for a minor part of the inconsistency
M UON COUNTING
The simulated data utilized in this study is categorized into 18 families, based on three energy levels, two zenith angles, and three distance intervals from the shower core The input parameters for the simulation include energies of 10^18.5 eV, 10^19 eV, and 10^19.5 eV, alongside zenith angles of 0° and 45° The distance intervals to the shower core are specifically tailored for each energy level, ensuring that each event sample maintains a similar size across the different categories.
D