Physical conditions in potential sources of ultra-high-energy cosmic rays: Updated Hillas plot and radiation-loss constraints

TL;DR

This paper updates the Hillas plot and radiation-loss constraints to identify astrophysical sources capable of accelerating cosmic rays to ultra-high energies, emphasizing the roles of active galactic nuclei, radio galaxies, and blazars.

Contribution

It provides an updated analysis of potential UHECR sources using the latest data, refining the Hillas plot and constraining maximal energies based on black-hole mass and radiation losses.

Findings

Only the most powerful active galaxies can accelerate protons to UHECR energies.

Heavier nuclei can be accelerated in more common, lower-power Seyfert galaxies.

The maximal UHECR energy depends on black-hole mass and source type.

Abstract

We review basic constraints on the acceleration of ultra-high-energy (UHE) cosmic rays (CRs) in astrophysical sources, namely the geometrical (Hillas) criterion and restrictions from radiation losses in different acceleration regimes. Using the latest available astrophysical data, we redraw the Hillas plot and figure out potential UHECR accelerators. For the acceleration in central engines of active galactic nuclei, we constrain the maximal UHECR energy for a given black-hole mass. Among active galaxies, only the most powerful ones, radio galaxies and blazars, are able to accelerate protons to UHE, though acceleration of heavier nuclei is possible in much more abundant lower-power Seyfert galaxies.