Searches for Ultra-High-Energy Photons at the Pierre Auger Observatory

  Citation: The Pierre Auger Collaboration Searches for Ultra-High-Energy Photons at the Pierre Auger Observatory. Universe 2022,8, 579. https://doi.org/ 10.3390/universe8110579 Academic Editors: Mariangela Settimo and Piotr Homola Received: 28 September 2022 Accepted: 23 October 2022 Published: 2 November 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). universe Review Searches for Ultra-High-Energy Photons at the Pierre Auger Observatory The Pierre Auger Collaboration † Av. San Martín Norte 304, Malargue 5613, Argentina; [email protected] † All authors provided in Appendix A. Abstract: The Pierre Auger Observatory, which is the largest air-shower experiment in the world, offers unprecedented exposure to neutral particles at the highest energies. Since the start of data collection more than 18 years ago, various searches for ultra-high-energy (UHE, E& 10 17 eV ) photons have been performed, either for a diffuse flux of UHE photons, for point sources of UHE photons or for UHE photons associated with transient events such as gravitational wave events. In the present paper, we summarize these searches and review the current results obtained using the wealth of data collected by the Pierre Auger Observatory. Keywords: photons; ultra-high energies; air showers; Pierre Auger Observatory; upper limits; transients 1. Introduction For many years, the search for neutral particles—in particular photons and neutrinos— of cosmic origin at the highest energies has been one of the major scientific objectives of the Pierre Auger Observatory. From the theory side, such searches are well motivated: many models for the origin of ultra-high-energy (UHE) cosmic rays predict at least some neutral particles as by-products, either directly at the sources or during the propagation through the universe (see, e.g., [ 1 – 5 ]). In fact, even though no UHE photons have been unambiguously identified so far, the upper limits on their incoming flux have been already used to severely constrain so-called top-down models for the origin of UHE cosmic rays involving, e.g., topological defects or super-heavy dark matter (see, e.g., [ 6 – 9 ]). In addition, the recent observations of photons with energies up to 10 15 eV [ 10 ] further motivate searches for photons at even higher energies. An observation of such photons would also be key to completing the multi-messenger approach aimed at understanding the most extreme processes in the universe, taking advantage of the fact that neutral particles directly point back to their production site. However, one has to take into account that UHE photons, unlike neutrinos, interact with the background photon fields permeating the universe, reducing their attenuation length to about 30 kpc around 10 15 eV , which increases to the order of 10 Mpc around 10 19 eV [ 11 ]. In the present paper, we review the current state of such searches at the Pierre Auger Observatory. After a short introduction addressing the specificities of air showers initiated by photons (Section 2), we briefly describe the Pierre Auger Observatory (Section 3). We then focus first on the searches for a diffuse flux of UHE photons using the different detector systems of the Observatory (Section 4), before we describe the searches for UHE photons from point sources and transient events (Section 5). We close with a short discussion (Section 6) of the ongoing detector upgrade of the Pierre Auger Observatory, dubbed AugerPrime. 2. Photon-Induced Air Showers When a UHE photon enters the Earth’s atmosphere, it may interact with a particle from the atmosphere—for example, a nitrogen nucleus—and induce an extensive air shower, much in the same way as a charged cosmic ray does. Hence, a cosmic-ray observatory Universe 2022,8, 579. https://doi.org/10.3390/universe8110579 https://www.mdpi.com/journal/universe Universe 2022,8, 579 2 of 20 detecting air showers is also, by construction, a photon observatory—and even a neutrino observatory, highlighting the importance of such observatories for multi-messenger astrophysics. In fact, since the incoming flux of UHE cosmic particles is so low (to the order of one particle per square kilometer per year and less), measuring the extensive air showers they initiate in the atmosphere with large detector arrays on ground is the only way to efficiently detect them. The challenge lies in distinguishing air showers induced by photons from the vast background of air showers that are initiated by charged cosmic rays, i.e., protons and heavier nuclei (for a review, see, e.g., [ 11 ]). The two main differences between photonand nucleus-induced air showers are shown schematically in Figure 1. The longitudinal development of an air shower, as a function of the slant depth X , is delayed for a primary photon with respect to primary nuclei, due to the lower multiplicity of electromagnetic interactions (compared to hadronic interactions) that dominate in a photon-induced air shower. The maximum of the shower development within the atmosphere, Xmax , is reached later. For example, at primary energy of 10 19 eV , the difference is about 200 g cm−2 . Since the mean free path for photo-nuclear interactions is much larger than the radiation length, only a small fraction of the electromagnetic component in a photon-induced shower is transferred to the hadronic component, and subsequently to the muonic component. Showers induced by photons are thus characterized by a lower number of muons. On average, simulations show that photon-induced showers have nearly one order of magnitude less muons than those initiated by protons or nuclei of the same primary energy. In one way or another, all searches for UHE photons using air-shower data exploit these two key differences: Xmax , for example, can be directly measured using the air-fluorescence technique. The number of muons cannot yet be directly measured using the current detector systems of the Pierre Auger Observatory. However, one can measure the lateral distribution of secondary particles from the air shower at ground level, which depends on both the number of muons and the longitudinal development. In particular, the steepness of the lateral distribution is sensitive to the type of the primary particle. Figure 1. Schematic depiction of the main differences between photon-induced air showers and those initiated by primary nuclei (protons or heavier nuclei). Universe 2022,8, 579 3 of 20 The difference in Xmax between photonand proton-induced air showers is amplified by the Landau–Pomeranchuk–Migdal (LPM) effect [ 12 , 13 ], i.e., the suppression of the bremsstrahlung and pair production cross sections at high energies. In addition, the preshower effect [ 14 – 16 ] also has to be taken into account: depending on its incident direction with respect to the local geomagnetic field, a UHE photon can initiate an electromagnetic cascade in the Earth’s magnetic field even before entering the atmosphere. This is known as a preshower. The observed air shower is, therefore, a superposition of the individual cascades of the photons and electrons/positrons from the preshower, leading on average to a smaller measured Xmax than for non-preshowering photons of the same primary energy. 