Energy spectrum of fast second order Fermi accelerators as sources of ultra-high-energy cosmic rays

Abstract

Stochastic acceleration of cosmic rays in second order Fermi processes is usually considered too slow to reach ultra-high energies, except in specific cases. In this paper we present the energy spectrum obtained from second order Fermi acceleration in highly turbulent magnetic fields as e.g. found in the outskirts of AGN jets in situations where it can be sufficiently fast to accelerate particles to the highest observed energies. We parametrize the resulting non-power-law spectra and show that these can describe the cosmic ray energy spectrum and mass-composition data at the highest energies if propagation effects are taken into account.

Combined fit of spectrum and composition data as measured by the Pierre Auger Observatory

“…Sufficiently below the maximal energy these mechanisms typically give rise to power-law spectra dN/dE ∝ E −γ , with γ ≃ 2.2 for relativistic shocks, and γ ranging from ≃ 2.0 to ≃ 1.0 for the other cases. Other processes can even result in 'inverted' spectra, with γ < 0 [33][34][35][36]. A common representation of the maximal energy of the sources makes use of an exponential cutoff; yet not all of these scenarios predict power law particle spectra with an exponential cut-off [37].…”

“…If interactions in the magnetospheres can be neglected this also gives rise to γ ≈ 1. Also, second order Fermi acceleration has been proposed to give rise to even harder spectra [36]. Close to the maximal energy, where interactions can become significant, the species dependent interaction rates can give rise to complex all-particle spectra and individual spectra whose maximal energies are not simply proportional to the charge Z [34].…”

CRPropa 3.2: a framework for high-energy astroparticle propagation

“…In particular, first-and second-order Fermi acceleration are available, generalising the implementation of ref. [17].…”

Test particle simulations of cosmic rays

“…There are however situations where even Galactic transport is not diffusive or where the diffusive picture is questionable. These include the escape of Galactic CRs from the CR halo around the knee (DeMarco et al 2007;Giacinti et al 2015), near source transport Kachelrieß et al 2015), stochastic acceleration (O'Sullivan et al 2009;Winchen and Buitink 2018), also in relativistic turbulence (Demidem et al 2019), and the study of CR anisotropies Schwadron et al 2014;Mertsch and Funk 2015;Ahlers and Mertsch 2015;López-Barquero et al 2016;Pohl and Rettig 2016;Kumar et al 2019;Mertsch and Ahlers 2019). In the following, we will briefly review the use of test particle simulations and discuss the results for a few physics cases.…”