Effects of extragalactic magnetic field on the spectra of ultra-high-energy cosmic rays from jetted sources

TL;DR

The study tackles how extragalactic magnetic fields (EGMF) and jet emission geometry influence the observed spectra of ultra-high-energy cosmic rays (UHECRs). It employs CRPropa-based simulations of a single source in a turbulent EGMF, with jet opening angles and Earth-facing orientations, incorporating energy losses and nuclear interactions. The results show that emission geometry can decisively shape the spectrum, with diffusion and magnetic horizons altering energy distributions and composition, especially for heavier nuclei and larger source–Earth distances. These findings imply that isotropy-based interpretations may misattribute spectral features and underscore the need for realistic 3D EGMF models and joint multi-messenger constraints to reliably infer UHECR source properties.

Abstract

The origins and acceleration mechanisms of ultra-high-energy cosmic rays (UHECRs) are unknown. Many models attribute their extreme energies to powerful astrophysical jets. Understanding whether jet geometry -- specifically the opening angle and its orientation relative to Earth -- affects observational signatures is crucial for interpreting UHECR data. In this work, we perform numerical simulations of UHECR propagation in a magnetized universe to investigate the spectral signatures of jetted and nonjetted astrophysical sources. We demonstrate, for the first time, that under certain conditions, emission geometry can play a decisive role in shaping the observed spectrum of individual UHECR sources. These findings provide new insights into the conditions necessary for detecting UHECRs from jets, and highlight how the interplay between emission geometry and magnetic fields influences observed energy spectra.

Figures (12)

• Figure 1: Illustration of the simulation setup. Particles are injected isotropically from the source (yellow star), and are collected as they cross the surface of a sphere with radius $R \equiv \left| \vec{r}_{\text{det}}\right|$. Each detection position $\vec{r}_\text{det}$ represents a possible Earth-like observer location. A simulated event with initial momentum $\vec{p}_0$ (dotted purple line) that satisfies the angular condition $\theta - \Psi/2 \leq \phi \leq \theta + \Psi/2$ is considered to originate from a jet with opening angle $\Psi$, oriented at an angle $\theta$ relative to the line of sight between the source and the Earth. The orange line illustrates the trajectory of an event.
• Figure 2: Modification factor obtained for proton primaries. Each column corresponds to a different source-Earth distance ($R$), where $R=$ 10, 40, and 100 Mpc, respectively, from left to right. The rows correspond to different viewing angles ($\theta$), namely $\theta=0^\circ$, $40^\circ$, and $80^\circ$, from top to bottom. The jet opening angle is assumed to be $\Psi=15^\circ$. Line styles indicate different magnetic field strengths ($B$), while line colors correspond to different coherence lengths, $L_B$. Vertical lines mark the critical energy, defined as in Eq. \ref{['critical_energy']}, with the color and line style matching the respective coherence length and magnetic field.
• Figure 3: Event count distribution as a function of the energy ($E$) and the trajectory elongation ($d$). Figure (a) presents the case where $\theta= 0^{\circ}$, $B= 10.0 \; \text{nG}$, $L_B= 0.1 \; \text{Mpc}$ and $R= 100 \; \text{Mpc}$, while figure (b) shows the results for $\theta= 80^{\circ}$, $B= 10.0 \; \text{nG}$, $L_B= 0.1 \; \text{Mpc}$ and $R= 100 \; \text{Mpc}$.
• Figure 4: Modification factor obtained for primary nitrogen nuclei. The columns represent different source-Earth distances ($R$, and the rows vary according to the angle between the jet direction and the line of sight ($\theta$). The line styles indicate different magnetic field strengths ($B$) while the line colors correspond to different coherence lengths ($L_B$). Vertical lines mark the critical energy, with the color and line style matching the respective coherence length and magnetic field.
• Figure 5: Energy distribution for primary nitrogen nuclei, for different arriving compositions. The figures show the results for the case where the jet direction is $\theta= 0^\circ$, the magnetic strength considered is $B= 0.1$ nG and $L_B= 0.1$ Mpc. The columns vary in source-Earth distance, $R= 10, \; 40, \; 100 \; \text{Mpc}$ from left to right.