Constraints on the source of ultra-high-energy cosmic rays using anisotropy versus chemical composition

The joint analysis of anisotropy signals and chemical composition of ultra-high-energy cosmic rays offers strong potential for shedding light on the sources of these particles. Following up on an earlier idea, this paper studies the anisotropies produced by protons of energy >E/Z, assuming that anisotropies at energy >E have been produced by nuclei of charge Z, which share the same magnetic rigidity. We calculate the number of secondary protons produced through photodisintegration of the primary heavy nuclei. Making the extreme assumption that the source does not inject any proton, we find that the source(s) responsible for anisotropies such as reported by the Pierre Auger Observatory should lie closer than ∼20-30, 80-100, and 180-200 Mpc if the anisotropy signal is mainly composed of oxygen, silicon, and iron nuclei, respectively. A violation of this constraint would otherwise result in the secondary protons forming a more significant anisotropy signal at lower energies. Even if the source were located closer than this distance, it would require an extraordinary metallicity ≳ 120, 1600, and 1100 times solar metallicity in the acceleration zone of the source, for oxygen, silicon, and iron, respectively, to ensure that the concomitantly injected protons do not produce a more significant low-energy anisotropy. This offers interesting prospects for constraining the nature and the source of ultra-high-energy cosmic rays with the increase in statistics expected from next-generation detectors.