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Motivated by Pierre Auger Observatory results favoring a heavy nuclearcomposition for ultrahigh-energy (UHE) cosmic rays, we investigate implicationsfor the cumulative neutrino background. The requirement that nuclei not bephotodisintegrated constrains their interactions in sources, therefore limitingneutrino production via photomeson interactions. Assuming a $dN_{\rmCR}/dE_{\rm CR} \propto E_{\rm CR}^{-2}$ injection spectrum andphotodisintegration via the giant dipole resonance, the background flux ofneutrinos is lower than $E_\nu^2 \Phi_\nu \sim {10}^{-9} {\rm GeV} {\rmcm}^{-2} {\rm s}^{-1} {\rm sr}^{-1}$ if UHE nuclei ubiquitously survive intheir sources. This is smaller than the analogous Waxman-Bahcall flux for UHEprotons by about one order of magnitude, and is below the projected IceCubesensitivity. If IceCube detects a neutrino background, it could be due to othersources, e.g., hadronuclear interactions of lower-energy cosmic rays; if itdoes not, this supports our strong restrictions on the properties of sources ofUHE nuclei.

Neutrino Background Flux from Sources of Ultrahigh-Energy Cosmic-Ray Nuclei