3. The Pierre Auger Observatory The Pierre Auger Observatory [ 17 ], located near the town of Malargüe in the Argentinian Pampa Amarilla, is the largest cosmic-ray observatory to date, offering an unprecedented exposure to UHE photons. A key feature of the Pierre Auger Observatory is the hybrid concept, combining a Surface Detector array (SD) with a Fluorescence Detector (FD); see Figure 2. The SD consists of 1600 water-Cherenkov detectors arranged on a triangular grid with a spacing of 1500 m, covering a total area of about 3000 km2 . The SD is overlooked by 24 fluorescence telescopes, located at four sites at the border of the array. The SD samples the lateral shower profile at ground level, i.e., the distribution of particles as a function of the distance from the shower axis, with a duty cycle of ∼ 100%, while the FD records the longitudinal shower development in the atmosphere above the SD. The FD can only be operated on clear, moonless nights, reducing the duty cycle to ∼ 15%. By combining measurements from both detector systems in hybrid events, a superior accuracy of the air-shower reconstruction can be achieved than with just one system [ 18 ]. In the western part of the SD array, 50 additional SD stations have been placed between the existing SD stations, forming a sub-array with a spacing of 750 m and covering a total area of about 27.5 km2 . With this sub-array, air showers of lower primary energy (below 10 18 eV ) with a smaller footprint on ground can be measured. To allow also for hybrid measurements in this energy range, where air showers develop above the field of view of the standard FD telescopes, three additional High-Elevation Auger Telescopes (HEAT) have been installed at the FD site Coihueco, overlooking the 750 m SD array. The HEAT telescopes operate in the range of elevation angles from 30◦to 60◦, complementing the Coihueco telescopes operating in the 0 ◦ to 30 ◦ range. The combination of the data from both HEAT and Coihueco (“HeCo” data) enables fluorescence measurements of air showers over a large range of elevation angles. Figure 2. Left : map of the Pierre Auger Observatory [ 17 ]; each dot represents one SD station; the four FD sites at the border of the SD array are also shown. Top right : the fluorescence telescopes at the FD site Los Leones; even though the picture was taken during the daytime, the shutters were had been opened for maintenance. Bottom right: a single SD station in the Pampa Amarilla. Universe 2022,8, 579 4 of 20 4. Searches for a Diffuse Flux of UHE Photons First, we focus on the searches for a diffuse—i.e., direction independent, unresolved— flux of photons. At the Pierre Auger Observatory, such searches have been performed in the past using hybrid data (with the analysis based on Xmax only [ 19 , 20 ], or based on a combination of Xmax and additional SD-related quantities [ 21 ]) as well as SD-only data [ 22 ]. In the following, we briefly summarize the three most up-to-date publications [ 23 – 25 ] in different energy ranges and the corresponding results. 4.1. A Search for Photons with Energies above 2×1017 eV Using Hybrid Data from the Low-Energy Extensions of the Pierre Auger Observatory We first discuss the photon search targeting the lowest energy range, which starts from 2 × 10 17 eV [ 23 ]. In this energy range, data from the low-energy extensions of the Pierre Auger Observatory, i.e., from the 750 m SD array combined with HeCo data, can be used to efficiently search for photons. Three observables are used in the analysis: Xmax , measured directly with the fluorescence telescopes, is used together with the SD quantities Sb and Nstations.Sb[26] is defined through Sb=∑ i Si×Ri 1000 mb , (1) where Si denotes the measured signal in the i -th SD station at a perpendicular distance Ri to the shower axis, and the parameter b has been chosen as b= 4 to optimize the photon–hadron separation. By construction, Sb is sensitive to the lateral distribution, which in turn depends on the depth of the air-shower development in the atmosphere and the number of muons, as stated in Section 2. The third observable, Nstations is the number of triggered SD stations, as it has been shown previously that it can significantly improve the overall performance of the analysis [21]. These three quantities are combined in a multivariate analysis (MVA) using the Boosted Decision Tree (BDT) method. To take into account energy and zenith angle dependencies, the photon energy Eγ (defined as the calorimetric energy obtained through the integration of the longitudinal profile, plus a missing-energy correction of 1% appropriate for primary photons [ 21 ]) and the reconstructed zenith angle θ are also included in the MVA. A large sample of simulated events has been used to study the photon–hadron separation of the observables mentioned before, to train the multivariate analysis, and to evaluate its performance. For these samples, both primary photons (as a signal sample) and primary protons (as a conservative, “worst-case” assumption for the background sample) have been simulated using CORSIKA and the Auger Offline Software Framework. The analysis is eventually applied to hybrid data collected by the Coihueco and HEAT telescopes and the 750 m SD array between 1 June 2010 and 31 December 2015—in total, more than 500,000 events. A number of selection criteria are applied to both the data sample and the simulated samples to select only well-reconstructed, reliable events. These selection criteria are described in detail in [ 23 ]. After all criteria have been applied, 2204 events remain in the data sample with a photon energy Eγabove 2 ×1017 eV. In Figure 3, the normalized distributions of the discriminating observables Xmax , Sb and Nstations are shown for the simulated samples as well as the data sample. In addition, the corresponding distributions of the output from the BDT β , which is used as the final discriminator for separating photon-induced air showers from the hadronic background, are displayed. A more detailed discussion of these distributions can be found in [ 23 ]. Here, we only note that for β , the photon and proton distributions are well separated. The background rejection at a signal efficiency of 50%, i.e., the