  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, 1100 times solar metallicity
in the acceleration zone of the source, for oxygen, silicon and iron
respectively, to ensure that the concomitantly injected protons not to 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.
