Exploring the role of accretion shocks in galaxy clusters as sources of ultrahigh-energy cosmic rays

TL;DR

This study tests accretion shocks in galaxy clusters as sources of ultrahigh-energy cosmic rays (UHECRs) by constructing a hybrid source model that combines a discrete, nearby-cluster component (notably Virgo) with a continuous distribution from the halo mass function. Particles of multiple nuclear species are accelerated via first-order Fermi mechanisms at cluster outskirts, with maximum energies set by the balance between acceleration and interaction losses, and luminosities normalized to a CR conversion efficiency $f_{CR}$. Fitting to Pierre Auger Observatory data on the energy spectrum and composition moments (mean and variance of $\ln A$) shows that Virgo can dominate the high-energy end, but reconciling the flux suppression requires specific shock geometries and magnetic-field strengths, or additional reacceleration processes. Overall, accretion shocks can contribute significantly to the UHECR flux below the suppression, with inferred spectral indices $\gamma$ in the range $\sim0.7$–$1.6$ and efficiencies of a few percent, while the highest-energy end likely necessitates extra physics beyond standard cluster shocks.

Abstract

Recently, the Pierre Auger Observatory has found strong evidence supporting the extragalactic origin of the most energetic cosmic rays. Despite several observed excesses in the distribution of arrival directions for the highest energy cosmic rays, the sources remain unidentified. Accretion shocks in galaxy clusters have been proposed as potential sources in the past. These immense shock waves, which can have radii on the order of megaparsecs, are generated by the infall of material from the intergalactic medium into the gravitational potential wells of galaxy clusters. In this work, we investigate the possibility that ultrahigh-energy cosmic rays are accelerated in these regions. Nearby massive galaxy clusters, including Virgo, are treated as a discrete component of the cluster mass distribution. Less massive galaxy clusters, as well as distant massive ones, are assumed to follow a continuous distribution in agreement with cluster mass statistics. We fit the flux at Earth and the composition profile measured by the Pierre Auger Observatory, assuming the injection of different nuclear species by these sources, to determine the values of the model parameters. Our results indicate that cosmic ray acceleration in cluster accretion shocks may account for at least a fraction of the observed UHECR flux at energies below the suppression scale. At higher energies, direct acceleration from the thermal pool would be feasible only if local fluctuations create favorable conditions, such as magnetic fields about an order of magnitude stronger than those typically expected in cluster accretion shocks, or for particular shock normal-magnetic field configurations.

Figures (9)

• Figure 1: Mean interaction and acceleration times as a function of the logarithm of primary energy for model C, $\eta=1$, $\theta=45^\circ$, and $\beta=100$ for all nuclear species considered.
• Figure 2: Maximum energy as a function of the cluster redshift for different values of the cluster virial mass, for accretion shock model C, $\eta=1$, $\theta=45^\circ$, and $\beta = 100$ for protons (top panel), and iron nuclei (bottom panel).
• Figure 3: The weight of each galaxy cluster in the local sample as a function of comoving distance. The masses and distances are normalized to the corresponding values of Virgo. The galaxy clusters are at comoving distances smaller than $110\,$Mpc.
• Figure 4: Top panel: the cosmic ray flux, multiplied by the cube of the energy, as a function of the logarithm of the primary energy. Different cluster contributions to the total flux are shown (see text for details). Middle panel: mean value of $\ln A$ as a function of the logarithm of primary energy. Bottom panel: variance of $\ln A$ as a function of the logarithm of primary energy. In the three plots the data points represent the Auger measurements and the red solid line our best-fit model for $\log(M_\textrm{min}/{\rm M}_\odot)=13$ and $\beta=100$. The vertical lines mark the lower energy limit of the data used in the fit. The brackets in the composition data represent the systematic uncertainties.
• Figure 5: Spectral index (top panel) and cosmic ray fraction (bottom panel) as a function of $\theta$ for all cases under consideration, except $\theta=0^{\circ}$ and $\eta=10$. The minimum value of the galaxy cluster mass considered here is $\log(M_\textrm{min}/{\rm M}_\odot)=13$ and $\beta=100$.