fraction of proton-induced events with β larger than the median of the photon distribution—which is used as the photon candidate cut, marked with the dashed line—is ( 99.91 ± 0.03 ) % for energies Eγ≥2×1017 eV. Universe 2022,8, 579 5 of 20 ] -2 [g cm max X 500 600 700 800 900 1000 1100 Entries (normalized) 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 Data Photon Sim. (Test) Proton Sim. (Test) Photon Sim. (Training) Proton Sim. (Training) [VEM]) b (S 10 log 3−2−1−0 1 2 3 Entries (normalized) 0 0.2 0.4 0.6 0.8 1 1.2 Data Photon Sim. (Test) Proton Sim. (Test) Photon Sim. (Training) Proton Sim. (Training) stations N 0 2 4 6 8 10 12 14 16 18 20 Entries (normalized) 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Data Photon Sim. (Test) Proton Sim. (Test) Photon Sim. (Training) Proton Sim. (Training) β 0.4−0.2−0 0.2 0.4 0.6 Entries (normalized) 0 1 2 3 4 5 6 7 8Data Photon Sim. (Test) Proton Sim. (Test) Photon Sim. (Training) Proton Sim. (Training) 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 0.25 Figure 3. Normalized distributions of the three discriminating observables Xmax , Sb and Nstations used in the photon search based on HeCo data. The (simulated) photon sample is shown in blue, the (simulated) proton sample in red, and the data sample in black. In addition, normalized distributions of the final discriminator β —which is based on a MVA combining Xmax , Sb and Nstations as well as the photon energy and the zenith angle—are displayed. The dashed line denotes the median of the photon test sample, which is used as the photon candidate cut. In all plots, only events with Eγ>2×1017 eV are shown. For more details, see [23]. Zero events from the data sample have a β value above the candidate cut value; hence, no photon candidate events are identified in this analysis. The final results of this study are therefore given in terms of upper limits on the integral flux of photons ΦC.L. γ, U.L.(Eγ>E0) . The integrated, efficiency-weighted exposure for photons needed to calculate these upper limits is obtained from simulations. In the energy range of interest between 2 × 10 17 eV and 10 18 eV , the weighted exposure varies between 2.4 and 2.7 km2sr yr under the assumption of a power-law spectrum ∝E−2 . Upper limits on the integral photon flux are placed at threshold energies of 2, 3, and 5 × 10 17 eV , as well as 10 18 eV , at a confidence level of 95%. At these threshold energies, the upper limits are 2.72, 2.50, 2.74, and 3.55 km−2sr−1yr−1 , respectively. Using the energy spectrum of cosmic rays measured by the Pierre Auger Observatory [ 27 ], the upper limits on the integral photon flux can be translated into upper limits on the integral photon fraction. At a confidence level of 95%, these are 0.28%, 0.63%, 2.20% and 13.8% for the same threshold energies as above. 4.2. A Search for Ultra-High-Energy Photons at the Pierre Auger Observatory Exploiting Air-Shower Universality The photon search in the energy range between 10 18 and 10 19 eV [ 24 ] is performed by exploiting the hybrid configuration of the Pierre Auger Observatory, much like in the previous analysis. As before, Xmax can be measured directly with the FD. The muon content of a measured air shower is accessed through the parameter Fµ , which is derived from the SD signals by using the air-shower universality concept [ 28 ]. A universality-based model [ 29 ] is used to predict the signals induced by the secondary particles in the individual SD stations. This model describes the total signal as the sum of four components: two electromagnetic components, one related to high-energy pions ( Seγ ) and one related to lowenergy hadrons ( Seγ(had) ), and two muon-related components, a pure muon component ( Sµ ) and one related to electrons and photons resulting from muon decays ( Seγ(µ) ). The predicted signal, Spred, can then be expressed as Universe 2022,8, 579 6 of 20 Spred = 4 ∑ i=1 βi(Fµ)·Si comp(E,Xmax, geometry), (2) where i runs over the four components. Each of the four signal components, Si comp , has a universal behavior, which can be parameterized as a function of the primary energy E , Xmax , and the geometry of the air shower. The relative contributions βi of each of the four components depend only on the mass of the primary particle through a parameter, Fµ , representing the number of muons in the air shower. Following the approach developed in [ 30 ], the universality-based signal model is applied to the case of hybrid events measured by the FD and the SD. As the hybrid reconstruction provides E , Xmax and the shower geometry, the four components Si comp can be directly calculated for each SD station involved in a hybrid event. Thus, given the reconstructed signal, Srec , in a station of the SD, Fµ can be calculated for each station in an event by matching Srec to Spred from Equation (2). To obtain an event-wise estimate of the muon content, the average Fµ of all SD stations is assigned to an event if more than one station is available. Overall, Fµ provides a very good photon–hadron separation (see Figure 4, top left). To fully exploit the hybrid approach, it is combined in this analysis with Xmax in a linear Fisher discriminant analysis [31]. The resulting distributions of the Fisher discriminant f are shown in the top right panel of Figure 4, for simulations of primary protons (red) and photons (blue), as well as for 5% of the data sample (black), which is used as a burnt sample. The distributions of f obtained for the proton and photon samples are well separated, resulting in a background rejection of about 99.90% at a signal efficiency of 50%, corresponding to the dashed blue line in the top right panel of Figure 4. The burnt sample and the photon distributions are even more separated; therefore, the events contained in the burnt sample can be considered as background events only, and can then be used to derive a data-driven estimate of the expected background. Due to the limited number of events in the burnt sample, in the first step, we used the rightmost tail of the proton distribution, specifically only the events with f>− 1.3 (red dashed line in Figure 4, top right), to derive the functional form of the background distribution. Then, the expected background distribution was derived through a fit to the burnt sample and scaled up linearly with time to match the full data sample. Finally, the analysis has been applied to hybrid events above 10 18 eV recorded by the Pierre Auger Observatory between 1 January 2005 and 31 December 2017. Of the total dataset, which consists of approximately 32 , 000 events, the rightmost tail of the distribution of the Fisher discriminant f (black dots) is shown in the bottom panel of Figure 4. The data distribution resembles the background expectation, shown as the shaded blue bands, representing the uncertainties in its estimation for different σ levels. After applying the photon selection cut (dashed vertical line), corresponding to the median of the photon distribution (dashed blue line in Figure 4, top right), 22 photon-candidate events are selected. This number is consistent with the background expectation of 30 ± 15 falsepositive candidate events. Since no significant excess with respect to the background has been found, the final results of this study are given in terms of upper limits on the integral flux of photons ΦC.L. γ, U.L.