Excitation of the non-resonant streaming instability around sources of Ultra-High Energy Cosmic Rays

Abstract

The interpretation of the ultra-high-energy cosmic ray spectrum (UHECRs) and composition suggests a suppression of the flux below $\sim$1 EeV, as observed by the Pierre Auger Observatory and Telescope Array. A natural explanation for this phenomenon involves magnetic confinement effects. We investigate the possibility that UHECRs self-generate the magnetic turbulence necessary for such confinement via current-driven plasma instabilities. Specifically, we show that the electric current produced by escaping UHECRs can excite a non-resonant streaming instability in the surrounding plasma. This instability reduces the diffusion coefficient in the source environment, effectively trapping particles with energies $E \lesssim 0.6$ EeV $\mathcal{L}_{45}^{1/2} R_{\text{Mpc}}^{-1} λ_{10}^{2}$ for times exceeding the age of the Universe. Here, $\mathcal{L}_{45}$ is the source luminosity in units of $10^{45}$ erg/s, $R_{\text{Mpc}}$ is the radial size in Mpc, and $λ_{10}$ is the intergalactic magnetic field coherence length in units of 10 Mpc. We discuss in detail the conditions, in terms of source luminosity, initial magnetic field, and the environment in which this phenomenon occurs, that need to be fulfilled in order for self-confinement to take place near a source of UHECRs. By modeling a population of UHECR sources with a luminosity function typical of extragalactic gamma-ray sources, we connect the spectrum of escaping particles to the luminosity distribution. Furthermore, we calculate the contribution of these confined particles to cosmogenic neutrino production, finding consistency with current observational constraints. Our results suggest that self-induced turbulence may play an important role in shaping the UHECR spectrum and, in particular, may account for the flux suppression near their sources, offering a promising framework for interpreting current observations.