Displacement of ultra-high-energy cosmic ray source images by the intergalactic magnetic field: the cases of Cen A and M83

TL;DR

The paper investigates how a turbulent intergalactic magnetic field (IGMF) alters ultra-high-energy cosmic ray (UHECR) source images, focusing on a regime where the source size is smaller than the IGMF correlation length. Using 3D simulations with a Kolmogorov-spectrum IGMF, it compares correlated and uncorrelated trajectory regimes to show that, in the focusing regime, images can be smaller than diffusion-based expectations and can experience a systematic shift from the true source direction. The authors apply these findings to the Centaurus region, examining deflections from the Galactic magnetic field (GMF) and showing that Cen A’s image could be shifted toward M83 by the GMF, while an IGMF shift could compensate this to align with the observed excess; alternatively, Cen A could remain the true source for certain IGMF realizations. These results highlight the critical role of IGMF realization and GMF in interpreting UHECR anisotropies, complicating source identification and motivating joint treatment of IGMF and GMF in UHECR astronomy.

Abstract

The standard assumption about the influence of the turbulent intergalactic magnetic field (IGMF) on the images of ultra-high-energy cosmic rays (UHECR) sources is that the latter are formed in a random walk mode in the deflection angle. As a result, the images are symmetrically broadened to angular scales proportional to the IGMF strength and the square root of its correlation length. We demonstrate that when the size of the emitting region is smaller than the correlation length of the IGMF, a new focusing regime emerges. In this regime, significant deviations from the standard random walk approximation occur even when the distance between the source and the observer exceeds several tens of IGMF correlation lengths. The angular size of the resulting images is typically smaller than predicted by random walk, and the IGMF causes a systematic shift of the entire image away from the true source direction. This introduces additional uncertainty in the search for UHECR sources. We show that the excess observed by Pierre Auger Observatory in the direction of Cen A can be explained by the contribution of M83, provided that the image shift occurs as predicted by some models of the Galactic magnetic field (GMF) and that the IGMF plays a minor role due to its low strength and short coherence length. Alternatively, Cen A may indeed be the true source of the excess, as certain realizations of the IGMF can compensate the deflection caused by the GMF.

Figures (7)

• Figure 1: Particles' deflection angle $\alpha$, image size $\delta$ and image shift $\theta$ as a function of the IGMF correlation length for the case of uncorrelated trajectories (each particle was propagated in its own realization of the IGMF, see Sec.\ref{['sec:approximation_uncorr']} for details). Solid lines represent the RMS values inferred from the numerical simulations using Eq. (\ref{['eq:angles']}). Dashed lines show the analytical expectations based on Eq. (\ref{['eq:angles_theor']}). The IGMF strength was fixed to $B=1.5$ nG while the distance to the source was set to $D=4$ Mpc.
• Figure 2: Angular size $\delta$ of the UHECR source image as a function of the IGMF correlation length for the realistic case where particles are emitted into the same realization of the IGMF (see Sec. \ref{['sec:image_shift']} for details). Solid lines indicate the mean image size while the shaded regions indicate its standard deviation. Both the mean and standard deviation were calculated from 30 different IGMF realizations. For comparison, dashed lines show the analytical expectation for the case of uncorrelated trajectories, based on Eq. (\ref{['eq:angles_theor']}). The distance to the source was set to $D=4$ Mpc.
• Figure 3: Same as Fig. \ref{['fig:SpotSizeL']}, but here the solid lines and shaded regions represent the mean and standard deviation of the image shift $\theta$. The dashed lines are the same as in Fig. \ref{['fig:SpotSizeL']} and show the analytical expectation of the image size $\delta$ for uncorrelated trajectories, based on Eq. (\ref{['eq:angles_theor']}).
• Figure 4: Angular size $\delta$ of the UHECR source image as a function of the distance to the source for the realistic case where particles are emitted into the same realization of the IGMF (see Sec. \ref{['sec:image_shift']} for details). Different colors correspond to the different correlation lengths of the IGMF. The IGMF strength was fixed to $B=3$ nG. As in Fig. \ref{['fig:SpotSizeL']}, the solid lines and shaded regions represent the mean and standard deviation of the image sizes, while dashed line corresponds to Eq. (\ref{['eq:angles_theor']}).
• Figure 5: Same as Fig. \ref{['fig:SpotSizeD']} but here solid and dashed lines indicate the mean and standard deviation of the image shift $\theta$.