(Eγ>E0) . Five different energy thresholds (1, 2, 3, and 5 × 10 18 eV , as well as 10 19 eV ) were considered. The number of photon-candidate events found for each energy threshold were 22, 2, 0, 0 and 0, respectively. The upper limits are determined taking into account the expected number of background events derived from the burnt sample for each threshold (30 ± 15, 6 ± 6, 0.7 ± 1.9, 0.06 ± 0.25 and 0.02 ± 0.06, respectively) as well as the integrated, efficiency-weighted exposure for photons, which was again determined from simulations. In the energy range between 10 18 and 10 19 eV , the weighted exposure increases from 420.7 to 1245.9 km2sr yr , under the assumption of a power-law spectrum ∝E−2 . The resulting upper limits (at a confidence level of 95%) on the integral flux of photons for the aforementioned thresholds are 4.0, 1.1, 0.35, 0.23 and 0.0021 km−2sr−1yr−1 . These results are preliminary and will be updated in a forthcoming journal publication. Universe 2022,8, 579 7 of 20 Figure 4. ( Top left ) scatter plot of Xmax and Fµ , i.e., the observables used in the hybrid search for photons using air-shower universality, for simulated primary photons (blue) and protons (red); The contour lines enclose 90%, 50% and 10%, respectively, of the events. ( Top right ) distributions of the Fisher discriminant f for simulated primary photons (signal, blue) and protons (background, red), and for the burnt sample (black); the dashed red line marks the tail of the proton distribution; the dashed blue line indicates the median of the photon distribution. ( Bottom ) the tail of the distribution of f for the hybrid data sample (black dots); the dashed line represents the photon-candidate cut; the shaded blue regions show the 1 σ , 2 σ and 3 σ uncertainty bands for background expectation. For more details, see [24]. 4.3. Search for Photons above 1019 eV with the Surface Detector of the Pierre Auger Observatory In the energy range above 10 19 eV , UHE photons are searched for among the data collected with the 1500 m SD array of the Pierre Auger Observatory [ 25 ]. While the photon search using SD-only data can profit from the large exposure due to the high duty cycle of the SD, the lack of a corresponding fluorescence measurement for the bulk of the data poses some challenges. For example, there is no direct measurement of Xmax available. Additionally, the primary energy can only be accessed indirectly, using S( 1000 ) —the interpolated signal in the SD stations at a perpendicular distance of 1000 m from the shower axis—as a proxy. Two observables are used in this analysis, one related to the thickness of the shower front at ground and one based on the steepness of the lateral distribution. These two properties of an air shower depend on the type of the primary particle initiating the shower, hence they can be used for photon–hadron separation. The first observable, ∆ , is based on the risetime t1/2 in the individual SD stations, which is defined as the time at which the integrated signal in the measured time trace rises from 10% to 50% of its total value. For showers of the same primary energy and zenith angle, t1/2 is expected to be larger for Universe 2022,8, 579 8 of 20 primary photons with respect to primary nuclei due to the reduced muonic content, which implies larger scattering and attenuation of secondary particles, and to Xmax being closer to the ground. ∆is defined as: ∆=1 N∑ i (ti 1/2 −tbench 1/2 ) σt1/2 , (3) which can be taken as the average deviation of the measured rise times from a data benchmark tbench 1/2 , describing the average rise time of all of the SD data (assumed to be overwhelmingly constituted by primary nuclei) [ 32 ], in units of sampling fluctuations σt1/2 . Details on the selection criteria for the SD stations can be found in [ 25 ]. By construction, ∆ is expected to average to zero for data and to be significantly positive for photon-induced air showers. As photon-induced air showers are also expected to have a steeper lateral distribution of the signals in the SD stations than the average of all SD data, a second observable LLDF is introduced to quantify the departure of the observed lateral distribution function (LDF) from the average of all SD data (see [33]): LLDF =log10 1 N N ∑ i=1 Si fLDF(ri)!, (4) where Si is the total signal measured in the i -th selected station and fLDF(ri) gives the average signal, obtained from all SD data, for a station at the same distance ri from the shower axis. The photon energy Eγ is determined for each measured air-shower event, taking into account S( 1000 ) and the reconstructed zenith angle. For this purpose, a look-up table has been constructed using a large simulation sample. Only non-preshowering photon events are used, which are weighted according to a reference spectrum ∝E−2 . In Figure 5, the distributions of the two observables are shown as a function of the photon energy. In particular ∆ shows a good separation between photons and data. Finally, the two variables are combined using a Fisher discriminant analysis, with the burnt sample representing the background and photon simulations representing the signal. The analysis is applied to SD data collected between 1 January 2004 and 30 June 2020. Only air-shower events with a reconstructed zenith angle between 30 ◦ and 60 ◦ are taken into account to ensure that the majority of possible selected photon-induced showers reach their maximum development before reaching ground level. A number of selection criteria are applied to ensure a reliable reconstruction of the two observables. These criteria are described in detail in [ 25 ]. Overall, the data sample (search sample) consists of 48 , 061 selected events with a photon energy Eγ≥ 10 19 eV , excluding the burnt sample, which consists of 886 events (1.8% of the total number of selected events). The results of the analysis are shown in Figure 5, bottom. Overall, 16, 2 and 0 events above energy thresholds of 1, 2 and 4 × 10 19 eV , respectively, had a value of the Fisher discriminant above the photon-candidate cut, which was fixed to the median of the Fisher distribution for non-preshowering primary