Origin of Ultra-High-Energy Galactic Cosmic Rays: The Isotropy Problem

Abstract

We study the propagation of ultra-high-energy cosmic rays (UHECRs) in the Galaxy, concentrating on the energy range below the ankle in the spectrum at 4 EeV. A Monte Carlo method, based on analytical solutions to the time-dependent diffusion problem, is used to account for intermittency by placing sources at random locations. Assuming a source population that scales with baryon mass density or star formation (e.g., long GRB), we derive constraints arising from intermittency and the observational limits on the composition and anisotropy. It is shown that the composition and anisotropy at 10 18 eV are difficult to reproduce and require that either (1) the particle mean free path is much smaller than a gyroradius, implying the escape time is very long, (2) the composition is heavier than suggested by recent Auger data, (3) the ultra-high-energy sub-ankle component is mostly extragalactic, or (4) we are living in a rare lull in the UHECR production, and the current UHECR intensity is far below the Galactic time average. We therefore recommend a strong observational focus on determining the UHECR composition around 10 18 eV.

Can Ultrahigh-Energy Cosmic Rays Come From Gamma-Ray Bursts? Cosmic Rays Below the Ankle and Galactic Gamma-Ray Bursts

“…Even in the sub-ankle range, the observational limits on anisotropy pose strong constraints on the models. Below, and in (Part III : Pohl & Eichler 2011), this is further quantified.…”

LARGE-SCALE DISTRIBUTION OF ARRIVAL DIRECTIONS OF COSMIC RAYS DETECTED ABOVE 1018 eV AT THE PIERRE AUGER OBSERVATORY

“…For cosmic rays that are mostly heavy and originate from stationary sources located in the Galactic disk, some estimates are based on diffusion and drift motions (Ptuskin et al 1993;Candia et al 2003) as well as direct integration of trajectories (Zirakashvili et al 1998;Giacinti et al 2012), which show that dipolar anisotropies at the level of a few percent could be imprinted in the energy range just below the ankle energy. Even larger amplitudes could result in light primaries, unless sources are strongly intermittent and pure diffusion motions hold up to EeV energies (Calvez et al 2010;Eichler & Pohl 2011).…”

Transition from Galactic to extragalactic cosmic rays and cosmic ray anisotropy

“…However, such sources are unlikely to be responsible for the sub-ankle CR flux if it were to be of Galactic origin. Indeed, one can for example hardly match the bumpy CR spectrum resulting from rare Galactic transients to the observed smooth power law spectrum [17].…”