Self-Confinement of Ultra-High-Energy Cosmic Rays

Ultra-High-Energy Cosmic Rays (UHECRs) are high-energy protons and nuclei of astrophysical origin that reach the Earth after traveling through intergalactic space. Since the late 20th century, large observatories, such as the Pierre Auger Observatory (Auger), have been built to measure the UHECR arrival direction, energy spectrum, and mass composition. The observed pattern of UHECR arrival direction, which is mostly determined by the location of their sources in the sky, proves that UHECRs with energies E > 8 EeV are accelerated in extragalactic sources. Conversely, the UHECR energy spectrum and mass composition depend on how they are accelerated and how they propagate in the intergalactic space. During propagation, UHECRs interact with the Cosmic Microwave Background and the Extragalactic Background Light, losing part of their energy. These interactions shape the observed UHECR energy spectrum, alter their mass composition, and also result in the production of high-energy neutrinos and gamma-rays. At the same time, intergalactic magnetic fields affect UHECR propagation, potentially preventing them from reaching the Earth. To infer the properties of UHECR sources, their energy spectrum and mass composition are simultaneously fitted to the results of numerical simulations that account for these propagation effects. The most recent combined fits of the UHECR spectrum and mass composition, performed by the Auger collaboration, highlighted several features that are in tension with existing astrophysical models. In particular, to explain the observed mass composition within standard assumptions regarding their propagation across the intergalactic space, UHE nuclei should exhibit hard spectra at the sources. Such spectra cannot arise from the most common acceleration mechanisms. They might be the result of more complex acceleration mechanisms, including propagation effects not accounted for in standard analysis. Two main classes of models, based on the impact of intergalactic magnetic fields on the UHECR propagation, have been proposed to reconcile the observations with standard acceleration models, the magnetic horizon and in-source confinement. In the magnetic horizon scenario, strong intergalactic magnetic fields delay the UHECR propagation, effectively suppressing their flux at low rigidities, thereby mimicking the hard injection spectra at the sources. However, the strength of the intergalactic magnetic fields needed to reproduce UHECR observations might be in tension with the constraints set through observations of residual polarization of radio waves. Conversely, in the in-source confinement scenario, high magnetic fields are only localized close to UHECR sources and delay the escape of UHECRs from the near-source environment. The additional time spent in the near-source environment results in additional disintegration of nuclei and production of secondary protons, providing a good description of the observed mass composition. In this work, we investigate the possibility that UHECRs are themselves responsible for the magnetic field that confines them near their sources. We refer to this scenario as self-confinement. We will show how the nonresonant streaming instability (NRSI) of astrophysical plasmas might be excited by the current of UHECRs leaking out from their sources, producing strong magnetic turbulence. The resulting magnetic turbulence, in turn, diffuses UHECRs in the near-source environment, delaying their escape from the turbulent region for timescales potentially exceeding the age of the Universe. The resulting delay depends on rigidity and leads to an effective low-rigidity suppression of the UHECR emissivity as in the magnetic horizon scenario. Similarly to in-source confinement scenarios, the increased time spent by UHE nuclei in the near-source environment increases the amount of secondary protons produced through photodisintegration, also increasing the production of secondary neutrinos and gamma-rays. We discuss the evolution of self-confinement and its dependence on key astrophysical quantities, such as the source's power and the intergalactic magnetic field correlation length, and we show that self-confinement might reconcile UHECR observations with the most common acceleration models. We analyze the constraints on the parameters of the model set by the observed UHECR mass composition, as well as the constraints set by multi-messenger observations of neutrinos and gamma-rays, and the relation between the flux of secondary particles and the proton content of the UHECR spectrum, providing additional information to discriminate among different scenarios of UHECR acceleration and propagation. Finally, we discuss realistic astrophysical scenarios in which self-confinement may occur. Within the self-confinement framework, the source is a complex structure hosting one or more UHECR accelerators, rather than the accelerator itself. This situation is best represented by galaxy clusters, which are expected to host the majority of putative UHECR accelerators. We identify the best parameter set to reproduce the UHECR observables to be compatible with self-confinement taking place in the magnetized structures bridging clusters, known as cosmic filaments. Within these structures, our requirements and findings regarding the intergalactic magnetic field are compatible with current observational constraints.