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Most precise measurement of the cosmic-ray energy spectrum at ultra-high energies

Recently, the Pierre Auger Collaboration has presented the most precise measurement of the cosmic-ray (CR) energy spectrum at ultra-high energies using the events recorded over more than 14 years by the surface detector (SD). The data set consists on 215,030 events with zenith angles below 60° and energies larger than 2.5x1018 eV.

The energy spectrum plays a key role in understanding CRs and its measurement is particularly challenging given the rapid fall off of the flux with energy. A key feature of the work is that the estimates of the energies are independent of assumptions about the unknown hadronic physics or of the primary mass composition. This is attained setting the energy scale of the Observatory with the calorimetric measurement of the shower energy performed with the fluorescence detector (FD). Moreover, the measurement is performed in a regime of full efficiency of the array, reducing the calculation of the exposure to a geometrical problem and live-time of the detector.

The determination of the shower energy is a multi-step process: from the analysis of the signals recorded in the SD stations triggered by a shower, a first estimate of the shower size is obtained reconstructing the signal at 1000 m from the core (S(1000)). For a given energy, S(1000) decreases with zenith angle (θ) due to the attenuation of the shower particles and a correction is applied using the Constant Intensity Cut method. The S(1000) attenuation curves derived with this method for three different intensity thresholds are shown in the left panel of figure 1. They are used to obtain S38, the signal S(1000) that the shower would have produced at θ = 38°. Finally S38 is calibrated against the FD energies. The calibration curve derived from the correlation between S38 and EFD for 3,338 high quality hybrid events triggered independently by the SD and FD is shown in the middle panel of figure 1. The resolution in the resulting SD energy is measured from the width of the distributions of the ratio of ESD to EFD knowing the resolution in EFD and it is shown in the right panel.

2020-09 paper spectrum fig1

Figure 1: Left: Attenuation curves of S(1000) derived with the Constant Intensity Cut method. Center: Correlation between the corrected shower size and the FD energy. Right: Resolution as a function of energy.

The energy spectrum obtained with an accumulated exposure of 60,400 km2 sr yr is shown in figure 2 together with the number of detected events in each energy bin. The analysis accounts for the migration of the events between bins, particularly from lower to higher energies, due to the finite energy resolution. Thanks to the excellent performance of the array, such resolution effects are small at all energies, affecting the flux by 10% at maximum.

2020-09 paper spectrum fig2

Figure 2: Energy spectrum measured at the Observatory with superimposed numbers of events detected in each energy bin. Upper limits are at the 90% con dence level.

The spectrum multiplied by E3 is shown in the left panel of figure 3 superimposed by a sequence of four power-laws (E−γ ) fitted to the data. The values of the spectral index γ are reported in the same figure confirming the flattening of the flux near 5×1018 eV, the so-called "ankle", and the abrupt suppression at around 5×1019 eV. The flux shows also a steepening at about 1019 eV, calling for a 2-step suppression. This feature was never observed previously.

The wide declination range covered in arrival directions, from δ = −90° to δ = +24.8° , has allowed a search for dependences of energy spectra on declination. The spectral features obtained in three declination bands of equal exposure have been found in statistical agreement, allowing us to claim a second new result, namely that the energy spectrum does not vary as a function of declination other than a mild excess from the Southern Hemisphere that is consistent with the anisotropy observed above 8×1018 eV.

The features of the spectrum have been interpreted using a benchmark scenario in which the electromagnetic fields permeate source environments where nuclei are accelerated to a maximum energy proportional to their charge (Z ). The best reproduction of the data by simultaneously fitting the energy spectrum above 5×1018 eV and the distribution  of the depths of the shower maximum measured with the FD, which is mass-sensitive, is shown in the right panel of figure 3.  In this scenario, the steepening observed above 5×1019 eV results from the combination of the maximum energy of acceleration of the heaviest nuclei at the sources and the Greisen-Zatsepin-Kuzmin effect, while the steepening at 1019 eV reflects the interplay between the flux contributions of the helium and carbon-nitrogen-oxygen  components injected at the source. In the figure, the  spectrum is presented in terms of differential energy density (∝ E2 J (E)), allowing us to put constraints in the luminosity density of the CR’s sources.

2020-09 paper spectrum fig3

Figure 3: Left: Energy spectrum with superimposed the t function used to determine the spectral features. Right: Energy spectrum reproduced in a model with energy-dependent mass composition.

Related papers:

Features of the energy spectrum of cosmic rays above 2.5 x 10^18 eV using the Pierre Auger Observatory
The Pierre Auger Collaboration, Phys. Rev. Lett. 125, 121106 (2020)
[] [doi: 10.1103/PhysRevLett.125.121106]

Measurement of the cosmic ray energy spectrum above 2.5 x 10^18 eV using the Pierre Auger Observatory
The Pierre Auger Collaboration, Phys. Rev. D 102, 062005 (2020)
[] [doi: 10.1103/PhysRevD.102.062005]


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