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

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 lowerpower Seyfert galaxies.

Extragalactic propagation of ultrahigh energy cosmic-rays

“…These type of sources, as well as very powerful AGNs in general, are, however, extremely rare in the local universe (e.g, within the horizon of UHECR protons), while the simple luminosity requirement is much looser for nuclei (especially with large Z). It does not thus look unreasonable to assume that sources of protons above 10 19 eV might be outnumbered and dominated in their total contribution to the UHECR flux by less powerful sources that can only reach the highest energies for highly charged heavy nuclei (see discussions in [94,95,96,97]). …”

Constraints on direct acceleration of UHECRs in astrophysical sources

“…However, the field is constrained and, in particular, cannot be too high (see Ref. [10] for a detailed discussion). The maximal value of the magnetic field is determined [15,16] by the so-called Eddington limit, B Ed = 10 4 ( M 10 9 M ) −1/2 G. For finding the spectrum of cosmic rays in the frameworks of this model, we need to know the actual maximal particle energy as a function of black-hole mass M, rather than its upper limit.…”

“…[8,9]) leave just a few candidate classes of sources capable of acceleration of particles to UHE energies [10]. The conventional diffusive (e.g., relativistic or nonrelativistic shock) acceleration may work only in ultrarelativistic jets, hot spots and lobes of exceptional active galaxies (powerful radio galaxies and blazars) which are not that abundant in the nearby Universe.…”

Towards a model of population of astrophysical sources of ultrahigh-energy cosmic rays

“…[13,14]). Analysis of the modern astrophysical data demonstrates [15] that the combination of these constraints leaves just a few candidate classes of sources capable of acceleration of particles to UHE energies. Leaving aside large-scale structures where interaction losses are expected to suppress the energy gain, the conventional diffusive (e.g., relativistic or non-relativistic shock) acceleration may work only in ultrarelativistic jets, hot spots and lobes of exceptional active galaxies (powerful radio galaxies and blazars) which are not that abundant in the nearby Universe.…”

“…The reason to choose this particular model is twofold. First, unlike many other models, it allows [15] for UHECR acceleration in numerous nearby sources. Second, as we will see below, within some realistic assumptions, the acceleration capabilities of a source are determined by a single parameter, the SMBH mass.…”