The energy spectrum and mass composition data from the Pierre Auger Observatory constrain the source properties.
The origin of ultra-high-energy cosmic rays (UHECRs), the most energetic particles in the universe, is one of the biggest mysteries in astrophysics. These particles have energies much higher than those produced by any human-made accelerator, and they can travel across vast distances in space before reaching Earth. There still are several open questions about their nature. How and where are they accelerated? What is their mass composition? How are they affected by radiation fields and magnetic fields along their way to the Earth?
The Pierre Auger Observatory measures the energy spectrum of cosmic rays up to 1020.2 eV with unprecedented precision and provides an estimate of their mass composition from the distributions of depth of maximum development of the showers. The observed features can give clues about the sources of UHECRs, as well as the physical processes that affect them during their propagation.
In this paper, a new analysis is presented, which combines both the energy spectrum and the mass composition data measured by the Pierre Auger Observatory in a wide energy range, both below and above what is called the "ankle" feature, a sharp change in the slope of the energy spectrum around 5 · 1018 eV. The energy region between the second knee, a softening of the spectrum at few 1017 eV, and the ankle is believed to be the one where Galactic cosmic rays leave room to extragalactic ones. Its inclusion in the fit is particularly important to draw a complete description of the origin of UHECRs.
We use a simple astrophysical model that assumes two populations of extragalactic sources emitting a flux of UHECRs with different characteristics. For each extragalactic population, the ejected flux at the souces has several free parameters estimated during the fit procedure: the spectral index, the rigidity cutoff (i.e. the maximum energy that a particle can reach depending on its charge) and the mass fractions in the energy range of interest. In order to keep the number of free parameters manageable, the differences among sources within the same population are neglected, so that all the estimated parameters are the effective ones which characterise the total escape spectrum from all sources in the population. Besides, in order to leave open the option of a Galactic contribution still significant up to ∼ 1018 eV, the possibility of a Galactic component at Earth at low energies is also investigated.
The main result is that the observed data can be well explained by this model if the sources contributing above the ankle emit a mixed and increasingly heavier composition with a hard spectrum and a low rigidity cutoff. On the other hand, the sources dominating below the ankle are required to eject a mix of protons and intermediate-mass nuclei (e.g. nitrogen), with a very soft spectrum and a very high rigidity cutoff. The estimated generation rate at the sources is shown in the left panel of Fig. 1 for each component and each ejected nuclear species; the right panel shows the corresponding total flux and the partial contributions to the energy spectrum at the top of the atmosphere grouped according to mass number, along with the measurement uncertainties. However, it should be noted that a Galactic origin for this intermediate-mass component cannot be excluded, since such an hypothesis provides a comparable goodness-of-fit.
Figure 1: Left: The estimated generation rate at the sources for each component (dashed: low-energy; solid: high-energy) and each ejected nuclear species. Right: The corresponding partial contributions to the energy spectrum at the top of the atmosphere, grouped according to mass number. The bands are given by the experimental uncertainties.
Figure 2: The predicted fluxes of neutrinos corresponding to a source evolution with m=3 (left) and m=5 (right) for the low-energy component. The different black curves represent the fluxes corresponding to various choices of maximum redshift zmax, from 1 to 5.
This analysis also investigates the dependence of the results on various uncertainties, such as those related to the experimental measurements, the propagation models, and the hadronic interaction models, which leave the main conclusions unchanged. Besides, the impact of the cosmological evolution of the two populations on the fit results is explored, which leads to the exclusion of a very strong source evolution for the high-energy component.
Additional information can also be obtained by considering the neutrinos that UHECRs produce when they interact with background photons in intergalactic space. These neutrinos are called cosmogenic neutrinos and do not undergo any interactions during their propagation, except for adiabatic energy losses due to the expansion of the Universe, so they can reach us from even higher redshifts than UHECRs. The expected cosmogenic neutrinos associated with the best-fit results can be used to put some additional constraints on the source properties. Even if the predicted fluxes of cosmogenic neutrinos are below the current upper limits set by Auger and IceCube, in Fig. 2 it is shown that for some of the considered scenarios the predictions of cosmogenic neutrino fluxes might reach the sensitivity range of the next-generation detectors, possibly excluding some source evolutions for the low-energy component and/or limiting the feasible values of its rigidity cutoff.
Related paper:
Constraining the sources of ultra-high-energy cosmic rays across and above the ankle with the spectrum and composition data measured at the Pierre Auger Observatory
The Pierre Auger Collaboration, JCAP 05 (2023) 024
[arxiv.org/abs/2211.02857] [doi: 10.1088/1475-7516/2023/05/024]
