Neutrino Background Flux from Sources of Ultrahigh-Energy Cosmic-Ray
  Nuclei
  Motivated by Pierre Auger Observatory results favoring a heavy nuclear
composition for ultrahigh-energy (UHE) cosmic rays, we investigate implications
for the cumulative neutrino background. The requirement that nuclei not be
photodisintegrated constrains their interactions in sources, therefore limiting
neutrino production via photomeson interactions. Assuming a $dN_{\rm
CR}/dE_{\rm CR} \propto E_{\rm CR}^{-2}$ injection spectrum and
photodisintegration via the giant dipole resonance, the background flux of
neutrinos is lower than $E_\nu^2 \Phi_\nu \sim {10}^{-9} {\rm GeV} {\rm
cm}^{-2} {\rm s}^{-1} {\rm sr}^{-1}$ if UHE nuclei ubiquitously survive in
their sources. This is smaller than the analogous Waxman-Bahcall flux for UHE
protons by about one order of magnitude, and is below the projected IceCube
sensitivity. If IceCube detects a neutrino background, it could be due to other
sources, e.g., hadronuclear interactions of lower-energy cosmic rays; if it
does not, this supports our strong restrictions on the properties of sources of
UHE nuclei.
