General constraints on sources of high-energy cosmic rays from the interaction losses

TL;DR

This paper refines the Hillas diagram for high-energy cosmic ray sources by incorporating interaction losses, especially for protons, to better constrain potential astrophysical accelerators like active galactic nuclei.

Contribution

It updates the Hillas diagram to include $p ext{-}mma$ and photopair interaction losses, linking source luminosity to acceleration constraints.

Findings

Constraints are strongest for bright, compact sources.

Updated diagram accounts for interaction losses in proton acceleration.

Source luminosity limits are derived for various astrophysical objects.

Abstract

Sources of high-energy cosmic rays are presently unknown, but can be constrained in various ways. Some of these constraints can be graphically presented on the so-called Hillas diagram. Previous versions of this diagram determined the range of geometrical sizes and magnetic fields of potential astrophysical accelerators, taking into account geometrical criteria and radiation losses. In this work, we update the Hillas diagram for protons, taking into account the losses associated with the $p\gamma$ and photopair interactions, relating the allowed regions to the source electromagnetic luminosity. The strongest constraints are obtained for bright compact sources such as the central regions of active galactic nuclei.