photons (shown as the solid black line in Figure 5, bottom). The number of observed candidate events is in statistical agreement with what is expected from the fit of an exponential to the tail of the distribution of the Fisher discriminant for the burnt sample. In addition, no peak-like features, which would indicate the presence of a photon population, are observed above the fall-off of the distribution. Overall, the results are consistent with the expectation for a background of UHE protons and nuclei; hence, upper limits on the integral flux of UHE photons are determined. To calculate these upper limits, the signal efficiency of the analysis is required. The efficiency has been determined from simulations, and it increases from 0.26 for a threshold energy of 10 19 eV to 0.39 for 4 × 10 19 eV , under the assumption of a power-law spectrum ∝E−2 . Upper limits on the integral photon flux are placed at threshold energies of 1, 2, and 4 × 10 19 eV , at a confidence level of 95%. At these threshold energies, the upper limits are 2.11, 0.312, and 0.172 ×10−3km−2sr−1yr−1 , respectively. These upper limits on the integral flux of photons correspond to upper limits on the integral photon fraction of 1.6%, 1.2%, and 3.2%, Universe 2022,8, 579 9 of 20 for the same threshold energies, and again for a confidence level of 95%. As before, the fraction limits have been calculated using the most up-to-date measurement of the energy spectrum of UHE cosmic rays from the Pierre Auger Observatory [27]. 4.4. Summary of the Searches for a Diffuse Flux of UHE Photons The upper limits on the integral photon flux derived through the three analyses discussed in the previous sections are compiled in Table 1and shown in Figure 6, together with upper limits published by other experiments. The Pierre Auger Observatory currently provides the most stringent limits over a wide energy range, spanning from 2 × 10 17 eV to the highest energies. In addition, the set of upper limits derived from HeCo data closed the gap between the upper limits at ultra-high energies (derived from hybrid and SD data) and those determined by smaller air-shower experiments such as KASCADE-Grande, leading to a full coverage of the aforementioned energy range. It is worth mentioning here that extensive systematic studies have been performed to test the robustness of the analyses and their results against various sources of uncertainties, for example in the hadronic interaction models used in the air-shower simulations or in the reconstruction of the different observables. Overall, the results proved to be very robust, more details on these studies can be found in [23–25]. 19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 20 /eV) γ (E 10 log 5− 0 5 10 15 20 ∆ photon MC (no preshower) Data - burn sample 19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 20 /eV) γ (E 10 log 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 LDF L photon MC (no preshower) Data - burn sample 4−2−0 2 4 6 8 Fisher 2− 10 1− 10 1 10 2 10 Events photon MC (no preshower) photon MC (preshower) Data - burn sample Data - search sample Figure 5. ( Top ) distributions of ∆ ( left ) and LLDF ( right ), i.e., the observables used in the search for photons based on SD-only data, as a function of the photon energy Eγ for simulated primary photons (in blue) and a fraction of the data sample (in red) that is used as a burnt sample; the bands represent one standard deviation of the photon distributions. ( Bottom ) distributions of the Fisher discriminant for the burnt sample (grey), the search sample (red) and simulated primary photons (non-preshowering in blue and preshowering in light blue), weighted with an E−2 spectrum; the search sample and the photon distributions are scaled to have the same integral as the burn sample one; the vertical line indicates the value of the photon-candidate cut; the dashed line shows the result of the fit of an exponential to the 5% of events in the burnt sample with the largest values of the Fisher discriminant. For more details, see [25]. Universe 2022,8, 579 16 of 20 L.M. Domingues Mendes 71, R.C. dos Anjos 24, J. Ebr 31, M. Eman 79,80, R. Engel 38,40, I. Epicoco 55,47, M. Erdmann 41, A. Etchegoyen 8,12, H. Falcke 79,81,80, J. Farmer 88, G. Farrar 87, A.C. Fauth 21, N. Fazzini d, F. Feldbusch 39, F. Fenu 62,51, B. Fick 86, J.M. Figueira 8, A. Filipˇciˇc 76,75, T. Fitoussi 40, T. Fodran 79, T. Fujii 88,e, A. Fuster 8,12, C. Galea 79, C. Galelli 58,48, B. García 7, H. Gemmeke 39, F. Gesualdi 8,40, A. GherghelLascu 72, P.L. Ghia 33, U. Giaccari 79, M. Giammarchi 48, J. Glombitza 41, F. Gobbi 10, F. Gollan 8, G. Golup 1, M. Gómez Berisso 1, P.F. Gómez Vitale 11, J.P. Gongora 11, J.M. González 1, N. González 14, I. Goos 1, D. Góra 69, A. Gorgi 53,51, M. Gottowik 78, T.D. Grubb 13, F. Guarino 59,49, G.P. Guedes 22, E. Guido 43, S. Hahn 40,8, P. Hamal 31, M.R. Hampel 8, P. Hansen 4, D. Harari 1, V.M. Harvey 13, A. Haungs 40, T. Hebbeker 41, D. Heck 40, C. Hojvat d, J.R. Hörandel 79,80, P. Horvath 32, M. Hrabovský 32, T. Huege 40,15, A. Insolia 57,46, P.G. Isar 73, P. Janecek 31, J.A. Johnsen 84, J. Jurysek 31, A. Kääpä 37, K.H. Kampert 37, B. Keilhauer 40, A. Khakurdikar 79, V.V. Kizakke Covilakam 8,40, H.O. Klages 40, M. Kleifges 39, J. Kleinfeller 10, F. Knapp 38, N. Kunka 39, B.L. Lago 16, N. Langner 41, M.A. Leigui de Oliveira 23, V. Lenok 38, A. Letessier-Selvon 34, I. LhenryYvon 33, D. Lo Presti 57,46, L. Lopes 71, R. López 63, L. Lu 90, Q. Luce 38, J.P. Lundquist 75, A. Machado Payeras 21, G. Mancarella 55,47, D. Mandat 31, B.C. Manning 13, J. Manshanden 42, P. Mantsch d, S. Marafico 33, F.M. Mariani 58,48, A.G. Mariazzi 4, I.C. Mari¸s 14, G. Marsella 60,46, D. Martello 55,47, S. Martinelli 40,8, O. Martínez Bravo 63, M.A. Martins 78, M. Mastrodicasa 56,45, H.J. Mathes 40, J. Matthews a, G. Matthiae 61,50, E. Mayotte 84,37, S. Mayotte 84, P.O. Mazur d, G. Medina-Tanco 67, D. Melo 8, A. Menshikov 39, S. Michal 32, M.I. Micheletti 6, L. Miramonti 58,48, S. Mollerach 1, F. Montanet 35, L. Morejon 37, C. Morello 53,51, A.L. Müller 31, K. Mulrey 79,80, R. Mussa 51, M. Muzio 87, W.M. Namasaka 37, A. Nasr-Esfahani 37, L. Nellen 67, G. Nicora 2, M. Niculescu-Oglinzanu 72, M. Niechciol 43, D. Nitz 86, I. Norwood 86, D. Nosek 30, V. Novotny 30, L. Nožka 32, A Nucita 55,47, L.A. Núñez 29, C. Oliveira 19, M. Palatka 31, J. Pallotta 2, G. Parente 78, A. Parra 63, J. Pawlowsky 37, M. Pech 31, J. Pe¸kala 69, R. Pelayo 64, E.E. Pereira Martins 38,8, J. Perez Armand 20, C. Pérez Bertolli 8,40, L. Perrone 55,47, S. Petrera 44,45, C. Petrucci 56,45, T. Pierog 40, M. Pimenta 71, M. Platino 8, B. Pont 79, M. Pothast 80,79, M. Pourmohammad Shavar 60,46, P. Privitera 88, M. Prouza 31, A. Puyleart 86, S. Querchfeld 37, J. Rautenberg 37, D. Ravignani 8, M. Reininghaus 38, J. Ridky 31, F. Riehn 71, M. Risse 43, V. Rizi 56,45, W. Rodrigues de Carvalho 79, J. Rodriguez Rojo 11, M.J. Roncoroni 8, S. Rossoni 42, M. Roth 40, E. Roulet 1, A.C. Rovero 5, P. Ruehl 43, A. Saftoiu 72, M. Saharan 79, F. Salamida 56,45, H. Salazar 63, G. Salina 50, J.D. Sanabria Gomez 29, F. Sánchez 8, E.M. Santos 20, E. Santos 31, F. Sarazin 84, R. Sarmento 71, R. Sato 11, P. Savina 90, C.M. Schäfer 40, V. Scherini 55,47, H. Schieler 40, M. Schimassek 40, M. Schimp 37, F. Schlüter 40,8, D. Schmidt 38, O. Scholten 15, H. Schoorlemmer 79,80, P. Schovánek 31, F.G. Schröder 89,40, J. Schulte 41, T. Schulz 40, S.J. Sciutto 4, M. Scornavacche 8,40, A. Segreto 52,46, S. Sehgal 37, S.U. Shivashankara 75, G. Sigl 42, G. Silli 8, O. Sima 72,b, R. Smau 72, R. Šmída 88, P. Sommers h, J.F. Soriano 85, R. Squartini 10, M. Stadelmaier 31, D. Stanca 72, S. Staniˇc 75, J. Stasielak 69, P. Stassi 35, M. Straub 41, A. Streich 38,8, M. Suárez-Durán 14, T. Sudholz 13, T. Suomijärvi 36, A.D. Supanitsky 8, Z. Szadkowski 70, A. Tapia 28, C. Taricco 62,51, C. Timmermans 80,79, O. Tkachenko 40, P. Tobiska 31, C.J. Todero Peixoto 18, B. Tomé 71, Z. Torrès 35, A. Travaini 10, P. Travnicek 31, C. Trimarelli 56,45, M. Tueros 4, R. Ulrich 40, M. Unger 40, L. Vaclavek 32, M. Vacula 32, J.F. Valdés Galicia 67, L. Valore 59,49, E. Varela 63, A. Vásquez-Ramírez 29, D. Veberiˇc 40, C. Ventura 26, I.D. Vergara Quispe 4, V. Verzi 50, J. Vicha 31, J. Vink 82, S. Vorobiov 75, C. Watanabe 25, A.A. Watson c, A. Weindl 40, L. Wiencke 84, H. Wilczy´nski 69, D. Wittkowski 37, B. Wundheiler 8, A. Yushkov 31, O. Zapparrata 14, E. Zas 78, D. Zavrtanik 75,76, M. Zavrtanik 76,75, L. Zehrer 75 1 Centro Atómico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina 2Centro de Investigaciones en Láseres y Aplicaciones, CITEDEF and CONICET, Villa Martelli, Argentina 3 Departamento de Física and Departamento de Ciencias de la Atmósfera y los Océanos, FCEyN, Universidad de Buenos Aires and CONICET, Buenos Aires, Argentina Universe 2022,8, 579 17 of 20 4IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 5Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA), Buenos Aires, Argentina 6 Instituto de Física de Rosario (IFIR)—CONICET/U.N.R. and Facultad de Ciencias Bioquímicas y Farmacéuticas U.N.R., Rosario, Argentina 7 Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), and Universidad Tecnológica Nacional—Facultad Regional Mendoza (CONICET/CNEA), Mendoza, Argentina 8 Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina 9 International Center of Advanced Studies and Instituto de Ciencias Físicas, ECyT-UNSAM and CONICET, Campus Miguelete—San Martín, Buenos Aires, Argentina 10 Observatorio Pierre Auger, Malargüe, Argentina 11 Observatorio Pierre Auger and Comisión Nacional de Energía Atómica, Malargüe, Argentina 12 Facultad Regional Buenos Aires, Universidad Tecnológica Nacional, Buenos Aires, Argentina 13 University of Adelaide, Adelaide, S.A., Australia 14 Université Libre de Bruxelles (ULB), Brussels, Belgium 15 Vrije Universiteit Brussels, Brussels, Belgium 16 Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Nova Friburgo, Brazil 17 Instituto Federal de Educação, Ciência e Tecnologia do Rio de Janeiro (IFRJ), Brazil 18 Escola de Engenharia de Lorena, Universidade de São Paulo,Lorena, SP, Brazil 19 Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, SP, Brazil 20 Instituto de Física, Universidade de São Paulo, São Paulo, SP, Brazil 21 Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil 22 Universidade Estadual de Feira de Santana, Feira de Santana, Brazil 23 Universidade Federal do ABC, Santo André, SP, Brazil 24 Universidade Federal do Paraná, Setor Palotina, Palotina, Brazil 25 Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil 26 Universidade Federal do Rio de Janeiro (UFRJ), Observatório do Valongo, Rio de Janeiro, RJ, Brazil 27 Universidade Federal Fluminense, EEIMVR, Volta Redonda, RJ, Brazil 28 Universidad de Medellín, Medellín, Colombia 29 Universidad Industrial de Santander, Bucaramanga, Colombia 30 Faculty of Mathematics and Physics, Institute of Particle and Nuclear Physics, Charles University, Prague, Czech Republic 31 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 32 Palacky University, RCPTM, Olomouc, Czech Republic 33 CNRS/IN2P3, IJCLab, Université Paris-Saclay, Orsay, France 34 Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Sorbonne Université, Université de Paris, CNRS-IN2P3, Paris, France 35 Université Grenoble Alpes, CNRS, Grenoble Institute of Engineering Université Grenoble Alpes, LPSCIN2P3, 38000 Grenoble, France 36 Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France 37 Department of Physics, Bergische Universität Wuppertal, Wuppertal, Germany 38 Karlsruhe Institute of Technology (KIT), Institute for Experimental Particle Physics, Karlsruhe, Germany 39 Karlsruhe Institute of Technology (KIT), Institut für Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany 40 Karlsruhe Institute of Technology (KIT), Institute for Astroparticle Physics, Karlsruhe, Germany 41 RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany 42 II. Institut für Theoretische Physik, Universität Hamburg, Hamburg, Germany 43 Department Physik—Experimentelle Teilchenphysik, Universität Siegen, Siegen, Germany 44 Gran Sasso Science Institute, L’Aquila, Italy 45 INFN Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila), Italy 46 INFN, Sezione di Catania, Catania, Italy 47 INFN, Sezione di Lecce, Lecce, Italy 48 INFN, Sezione di Milano, Milano, Italy 49 INFN, Sezione di Napoli, Napoli, Italy 50 INFN, Sezione di Roma “Tor Vergata”, Roma, Italy 51 INFN, Sezione di Torino, Torino, Italy 52 Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo (INAF), Palermo, Italy 53 Osservatorio Astrofisico di Torino (INAF), Torino, Italy 54 Politecnico di Milano, Dipartimento di Scienze e Tecnologie Aerospaziali , Milano, Italy 55 Dipartimento di Matematica e Fisica “E. De Giorgi”, Università del Salento, Lecce, Italy 56 Dipartimento di Scienze Fisiche e Chimiche, Università dell’Aquila, L’Aquila, Italy 57 Dipartimento di Fisica e Astronomia “Ettore Majorana”, Università di Catania, Catania, Italy 58 Dipartimento di Fisica, Università di Milano, Milano, Italy 59 Dipartimento di Fisica “Ettore Pancini”, Università di Napoli “Federico II”, Napoli, Italy 60 Dipartimento di Fisica e Chimica ”E. Segrè”, Università di Palermo, Palermo, Italy 61 Dipartimento di Fisica, Università di Roma “Tor Vergata”, Roma, Italy 62 Dipartimento di Fisica, Università Torino, Torino, Italy 63 Benemérita Universidad Autónoma de Puebla, Puebla, México Universe 2022,8, 579 18 of 20 64 Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas del Instituto Politécnico Nacional (UPIITA-IPN), México, D.F., México 65 Universidad Autónoma de Chiapas, Tuxtla Gutiérrez, Chiapas, México 66 Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán, México 67 Universidad Nacional Autónoma de México, México, D.F., México 68 Facultad de Ciencias Naturales y Formales, Universidad Nacional de San Agustin de Arequipa, Arequipa, Peru 69 Institute of Nuclear Physics PAN, Krakow, Poland 70 Faculty of High-Energy Astrophysics, University of Łód´z, Łód´z, Poland 71 Laboratório de Instrumentação e Física Experimental de Partículas—LIP and Instituto Superior Técnico— IST, Universidade de Lisboa—UL, Lisboa, Portugal 72 “Horia Hulubei” National Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania 73 Institute of Space Science, Bucharest-Magurele, Romania 74 University Politehnica of Bucharest, Bucharest, Romania 75 Center for Astrophysics and Cosmology (CAC), University of Nova Gorica, Nova Gorica, Slovenia 76 Experimental Particle Physics Department, J. Stefan Institute, Ljubljana, Slovenia 77 Universidad de Granada and C.A.F.P.E., Granada, Spain 78 Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela, Santiago de Compostela, Spain 79 IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands 80 Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Science Park, Amsterdam, The Netherlands 81 Stichting Astronomisch Onderzoek in Nederland (ASTRON), Dwingeloo, The Netherlands 82 Faculty of Science, Universiteit van Amsterdam, Amsterdam, The Netherlands 83 Case Western Reserve University, Cleveland, OH, USA 84 Colorado School of Mines, Golden, CO, USA 85 Department of Physics and Astronomy, Lehman College, City University of New York, Bronx, NY, USA 86 Michigan Technological University, Houghton, MI, USA 87 New York University, New York, NY, USA 88 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA 89 Department of Physics and Astronomy, Bartol Research Institute, University of Delaware, Newark, DE, USA 90 Department of Physics and WIPAC, University of Wisconsin-Madison, Madison, WI, USA aLouisiana State University, Baton Rouge, LA, USA balso at University of Bucharest, Physics Department, Bucharest, Romania cSchool of Physics and Astronomy, University of Leeds, Leeds, United Kingdom dFermi National Accelerator Laboratory, Fermilab, Batavia, IL, USA enow at Graduate School of Science, Osaka Metropolitan University, Osaka, Japan fMax-Planck-Institut für Radioastronomie, Bonn, Germany gColorado State University, Fort Collins, CO, USA hPennsylvania State University, University Park, PA, USA References 1. Gelmini, G.; Kalashev, O.E.; Semikoz, D.V. GZK photons as ultra high energy cosmic rays. J. Exp. Theor. Phys. 2008 ,106, 1061–1082. [CrossRef] 2. Sarkar, B.; Kampert, K.H.; Kulbartz, J.; Maccione, L.; Nierstenhoefer, N.; Sigl, G. Ultra-High Energy Photon and Neutrino Fluxes in Realistic Astrophysical Scenarios. In Proceedings of the 32nd International Cosmic Ray Conference, Beijing, China, 11–18 August 2011. 3. Bobrikova, A.; Niechciol, M.; Risse, M.; Ruehl, P. Predicting the UHE photon flux from GZK-interactions of hadronic cosmic rays using CRPropa 3. In Proceedings of the 37th International Cosmic Ray Conference PoS (ICRC2021), Berlin, Germany, 12–23 July 2021; Volume 449. [CrossRef] 4. Bérat, C.; Bleve, C.; Deligny, O.; Montanet, F.; Savina, P.; Torrès, Z. Diffuse flux of ultra-high energy photons from cosmic-ray interactions in the disk of the Galaxy and implications for the search for decaying super-heavy dark matter. Astrophys. J. 2022 , 929, 55. [CrossRef] 5. Gelmini, G.B.; Kalashev, O.E.; Semikoz, D. Upper limit on the diffuse extragalactic radio background from GZK photon observation. Universe 2022,8, 402. [CrossRef] 6. Aloisio, R.; Matarrese, S.; Olinto, A.V. Super Heavy Dark Matter in light of BICEP2, Planck and Ultra High Energy Cosmic Rays Observations. J. Cosmol. Astropart. Phys. 2015,2015, 024, [CrossRef] 7. Anchordoqui, L.A.; Bérat, C.; Bertaina, M.E.; Castellina, A.; Deligny, O.; Engel, R.; Farrar, G.R.; Ghia, P.L.; Hooper, D.; Kalashev, O.; et al. Hunting super-heavy dark matter with ultra-high energy photons. Astropart. Phys. 2021,132, 102614, [CrossRef] 8. Abreu, P. et al. [Pierre Auger Collaboration] Limits to gauge coupling in the dark sector set by the non-observation of instantoninduced decay of Super-Heavy Dark Matter in the Pierre Auger Observatory data. arXiv 2022, arXiv:2203.08854. 9. Abreu, P. et al. [Pierre Auger Collaboration] Cosmological implications of photon-flux upper limits at ultra-high energies in scenarios of Planckian-interacting massive particles for dark matter. arXiv 2022, arXiv:2208.02353. Universe 2022,8, 579 19 of 20 10. Cao, Z.; Aharonian, F.A.; An, Q.; Bai, L.X.; Bai, Y.X.; Bao, Y.W.; Bastieri, D.; Bi, X.J.; Bi, Y.J.; Cai, H.; et al. Ultrahigh-Energy Photons up to 1.4 Petaelectronvolts from 12 Gamma-Ray Galactic Sources. Nature 2021,594, 33–36. [CrossRef] 11. Risse, M.; Homola, P. Search for ultrahigh energy photons using air showers. Mod. Phys. Lett. A 2007,22, 749–766. [CrossRef] 12. Landau, L.D.; Pomeranchuk, I. Limits of applicability of the theory of bremsstrahlung electrons and pair production at highenergies. Dokl. Akad. Nauk Ser. Fiz. 1953,92, 535–536. 13. Migdal, A.B. Bremsstrahlung and pair production in condensed media at high-energies. Phys. Rev. 1956 ,103, 1811–1820. [CrossRef] 14. Erber, T. High-energy electromagnetic conversion processes in intense magnetic fields. Rev. Mod. Phys. 1966 ,38, 626–659. [CrossRef] 15. McBreen, B.; Lambert, C.J. Interactions of High-energy ( E> 5 × 10 19 -eV) Photons in the Earth’s Magnetic Field. Phys. Rev. D 1981,24, 2536–2538. [CrossRef] 16. Homola, P.; Risse, M.; Engel, R.; Gora, D.; Pekala, J.; Wilczynska, B.; Wilczynski, H. Characteristics of geomagnetic cascading of ultrahigh energy photons at the southern and northern sites of the Pierre Auger Observatory. Astropart. Phys. 2007 ,27, 174–184. [CrossRef] 17. The Pierre Auger Collaboration. The Pierre Auger Cosmic Ray Observatory. Nucl. Instrum. Methods Phys. Res. Sect. A 2015 , 798, 172–213. [CrossRef] 18. Fick, B. Hybrid performance of the Pierre Auger Observatory and reconstruction of hybrid events. In Proceedings of the 28th International Cosmic Ray Conference, Tsukuba, Japan, 31 July–7 August 2003; p. 449. 19. Abraham, J. et al. [Pierre Auger Collaboration] An upper limit to the photon fraction in cosmic rays above 10 19 -eV from the Pierre Auger Observatory. Astropart. Phys. 2007,27, 155–168. [CrossRef] 20. Abraham, J. et al. [Pierre Auger Collaboration] Upper limit on the cosmic-ray photon fraction at EeV energies from the Pierre Auger Observatory. Astropart. Phys. 2009,31, 399–406. [CrossRef] 21. Aab, A. et al. [Pierre Auger Collaboration] Search for photons with energies above 10 18 eV using the hybrid detector of the Pierre Auger Observatory. J. Cosmol. Astropart. Phys. 2017,4, 9; Erratum in J. Cosmol. Astropart. Phys. 2020,9, E02. [CrossRef] 22. Abraham, J. et al. [Pierre Auger Collaboration] Upper limit on the cosmic-ray photon flux above 10 19 eV using the surface detector of the Pierre Auger Observatory. Astropart. Phys. 2008,29, 243–256. [CrossRef] 23. Abreu, P. et al. [Pierre Auger Collaboration] A Search for Photons with Energies above 2 × 10 17 eV Using Hybrid Data from the Low-Energy Extensions of the Pierre Auger Observatory. Astrophys. J. 2022,933, 125. [CrossRef] 24. Savina, P. et al. [Pierre Auger Collaboration] A search for ultra-high-energy photons at the Pierre Auger Observatory exploiting air-shower universality. In Proceedings of the 37th International Cosmic Ray Conference PoS (ICRC2021), Berlin, Germany 12–23 July 2021; Volume 373. [CrossRef] 25. Abreu, P. et al. [Pierre Auger Collaboration] Search for photons above 1019 eV with the surface detector of the Pierre Auger Observatory. arXiv 2022, arXiv:2209.05926. 26. Ros, G.; Supanitsky, A.D.; Medina-Tanco, G.A.; del Peral, L.; D’Olivo, J.C.; Rodriguez-Frias, M.D. A new composition-sensitive parameter for Ultra-High Energy Cosmic Rays. Astropart. Phys. 2011,35, 140–151. [CrossRef] 27. Abreu, P. et al. [Pierre Auger Collaboration] The energy spectrum of cosmic rays beyond the turn-down around 10 17 eV as measured with the surface detector of the Pierre Auger Observatory. Eur. Phys. J. C 2021,81, 966. [CrossRef] 28. Lipari, P. Concepts of “age” and “universality” in cosmic ray showers. Phys. Rev. D 2009,79, 063001. [CrossRef] 29. Ave, M.; Engel, R.; Roth, M.; Schulz, A. A generalized description of the signal size in extensive air shower detectors and its applications. Astropart. Phys. 2017,87, 23–39. [CrossRef] 30. Savina, P.; Bleve, C.; Perrone, L. Searching for UHE photons in the EeV range: A two-variable approach exploiting air-shower universality. In Proceedings of the 36th International Cosmic Ray Conference PoS (ICRC2019), Madison, WI, USA, 24 July–1 August 2019; Volume 414. [CrossRef] 31. Fisher, R.A. The use of multiple measurements in taxonomic problems. Ann. Eugen. 1936,7, 179–188. [CrossRef] 32. Aab, A. et al. [Pierre Auger Collaboration] Inferences on mass composition and tests of hadronic interactions from 0.3 to 100 EeV using the water-Cherenkov detectors of the Pierre Auger Observatory. Phys. Rev. D 2017,96, 122003. [CrossRef] 33. Aab, A. et al. [Pierre Auger Collaboration] Reconstruction of events recorded with the surface detector of the Pierre Auger Observatory. J. Instrum. 2020,15, P10021. [CrossRef] 34. Apel, W.D. et al. [KASCADE-Grande Collaboration] KASCADE-Grande Limits on the Isotropic Diffuse Gamma-Ray Flux between 100 TeV and 1 EeV. Astrophys. J. 2017,848, 1. [CrossRef] 35. Fomin, Y.A.; Kalmykov, N.N.; Karpikov, I.S.; Kulikov, G.V.; Kuznetsov, M.Y.; Rubtsov, G.I.; Sulakov, V.P.; Troitsky, S.V. Constraints on the flux of ∼(1016 −1017.5)eV cosmic photons from the EAS-MSU muon data. Phys. Rev. D 2017,95, 123011. [CrossRef] 36. Abbasi, R.U.; Abe, M.; Abu-Zayyad, T.; Allen, M.; Azuma, R.; Barcikowski, E.; Belz, J.W.; Bergman, D.R.; Blake, S.A.; Cady, R.; et al. Constraints on the diffuse photon flux with energies above 10 18 eV using the surface detector of the Telescope Array experiment. Astropart. Phys. 2019,110, 8–14. [CrossRef] 37. Kalashev, O.E. et al. [Telescope Array Collaboration] Telescope Array search for EeV photons. In Proceedings of the 37th International Cosmic Ray Conference PoS (ICRC2021), Berlin, Germany, 12–23 July 2021; Volume 864. [CrossRef] 38. Kalashev, O.E.; Kuznetsov, M.Y. Constraining heavy decaying dark matter with the high energy gamma-ray limits. Phys. Rev. D 2016,94, 063535. [CrossRef] Universe 2022,8, 579 20 of 20 39. Kachelriess, M.; Kalashev, O.E.; Kuznetsov, M.Y. Heavy decaying dark matter and IceCube high energy neutrinos. Phys. Rev. D 2018,98, 083016. [CrossRef] 40. Greisen, K. End to the cosmic ray spectrum? Phys. Rev. Lett. 1966,16, 748–750. [CrossRef] 41. Zatsepin, G.T.; Kuzmin, V.A. Upper limit of the spectrum of cosmic rays. JETP Lett. 1966,4, 78–80. 42. Aab, A. et al. [Pierre Auger Collaboration] A search for point sources of EeV photons. Astrophys. J. 2014,789, 160. [CrossRef] 43. Aab, A. et al. [Pierre Auger Collaboration] A targeted search for point sources of EeV photons with the Pierre Auger Observatory. Astrophys. J. Lett. 2017,837, L25. [CrossRef] 44. Ruehl, P. et al. [Pierre Auger Collaboration] Follow-up Search for UHE Photons from Gravitational Wave Sources with the Pierre Auger Observatory. In Proceedings of the 37th International Cosmic Ray Conference PoS (ICRC2021), Berlin, Germany 12–23 July 2021; Volume 973. [CrossRef] 45. Cassiday, G.L.; Cooper, R.; Corbató, S.C.; Dawson, B.R.; Elbert, J.W.; Fick, B.E.; Green, K.D.; Kieda, D.B.; Ko, S.; Loh, E.C.; et al. Mapping the U.H.E. sky in search of point sources. Nucl. Phys. B-Proc. Suppl. 1990,14, 291–298. [CrossRef] 46. Abbott, B.P. et al. [LIGO Scientific Collaboration and Virgo Collaboration] Observation of Gravitational Waves from a Binary Black Hole Merger. Phys. Rev. Lett. 2016,116, 061102. [CrossRef] 47. Aab, A. et al. [Pierre Auger Collaboration] Ultrahigh-Energy Neutrino Follow-Up of Gravitational Wave Events GW150914 and GW151226 with the Pierre Auger Observatory. Phys. Rev. D 2016,94, 122007. [CrossRef] 48. Abbott, B.P. et al. [LIGO Scientific Collaboration and Virgo Collaboration] GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs. Phys. Rev. X 2019 ,9, 031040. [CrossRef] 49. Abbott, R. et al. [LIGO Scientific Collaboration and Virgo Collaboration] GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run. Phys. Rev. X 2021,11, 021053. [CrossRef] 50. Abbott, B.P. et al. [LIGO Scientific Collaboration and Virgo Collaboration] GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral. Phys. Rev. Lett. 2017,119, 161101. [CrossRef] 51. Abbott, B.P. et al. [LIGO Scientific Collaboration and Virgo Collaboration] Multi-messenger Observations of a Binary Neutron Star Merger. Astrophys. J. Lett. 2017,848, L12. [CrossRef] 52. Aab, A. et al. [Pierre Auger Collaboration] A Search for Ultra-high-energy Neutrinos from TXS 0506+056 Using the Pierre Auger Observatory. Astrophys. J. 2020,902, 105. [CrossRef] 53. Aartsen, M.G. et al. [IceCube Collaboration] Multimessenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A. Science 2018,361, eaat1378. [CrossRef] 54. Castellina, A. et al. [Pierre Auger Collaboration] AugerPrime: The Pierre Auger Observatory Upgrade. EPJ Web Conf. 2019 , 210, 06002. [CrossRef] 55. Aab, A. et al. [Pierre Auger Collaboration] The Pierre Auger Observatory Upgrade—Preliminary Design Report. arXiv 2016 , arXiv:1604.03637.